Skip to main content

Lawrence N. Virgin

Professor in the Thomas Lord Department of Mechanical Engineering and Materials Science
Thomas Lord Department of Mechanical Engineering and Materials Science
3393 Fciemas Building, Box 90300, Durham, NC 27708
3393 Fciemas, Duke Box 90300, Durham, NC 27708

Selected Publications


On the mechanics of monofilaments used in touch sensory perception.

Journal Article Medical engineering & physics · January 2024 The buckling of a slender monofilament is a standard clinical method used to assess touch sensory perception, with specific applications to somatosensory impairment in patients after a stroke, detecting carpal tunnel syndrome, and as a prognosis tool for d ... Full text Cite

Buckling of a Vertically Mounted Cantilevered Plate Under Static Torsional Corner Loads—Experiment and Theory

Journal Article Journal of Applied Mechanics, Transactions ASME · June 1, 2023 The results of an experimental study on the buckling of a vertically cantilevered plate under corner twisting forces are reported. In this configuration, an interesting and somewhat counter-intuitive behavior is observed in which a laterally loaded slender ... Full text Cite

A lateral–torsional buckling demonstration model using 3D printing

Journal Article Engineering Structures · April 1, 2023 It is well-established that beams of relatively narrow cross-section have a tendency to buckle laterally when loaded. This type of lateral–torsional instability, which has considerable practical importance in a variety of thin-walled structures, is a class ... Full text Cite

3D-printing and cylinder buckling: challenges and opportunities.

Journal Article Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · April 2023 Cylinder buckling is notoriously sensitive to small geometric imperfections. This is an underlying motivation for the use of knock-down factors in the design process, especially in circumstances in which minimum weight is a key design goal, an approach wel ... Full text Cite

On the elastic snapping of structural elements

Journal Article International Journal of Non-Linear Mechanics · March 1, 2023 A bistable structural component possesses more than one stable equilibrium configuration. In terms of the strain energy stored in bending, this can be thought of as a system with not only an initial equilibrium configuration represented by an isolated mini ... Full text Cite

Interrogating the Configuration Space of Postbuckled Beams

Journal Article Journal of Engineering Mechanics · March 1, 2023 This paper considers the global configuration space of postbuckled structures. Initially, a slender buckled beam is considered. The boundary conditions are pinned at one end and fully fixed at the other. The pin-end of the initially flat beam is moved towa ... Full text Cite

A shear center demonstration model using 3D-printing

Journal Article International Journal of Mechanical Engineering Education · July 1, 2022 Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment ab ... Full text Cite

Interrogating the Lead-Up to a Critical Speed in Rotordynamics

Journal Article Journal of Vibration and Acoustics · June 1, 2022 This paper presents a new approach to predicting an incipient critical speed in a rotating shaft. Based on the classical governing equations of motion for an eccentric mass on a flexible shaft (the Jeffcott rotor model), the approach is centered on examini ... Full text Cite

Experiments on the symmetry-breaking effect of orientation on a pair of connected cantilevers

Journal Article Mechanical Systems and Signal Processing · February 1, 2022 It is well established that axial loads tend to influence lateral stiffness and hence natural frequencies of slender structural components. For very slender structures, the axial loading can be caused by self-weight (in a gravitational field), and these ef ... Full text Cite

A note on lumped parameter modeling

Journal Article Mechanics Research Communications · September 1, 2021 This brief note examines the lumped dynamic modeling of two simple structural systems: 3D-printed cantilevers, and circular aluminum panels. In each case a set of stiffness and natural frequency measurements are made based on simple experiments, with a vie ... Full text Cite

Simultaneous buckling, contact, and load-carrying capacity

Journal Article Journal of Engineering Mechanics · May 1, 2021 This paper considers the case of a relatively large number of parallel columns that buckle simultaneously. The close proximity between columns results in the possibility of contact between adjacent columns as buckling proceeds, and this brings with it some ... Full text Cite

Large deflections of folded cantilever: Experiments and elastica analysis

Journal Article International Journal of Non-Linear Mechanics · March 1, 2021 Folded cantilevers have been utilized in MEMS devices, particularly for suspension. The structures consist of a horizontal beam segment fixed at its left end, a short downward connector (joint) at the right end, and a lower horizontal segment under the upp ... Full text Cite

A Pyramidal Lattice Frame: Pathways to Inversion

Journal Article International Journal of Structural Stability and Dynamics · February 1, 2021 This paper considers the load-deflection behavior of a pyramid-like, shallow lattice structure. It consists of four beams that join at a central apex and when subject to a lateral load, it exhibits a propensity to snap-through: A classical buckling phenome ... Full text Cite

Inferring unstable equilibrium configurations from observed dynamics

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2021 Unstable equilibria play an important organizing role in nonlinear dynamic systems in a global sense. However, it is difficult to measure them directly in a physical experiment. In this study, a digital image correlation (DIC) system is used to capture the ... Full text Cite

Force probing to access potential energy

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2021 Perhaps the two most common forms of potential energy are those associated with gravitational and elastic forces. In an experimental setting, if we can measure the force required to maintain equilibrium, then the extraction of potential energy is relativel ... Full text Cite

Experiments on probing the configuration space of post-buckled panels

Journal Article Journal of Applied Mechanics, Transactions ASME · December 1, 2020 This paper describes a primarily experimental study in which a nonlinear structural component (a slender, mechanically buckled panel) is subject to probing. That is, equilibrium configurations are explored when a specific location on the panel is subject t ... Full text Cite

Comparative structural stiffness: Exploiting 3D-printing

Journal Article American Journal of Physics · December 1, 2020 The teaching of structural stiffness is one of the keystones of the undergraduate curriculum in mechanics and the strength of materials. Standard linear theory, going back to Hooke's law, has proven to be very successful in predicting the performance of el ... Full text Cite

Stability and Bifurcation in Discrete Mechanical Systems: An Experimental and Analytical Study

Journal Article International Journal of Bifurcation and Chaos · July 1, 2020 The curse of dimensionality looms over many studies in science and engineering. Low-order systems provide conceptual clarity but often fail to reveal the extent of possible complexity, whereas high-order systems present a host of daunting challenges to the ... Full text Cite

The onset of chaotic motions of a moored semi-submersible.

Journal Article IN: PROC. ASME SIXTH (1987) INT. OFFSHORE MECHANICS AND ARCTIC ENGINEERING SYMP., (HOUSTON, U.S.A.: MAR. 1-6, 1987) · January 1, 2020 This paper describes a combined numerical and geometric approach to study the dynamic behaviour of a moored semi-submersible based on solutions of the non-linear differential equation used to model the system. Complex features including competing steady st ... Cite

Instabilities of nonconservative fluid-loaded systems

Journal Article International Journal of Bifurcation and Chaos · December 30, 2019 Nonlinear bifurcations and instabilities of autonomous nonconservative systems, mainly involving the fluid loading of a solid or structure, are reviewed and described in this accessible, pictorial overview. In contrast to the earlier papers in this series ... Full text Cite

On the mechanics of monofilaments used in touch sensory perception.

Journal Article Medical engineering & physics · January 2024 The buckling of a slender monofilament is a standard clinical method used to assess touch sensory perception, with specific applications to somatosensory impairment in patients after a stroke, detecting carpal tunnel syndrome, and as a prognosis tool for d ... Full text Cite

Buckling of a Vertically Mounted Cantilevered Plate Under Static Torsional Corner Loads—Experiment and Theory

Journal Article Journal of Applied Mechanics, Transactions ASME · June 1, 2023 The results of an experimental study on the buckling of a vertically cantilevered plate under corner twisting forces are reported. In this configuration, an interesting and somewhat counter-intuitive behavior is observed in which a laterally loaded slender ... Full text Cite

A lateral–torsional buckling demonstration model using 3D printing

Journal Article Engineering Structures · April 1, 2023 It is well-established that beams of relatively narrow cross-section have a tendency to buckle laterally when loaded. This type of lateral–torsional instability, which has considerable practical importance in a variety of thin-walled structures, is a class ... Full text Cite

3D-printing and cylinder buckling: challenges and opportunities.

Journal Article Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · April 2023 Cylinder buckling is notoriously sensitive to small geometric imperfections. This is an underlying motivation for the use of knock-down factors in the design process, especially in circumstances in which minimum weight is a key design goal, an approach wel ... Full text Cite

On the elastic snapping of structural elements

Journal Article International Journal of Non-Linear Mechanics · March 1, 2023 A bistable structural component possesses more than one stable equilibrium configuration. In terms of the strain energy stored in bending, this can be thought of as a system with not only an initial equilibrium configuration represented by an isolated mini ... Full text Cite

Interrogating the Configuration Space of Postbuckled Beams

Journal Article Journal of Engineering Mechanics · March 1, 2023 This paper considers the global configuration space of postbuckled structures. Initially, a slender buckled beam is considered. The boundary conditions are pinned at one end and fully fixed at the other. The pin-end of the initially flat beam is moved towa ... Full text Cite

A shear center demonstration model using 3D-printing

Journal Article International Journal of Mechanical Engineering Education · July 1, 2022 Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment ab ... Full text Cite

Interrogating the Lead-Up to a Critical Speed in Rotordynamics

Journal Article Journal of Vibration and Acoustics · June 1, 2022 This paper presents a new approach to predicting an incipient critical speed in a rotating shaft. Based on the classical governing equations of motion for an eccentric mass on a flexible shaft (the Jeffcott rotor model), the approach is centered on examini ... Full text Cite

Experiments on the symmetry-breaking effect of orientation on a pair of connected cantilevers

Journal Article Mechanical Systems and Signal Processing · February 1, 2022 It is well established that axial loads tend to influence lateral stiffness and hence natural frequencies of slender structural components. For very slender structures, the axial loading can be caused by self-weight (in a gravitational field), and these ef ... Full text Cite

A note on lumped parameter modeling

Journal Article Mechanics Research Communications · September 1, 2021 This brief note examines the lumped dynamic modeling of two simple structural systems: 3D-printed cantilevers, and circular aluminum panels. In each case a set of stiffness and natural frequency measurements are made based on simple experiments, with a vie ... Full text Cite

Simultaneous buckling, contact, and load-carrying capacity

Journal Article Journal of Engineering Mechanics · May 1, 2021 This paper considers the case of a relatively large number of parallel columns that buckle simultaneously. The close proximity between columns results in the possibility of contact between adjacent columns as buckling proceeds, and this brings with it some ... Full text Cite

Large deflections of folded cantilever: Experiments and elastica analysis

Journal Article International Journal of Non-Linear Mechanics · March 1, 2021 Folded cantilevers have been utilized in MEMS devices, particularly for suspension. The structures consist of a horizontal beam segment fixed at its left end, a short downward connector (joint) at the right end, and a lower horizontal segment under the upp ... Full text Cite

A Pyramidal Lattice Frame: Pathways to Inversion

Journal Article International Journal of Structural Stability and Dynamics · February 1, 2021 This paper considers the load-deflection behavior of a pyramid-like, shallow lattice structure. It consists of four beams that join at a central apex and when subject to a lateral load, it exhibits a propensity to snap-through: A classical buckling phenome ... Full text Cite

Inferring unstable equilibrium configurations from observed dynamics

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2021 Unstable equilibria play an important organizing role in nonlinear dynamic systems in a global sense. However, it is difficult to measure them directly in a physical experiment. In this study, a digital image correlation (DIC) system is used to capture the ... Full text Cite

Force probing to access potential energy

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2021 Perhaps the two most common forms of potential energy are those associated with gravitational and elastic forces. In an experimental setting, if we can measure the force required to maintain equilibrium, then the extraction of potential energy is relativel ... Full text Cite

Experiments on probing the configuration space of post-buckled panels

Journal Article Journal of Applied Mechanics, Transactions ASME · December 1, 2020 This paper describes a primarily experimental study in which a nonlinear structural component (a slender, mechanically buckled panel) is subject to probing. That is, equilibrium configurations are explored when a specific location on the panel is subject t ... Full text Cite

Comparative structural stiffness: Exploiting 3D-printing

Journal Article American Journal of Physics · December 1, 2020 The teaching of structural stiffness is one of the keystones of the undergraduate curriculum in mechanics and the strength of materials. Standard linear theory, going back to Hooke's law, has proven to be very successful in predicting the performance of el ... Full text Cite

Stability and Bifurcation in Discrete Mechanical Systems: An Experimental and Analytical Study

Journal Article International Journal of Bifurcation and Chaos · July 1, 2020 The curse of dimensionality looms over many studies in science and engineering. Low-order systems provide conceptual clarity but often fail to reveal the extent of possible complexity, whereas high-order systems present a host of daunting challenges to the ... Full text Cite

The onset of chaotic motions of a moored semi-submersible.

Journal Article IN: PROC. ASME SIXTH (1987) INT. OFFSHORE MECHANICS AND ARCTIC ENGINEERING SYMP., (HOUSTON, U.S.A.: MAR. 1-6, 1987) · January 1, 2020 This paper describes a combined numerical and geometric approach to study the dynamic behaviour of a moored semi-submersible based on solutions of the non-linear differential equation used to model the system. Complex features including competing steady st ... Cite

Instabilities of nonconservative fluid-loaded systems

Journal Article International Journal of Bifurcation and Chaos · December 30, 2019 Nonlinear bifurcations and instabilities of autonomous nonconservative systems, mainly involving the fluid loading of a solid or structure, are reviewed and described in this accessible, pictorial overview. In contrast to the earlier papers in this series ... Full text Cite

Probing the force field to identify potential energy

Journal Article Journal of Applied Mechanics, Transactions ASME · October 1, 2019 A small ball resting on a curve in a gravitational field offers a simple and compelling example of potential energy. The force required to move the ball, or to maintain it in a given position on a slope, is the negative of the vector gradient of the potent ... Full text Cite

On the loss of stability of periodic oscillations and its relevance to ship capsize

Journal Article Journal of Marine Science and Technology (Japan) · September 13, 2019 This research revisits the analysis of roll motion and the possible capsize of floating vessels in beam seas. Many analytical investigations of this topic have adopted the softening Duffing equation, which is similar to the ship roll equation of motion. He ... Full text Cite

On experimentally locating saddle-points on a potential energy surface from observed dynamics

Journal Article Mechanical Systems and Signal Processing · September 1, 2019 This paper details a new method to estimate the location of unstable equilibria, specifically saddle-points, based on transient trajectories from experiments. We describe a system in which saddle-points (not easily observed in a direct sense)influence the ... Full text Cite

Buckling of elastic columns with second-mode imperfections

Journal Article Meccanica · June 1, 2019 The pin-ended, slender, Euler strut has been used as the archetypal buckling problem for many years (Euler in Additamentum I de curvis elasticis, methodus inveniendi lineas curvas maximi minimivi proprietate gaudentes, Bousquet, Lausanne, 1744). Even thoug ... Full text Cite

Experiments on the thermal post-buckling of panels, including localized heating

Journal Article Journal of Sound and Vibration · January 20, 2019 The suppression of expansion in thin clamped panels subjected to elevated thermal loading often results in buckling. However, a number of possible post-buckled equilibrium configurations typically exist, and which shape ensues depends on a number of factor ... Full text Cite

Introduction to experimental nonlinear dynamics: A case study in mechanical vibration

Book · January 1, 2019 Nonlinear behavior can be found in such highly disparate areas as population biology and aircraft wing flutter. Largely because of this extensive reach, nonlinear dynamics and chaos have become very active fields of study and research. This book uses an ex ... Full text Cite

Curved structures that can elastically snap-through

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2019 Curved structures, such as beams, arches and panels are capable of exhibiting snap-through buckling behavior when loaded laterally. However, the propensity to maintain a stable snapped-through equilibrium position (in addition to the nominally unloaded equ ... Full text Cite

Structural behavior of shallow geodesic lattice domes

Journal Article International Journal of Solids and Structures · December 15, 2018 This paper describes experiments and analysis of the complete post-buckling behavior of shallow geodesic lattice domes. Although individual members are straight, their geometric arrangement approximates a curved surface and typical behavior is highly nonli ... Full text Cite

A tube dynamics perspective governing stability transitions: An example based on snap-through buckling

Journal Article International Journal of Mechanical Sciences · December 1, 2018 The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other equilibria presen ... Full text Cite

Experimental validation of phase space conduits of transition between potential wells

Journal Article Physical Review E · November 15, 2018 A phase space boundary between transition and nontransition trajectories, similar to those observed in Hamiltonian systems with rank-1 saddles, is verified experimentally in a macroscopic system. We present a validation of the phase space flux across rank- ... Full text Cite

Enhancing the teaching of elastic buckling using additive manufacturing

Journal Article Engineering Structures · November 1, 2018 This is the third part in a trilogy of papers examining ways in which additive manufacturing can be used to facilitate the introduction of basic principles in structural analysis. Each paper uses 3D-printing and simple, but non-trivial, slender geometric f ... Full text Cite

Tailored Buckling Constrained by Adjacent Members

Journal Article Structures · November 1, 2018 This paper exploits the accuracy and versatility of additive manufacturing to display interesting buckling behavior in slender elastic columns. A set of parallel columns were printed to relatively high precision, and then subjected to axial loading. The lo ... Full text Cite

Deformation and vibration of compressed, nested, elastic rings on rigid base

Journal Article Thin-Walled Structures · November 1, 2018 Vertical circular rings and a system of three nested rings are tested and analyzed. The rings are clamped to a flat rigid base and are loaded vertically at the top by either a concentrated load or a rigid plate. The tests involve rings made by 3D printing. ... Full text Cite

Applications of Bifurcation: Nonautonomous Periodically-Excited Systems

Journal Article International Journal of Bifurcation and Chaos · October 1, 2018 This paper reviews some examples of bifurcation in low-order, periodically driven dynamical systems. The generic loss of stability is a key component in dynamical systems theory, and provides a central pillar in assessing qualitative changes in system dyna ... Full text Cite

System identification of energy dissipation in a mechanical model undergoing high velocities: An indirect use of perpetual points

Journal Article Mechanical Systems and Signal Processing · August 1, 2018 Energy dissipation is often the most challenging component of system identification in the modeling of dynamical behavior in mechanical systems. Even for a relatively simple single-degree-of-freedom system such as the rigid-arm pendulum, it can be difficul ... Full text Cite

Sympathetic resonance

Journal Article American Journal of Physics · June 1, 2018 This short paper describes a useful teaching tool, ideal for demonstration purposes within the classroom or lab setting. It is based on the simple dynamic response of flexible cantilevers and evolves naturally from the underlying principles of a vibrating ... Full text Cite

Effect of stiffener geometry on the response of grid-stiffened panels

Journal Article Journal of Engineering Mechanics · February 1, 2018 It is well established that the lateral bending stiffness of thin panels is considerably enhanced by judicious use of ribs or stiffeners. This increase in stiffness is primarily due to a disproportionate increase in the second moment of area, and because r ... Full text Cite

Experimental study of isolas in nonlinear systems featuring modal interactions.

Journal Article PloS one · January 2018 The objective of the present paper is to provide experimental evidence of isolated resonances in the frequency response of nonlinear mechanical systems. More specifically, this work explores the presence of isolas, which are periodic solutions detached fro ... Full text Cite

Experimental investigation of perpetual points in mechanical systems

Journal Article Nonlinear Dynamics · December 1, 2017 In dissipative dynamical systems, equilibrium (stationary) points have a dominant organizing effect on transient motion in phase space, especially in nonlinear systems. These time-independent solutions are readily defined in the context of ordinary differe ... Full text Cite

Enhancing the teaching of structural dynamics using additive manufacturing

Journal Article Engineering Structures · December 1, 2017 This paper provides a companion study to a previous paper by the same author (Virgin, 2017). In that paper, 3D printing was used to provide a hands-on experience for students of (linear) structural analysis based on the lateral stiffness of plane frames. I ... Full text Cite

Enhancing the teaching of linear structural analysis using additive manufacturing

Journal Article Engineering Structures · November 1, 2017 Structural analysis forms a key component in many courses in civil, mechanical and aerospace engineering. Conventionally, the matrix stiffness method, a subset of finite element analysis, tends to occupy a central position in a typical syllabus, with a spe ... Full text Cite

Predicting critical speeds in various rotordynamics problems

Journal Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science · November 1, 2017 Rotating shafts often experience undesirable large-amplitude whirling oscillations associated with resonance at critical speeds. This paper further develops a nondestructive technique in which measured information about the growing nature of the response i ... Full text Cite

Snap-through under unilateral displacement control with constant velocity

Journal Article International Journal of Non-Linear Mechanics · September 1, 2017 When the side of a beverage can or the domed lid of a jar is pushed inward, all or part of the structure may suddenly snap into an inverted configuration. The velocity of the pushing motion affects this instability. Most previous analyses of snap-through h ... Full text Cite

Furthest reach of a uniform cantilevered elastica

Journal Article Mechanics Research Communications · July 1, 2017 A uniform elastic cantilever is subjected to a uniformly distributed load or a concentrated load at its tip. The angle of the fixed end with the horizontal is varied until the maximum horizontal distance (projection) from the fixed end to the horizontal lo ... Full text Cite

On the geometric conditions for multiple stable equilibria in clamped arches

Journal Article International Journal of Non-Linear Mechanics · June 1, 2017 Curved structures, such as beams, arches, and panels are capable of exhibiting snap-through buckling behavior when loaded laterally, that is they can exhibit multiple stable equilibria, sometimes after any external loading is removed. This is a consequence ... Full text Cite

On the flexural stiffness of 3D printer thermoplastic

Journal Article International Journal of Mechanical Engineering Education · January 1, 2017 This paper describes the process of estimating Young's modulus for the thermoplastic material commonly used in a type of 3D printer. Its twin goals are to compare and contrast a number of simple techniques from elementary structural analysis and to assess ... Full text Cite

The onset of chaotic motions of a moored semi-submersible.

Journal Article IN: PROC. ASME SIXTH (1987) INT. OFFSHORE MECHANICS AND ARCTIC ENGINEERING SYMP., (HOUSTON, U.S.A.: MAR. 1-6, 1987) · January 1, 2017 This paper describes a combined numerical and geometric approach to study the dynamic behaviour of a moored semi-submersible based on solutions of the non-linear differential equation used to model the system. Complex features including competing steady st ... Cite

Predicting Critical Speeds in Rotordynamics: A New Method

Conference Journal of Physics: Conference Series · October 3, 2016 In rotordynamics, it is often important to be able to predict critical speeds. The passage through resonance is generally difficult to model. Rotating shafts with a disk are analyzed in this study, and experiments are conducted with one and two disks on a ... Full text Cite

Inferring unstable equilibrium configurations from experimental data

Conference Journal of Physics: Conference Series · October 3, 2016 This research considers the structural behavior of slender, mechanically buckled beams and panels of the type commonly found in aerospace structures. The specimens were deflected and then clamped in a rigid frame in order to exhibit snap-through. That is, ... Full text Cite

Equilibria and vibration of a buckled beam with attached masses or spring–mass systems

Journal Article Journal of Sound and Vibration · September 29, 2016 A buckled beam with immovable pinned ends is considered. Attached to the beam are either one concentrated mass, two concentrated masses, a spring–mass system (that could model a human, robot, or passive vibration absorber), or a horizontal rigid bar with t ... Full text Cite

On the experimental identification of unstable static equilibria.

Journal Article Proceedings. Mathematical, physical, and engineering sciences · June 2016 This paper shows how the presence of unstable equilibrium configurations of elastic continua is reflected in the behaviour of transients induced by large perturbations. A beam that is axially loaded beyond its critical state typically exhibits two buckled ... Full text Cite

Experimental study of regular and chaotic transients in a non-smooth system

Journal Article International Journal of Non-Linear Mechanics · May 1, 2016 This paper focuses on thoroughly exploring the finite-time transient behaviors occurring in a periodically driven non-smooth dynamical system. Prior to settling down into a long-term behavior, such as a periodic forced oscillation, or a chaotic attractor, ... Full text Cite

A New Method for Predicting Critical Speeds in Rotordynamics

Journal Article Journal of Engineering for Gas Turbines and Power · February 1, 2016 The prediction of critical speeds of a rotating shaft is a crucial issue in a variety of industrial applications ranging from turbomachinery to disk storage systems. The modeling and analysis of rotordynamic systems is subject to a number of complications, ... Full text Cite

The effect of gravity on a slender loop structure

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2016 The deformation and vibration of vertical, highly flexible loops are investigated primarily from an experimental perspective. Both upright and hanging loops are considered with a small clamped length. The effects of self-weight on the loop static deformati ... Full text Cite

Experimental study of isolated response curves in a two-degree-of-freedom nonlinear system

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2016 In the present paper, the observation and characterization of isolated response curves (IRCs) are experimentally reported in the case of a nonlinear system consisting of two masses sliding on an horizontal guide. Transverse springs are attached to one mass ... Full text Cite

Experiments on a non-smoothly-forced oscillator

Journal Article Physica D: Nonlinear Phenomena · December 1, 2015 This paper describes some typical behavior encountered in the response of a harmonically-excited mechanical system in which a severe nonlinearity occurs due to an impact. Although such systems have received considerable recent attention (most of it from a ... Full text Cite

Snap-Through Phenomenon and Self-Contact of Spatial Elastica Subjected to Mid-Torque

Journal Article International Journal of Applied Mechanics · August 11, 2015 This paper presents the snap-through phenomenon and effect of self-contact of the spatial elastica subjected to mid-length torque. One end of the elastica is clamped while the other end is placed in a sleeve joint. The total arc-length of the elastica can ... Full text Cite

Adjacent Equilibria in Highly Flexible Upright Loop on Rigid Foundation

Journal Article Experimental Mechanics · July 5, 2015 For very slender structural components, self-weight may compete with elastic flexural stiffness in determining equilibrium configurations. In cases where the inherent elastic stiffness is low (relative to self-weight) we observe a variety of types of highl ... Full text Cite

Nonlinear dynamics of the CAM circadian rhythm in response to environmental forcing.

Journal Article Journal of theoretical biology · March 2015 Crassulacean acid metabolism (CAM) photosynthesis functions as an endogenous circadian rhythm coupled to external environmental forcings of energy and water availability. This paper explores the nonlinear dynamics of a new CAM photosynthesis model (Bartlet ... Full text Cite

Comment on "mechanical properties of suspended graphene sheets" [J. Vac. Sci. Technol., B 25, 2558 (2007)]

Journal Article Journal of Vacuum Science and Technology B: Nanotechnology and Microelectronics · March 1, 2015 Full text Cite

Coexisting equilibria and stability of a shallow arch: Unilateral displacement-control experiments and theory

Journal Article International Journal of Solids and Structures · February 1, 2015 The equilibria and stability of a shallow prestressed arch (beam-column) are investigated theoretically and experimentally. The deflection of the arch is unilaterally constrained by a displacement-control device. Both snap-through and remote coexisting equ ... Full text Cite

Stochastic interrogation of competing responses in a nonlinear distributed system

Journal Article Nonlinear Dynamics · January 1, 2015 In this paper, we examine the potential for coexisting responses in a harmonically forced buckled beam. It is shown experimentally that such structures may present many more responses than might be observed using frequency sweep-up and sweep-down testing, ... Full text Cite

Isolated response curves in a base-excited, two-degree-of-freedom, nonlinear system

Conference Proceedings of the ASME Design Engineering Technical Conference · January 1, 2015 In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the com ... Full text Cite

A driven system of impacting pendulums: Experiments and simulations

Journal Article Journal of Sound and Vibration · March 17, 2014 This paper studies a system composed of two pendulums attached to a common base that is oscillated horizontally. The pendulums share a common pivot line, but move independently and are only coupled together through collisions. Impact dynamics for the colli ... Full text Cite

Application of continuation methods to uniaxially loaded postbuckled plates

Journal Article Journal of Applied Mechanics, Transactions ASME · January 1, 2014 Continuation methods are used to examine the static and dynamic postbuckled behavior of a uniaxially loaded, simply supported plate. Continuation methods have been extensively used to study problems in mathematics and physics; however, they have not been a ... Full text Cite

Sensitivity in the structural behavior of shallow arches

Journal Article International Journal of Non-Linear Mechanics · January 1, 2014 It is well established that certain structural buckling problems are extremely sensitive to small changes in configuration: geometric imperfections, load application, symmetry, boundary conditions, etc. This paper considers the behavior of a very shallow a ... Full text Cite

Competing responses in a discrete mechanical system

Journal Article International Journal of Bifurcation and Chaos · January 1, 2014 This short paper takes a close look at a relatively simple harmonically-excited mechanical oscillator. Throughout the range of forcing frequencies the basins of attraction are investigated by applying strong perturbations to steady-state behavior. In this ... Full text Cite

Deformation and vibration of upright loops on a foundation and of hanging loops

Journal Article International Journal of Solids and Structures · 2014 Cite

Deformation and vibration of upright loops on a foundation and of hanging loops

Journal Article International Journal of Solids and Structures · January 1, 2014 The deformation and vibration of vertical flexible loops are investigated theoretically and experimentally. Both upright and hanging loops are considered. Potential applications include nanorings and carbon nanotubes as force sensors or structural componen ... Full text Cite

Co-existing responses in a harmonically-excited nonlinear structural system

Conference Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2014 A key feature of many nonlinear dynamical systems is the presence of co-existing solutions, i.e, nonlinear systems are often sensitive to initial conditions. While there have been many studies to explore this behavior from a numerical perspective, in which ... Full text Cite

Characterizing dynamic transitions associated with snap-through of clamped shallow arches

Journal Article Journal of Sound and Vibration · October 28, 2013 Slender curved structures can often be found as components of complex structures in civil, mechanical, and aerospace systems. Under extreme loadings, a curved structure might undergo snap-through buckling, i.e., the structure is forced to its inverted conf ... Full text Cite

Pendulum models of ponytail motion during walking and running

Journal Article Journal of Sound and Vibration · August 5, 2013 Steady-state motions of a woman's ponytail during level, straight, walking and running are examined. Based on reported data, formulas have been developed for the relationship of the forward speed to the frequencies of vertical and sideways motion of the he ... Full text Cite

On damping in the vicinity of critical points.

Journal Article Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · June 2013 The effect of damping on the behaviour of oscillations in the vicinity of bifurcations of nonlinear dynamical systems is investigated. Here, our primary focus is single degree-of-freedom conservative systems to which a small linear viscous energy dissipati ... Full text Cite

Michael Thompson: some personal recollections.

Journal Article Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · June 2013 Full text Cite

Characterizing dynamic transitions associated with snap-through: A discrete system

Journal Article Journal of Computational and Nonlinear Dynamics · January 30, 2013 Geometrically nonlinear structures often possess multiple equilibrium configurations. Under extreme conditions of excitation, it is possible for these structures to exhibit oscillations about and between these co-existing configurations. This behavior may ... Full text Cite

A numerical investigation of snap-through in a shallow arch-like model

Journal Article Journal of Sound and Vibration · January 22, 2013 Slender curved structures may experience a loss of stability called snap-through, causing the curvature on part or all of the structure to invert inducing fatigue damage. This paper presents a framework for analyzing the transient responses of slender curv ... Full text Cite

A driven system of impacting pendulums: Experiments and simulations

Journal Article Journal of Sound and Vibration · 2013 Cite

A harmonic balance approximation of dynamic snap-through boundaries in a single-degree-of-freedom structure

Journal Article Proceedings of the ASME Design Engineering Technical Conference · January 1, 2013 Under dynamic loading, systems with the requisite condition for snap-through buckling, that is co-existing equilibria, typically exhibit either small amplitude response about a single equilibrium configuration, or large amplitude response that transits bet ... Full text Cite

Parameter estimation for chaotic systems using a geometric approach: Theory and experiment

Journal Article Nonlinear Dynamics · October 1, 2012 A method for estimating model parameters based on chaotic system response data is described. This estimation problem is made challenging by sensitive dependence to initial conditions. The standard maximum likelihood estimation method is practically infeasi ... Full text Cite

Application of continuation methods to nonlinear post-buckled structures

Journal Article Conference Proceedings of the Society for Experimental Mechanics Series · June 6, 2012 Continuation and path following methods have been applied to many nonlinear problems in mathematics and physics. There is less widespread application of these methods, however, to structural systems. Since structural buckling and stability problems are pri ... Full text Cite

Exploiting Nonlinear Behavior in Structural Dynamics

Book · April 18, 2012 - Control and exploitation of nonlinearity in smart structures. The articles in this volume give an overview and introduction to nonlinear phenomena in structural dynamics. ... Cite

A heuristic method for identifying chaos from frequency content.

Journal Article Chaos (Woodbury, N.Y.) · March 2012 The sign of the largest Lyapunov exponent is the fundamental indicator of chaos in a dynamical system. However, although the extraction of Lyapunov exponents can be accomplished with (necessarily noisy) the experimental data, this is still a relatively dat ... Full text Cite

Stability of spatial elastica in a gravitational field

Journal Article International Journal of Structural Stability and Dynamics · March 1, 2012 This paper considers the behavior of a spatial elastica in a gravitational field. The slenderness of the system considered is such that the weight becomes an important consideration in determining elastic equilibrium configurations. Both ends of the elasti ... Full text Cite

Vibration isolation

Chapter · January 1, 2012 The ability to isolate a structure or machine from the undesirable effects of applied motion (especially vibration) has wide application. Suspension systems are incorporated into large buildings to protect them from earthquake excitation, mountain bikes an ... Full text Cite

Preface

Book · January 1, 2012 Cite

Introductory material

Chapter · January 1, 2012 This book is based on a one-week worksop at CISM. In order to fully appreciate the benefits of nonlinearity in certain engineering systems it is important to understand the underlying behavior of linear systems, and this first chapter provides a general ov ... Full text Cite

A parametrically forced nonlinear system with reversible equilibria

Journal Article International Journal of Bifurcation and Chaos · January 1, 2012 A nonlinear Duffing-type dynamical system, in which the stability of equilibria is modulated in a time-dependent manner, is investigated both experimentally and numerically. This is a low-order dynamical system with some interesting available choices in th ... Full text Cite

Multiplexing superparamagnetic beads driven by multi-frequency ratchets.

Journal Article Lab on a chip · December 2011 Here, we explore the single particle dynamics of superparamagnetic beads exposed to multifrequency ratchets. Through a combination of theory, simulation, and experiment, we determine the important tuning parameters that can be used to implement multiplexed ... Full text Cite

On the identification of chaos from frequency content

Journal Article Proceedings of the ASME Design Engineering Technical Conference · December 1, 2011 The characterization of chaos as a random-like response from a deterministic dynamical system with an extreme sensitivity to initial conditions is well-established, and has provided a stimulus to research in nonlinear dynamical systems in general. In a for ... Full text Cite

On snap-through buckling

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · December 1, 2011 Snap-through buckling can reduce the life-span of structural systems such as aircraft surface paneling. This is envisioned to be a specific problem in hypersonic vehicles in which severe thermal loading and acoustic excitation conspire to create an especia ... Full text Cite

Numerical and experimental analysis of the static behavior of highly deformed risers

Journal Article Ocean Engineering · September 1, 2011 This paper models a slender, flexible structure used as a drill string or riser in the offshore oil and gas industry that connects the well-head with a floating control vessel. These systems are used in deep-water drilling applications and present consider ... Full text Cite

Transport of superparamagnetic beads through a two-dimensional potential energy landscape.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · July 2011 The nonlinear dynamic behavior of superparamagnetic beads transported through a two-dimensional potential energy landscape is explored empirically and through numerical simulation. The beads are driven through a periodic array of micromagnets by an externa ... Full text Cite

Nonlinear flutter in fan stator vanes with time dependent fixity

Journal Article Journal of Turbomachinery · June 23, 2011 A new mechanism for fan stator vane failure in turbofan engines at high speed and high loading has been identified and reported in this paper. Highly destructive vane failures have been encountered at Honeywell in a development fan with composite stator va ... Full text Cite

Optimal design of cantilevered elastica for minimum tip deflection under self-weight

Journal Article Structural and Multidisciplinary Optimization · May 1, 2011 The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensib ... Full text Cite

Introduction to special issue on reflections in nonlinear mechanics

Journal Article IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) · February 1, 2011 Full text Cite

Stability of spatial elastica including weight effects

Journal Article International Journal of Structural Stability and Dynamics · 2011 Cite

Non-linear flutter in fan stator vanes with time dependent fixity

Journal Article ASME Journal of Turbomachinery · 2011 Cite

A block rocking on a seesawing foundation

Journal Article Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2011 Examples of vibro-impact mechanical and structural systems are not uncommon. Such systems are capable of exhibiting an interesting spectrum of non-smooth dynamic behavior when a characteristic changes abruptly. However, they present strong challenges to th ... Full text Cite

Structural dynamics of a frame including axial load effects

Journal Article Conference Proceedings of the Society for Experimental Mechanics Series · January 1, 2011 This paper considers the free vibration of a plane, rectangular, portal frame consisting of slender members. Natural frequencies and mode shapes are influenced by the addition of mass at the corners of the frame. The members are sufficiently slender that a ... Full text Cite

Non-linear flutter in fan stator vanes with time dependent fixity

Journal Article Proceedings of the ASME Turbo Expo · December 1, 2010 A new mechanism for fan stator vane failure in turbofan engines at high speed and high loading has been identified and reported in this paper. Highly destructive vane failures have been encountered at Honeywell in one of the development fans with composite ... Full text Cite

The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet.

Journal Article Lab on a chip · August 2010 We present theoretical, numerical, and experimental analyses on the non-linear dynamic behavior of superparamagnetic beads exposed to a periodic array of micro-magnets and an external rotating field. The agreement between theoretical and experimental resul ... Full text Open Access Cite

Static and dynamic behavior of highly deformed risers and pipelines

Journal Article Journal of Offshore Mechanics and Arctic Engineering · May 1, 2010 This paper models flexible risers and pipelines as slender elastica structures. The theoretical formulation leads to a type of nonlinear boundary value problem that can be solved numerically given appropriate boundary conditions. The offsetting effects of ... Full text Cite

Nonlinear dynamics of a ball rolling on a surface

Journal Article American Journal of Physics · March 1, 2010 An underlying potential energy function can provide visual and intuitive insight into a system's stability and overall behavior. In particular, the motion of a ball moving along a curve or surface in a gravitational field provides a macroscale demonstratio ... Full text Cite

Dynamic behavior of highly-deformed risers and pipelines

Journal Article ASME Journal of Offshore Mechanics and Arctic Engineering · 2010 Cite

Vibrations and large postbuckling deflections of optimal pinned columns with elastic foundations

Journal Article Structural and Multidisciplinary Optimization · January 1, 2010 The optimal distribution of material to maximize the critical load of columns has been studied extensively in the past, along with initial postbuckling behavior. Here, large postbuckling deflections are analyzed for optimal columns with pinned ends. Small ... Full text Cite

Effect of weight on the experimental modal analysis of slender cantilever beams

Journal Article Proceedings of the ASME Design Engineering Technical Conference · December 1, 2009 It is relatively well known that axial loads tend to influence lateral stiffness and hence natural frequencies of slender structural components. Tensile forces tend to increase the lateral stiffness and compressive forces tend to reduce lateral stiffness, ... Full text Cite

Vibration and snap-through of bent elastica strips subjected to end rotations

Journal Article Journal of Applied Mechanics, Transactions ASME · December 1, 2009 A flexible strip is rotated at its ends until it forms a deep circular arc above its ends. Then the ends are kept immovable and are rotated downward until the arch suddenly snaps into an inverted configuration. The strip is analyzed as an inextensible elas ... Full text Cite

Some non-smooth dynamical systems in offshore mechanics

Conference Lecture Notes in Applied and Computational Mechanics · December 1, 2009 Full text Cite

Nonlinear dynamics of superparamagnetic beads in a traveling magnetic-field wave.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · July 2009 The nonlinear dynamic behavior of superparamagnetic beads exposed to a periodic array of micromagnets and an external rotating field is simulated as a function of the relative size of the bead with respect to the micromagnet size and the strength of the ex ... Full text Cite

Vibration and snap-through of bent elastica strips subjected to end rotations

Journal Article Journal of Applied Mechanics · 2009 Cite

Large oscillations of beams and columns including self-weight

Journal Article International Journal of Non-Linear Mechanics · October 1, 2008 Large-amplitude, in-plane beam vibration is investigated using numerical simulations and a perturbation analysis applied to the dynamic elastica model. The governing non-linear boundary value problem is described in terms of the arclength, and the beam is ... Full text Cite

Vibration isolation using extreme geometric nonlinearity

Journal Article Journal of Sound and Vibration · August 19, 2008 A highly deformed, slender beam (or strip), attached to a vertically oscillating base, is used in a vibration isolation application to reduce the motion of a supported mass. The isolator is a thin strip that is bent so that the two ends are clamped togethe ... Full text Cite

Experimental modal analysis of solar sail booms

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · July 4, 2008 This paper presents the results of experimental modal analysis of a system of two very slender cantilever beams connected by a rigid hub. The effect of gravity is examined together with the influence of an attached cable. Natural frequencies and mode shape ... Cite

Nonlinear Vibration

Journal Article · April 8, 2008 Full text Cite

Cylindrical shell submerged in bounded acoustic media: A modal approach

Journal Article AIAA Journal · March 1, 2008 The dynamics of a simply supported cylindrical shell submerged in liquid hydrogen and liquid oxygen are considered. The shell itself is bounded by a rigid outer cylinder with closed rigid ends. This configuration gives rise to two fluid-filled cavities - a ... Full text Cite

Vibration isolation using buckled or pre-bent columns-Part 1: Two-dimensional motions of horizontal rigid bar

Journal Article Journal of Sound and Vibration · February 5, 2008 The use of buckled columns, or pairs of pre-bent columns bonded with a viscoelastic filler, as vibration isolators is analyzed. They support a horizontal rigid bar at its ends, and harmonic vertical motion is applied at the base of the isolators. The displ ... Full text Cite

Large deflections and vibration of a tapered cantilever pulled at its tip by a cable

Journal Article Journal of Sound and Vibration · February 5, 2008 The behavior of a slender, tapered, cantilever beam loaded through a cable attached to its free end is described. Large static deflections are computed (based on an elastica description) together with natural frequencies and mode shapes for small-amplitude ... Full text Cite

Vibration isolation using buckled or pre-bent columns-Part 2: Three-dimensional motions of horizontal rigid plate

Journal Article Journal of Sound and Vibration · February 5, 2008 This is a continuation of previous work to investigate the use of pairs of pre-bent columns, bonded with a viscoelastic filler, as vibration isolators. In this paper, four of these devices support the corners of a square, rigid plate. When the system is in ... Full text Cite

Nonlinear two-dimensional elastica analysis of subsea risers

Conference 7th European Conference on Structural Dynamics, EURODYN 2008 · January 1, 2008 This paper models two configurations of flexible risers and pipelines as slender elastica structures. The theoretical formulation leads to a type of nonlinear boundary value problem that can be solved numerically given appropriate boundary conditions. The ... Cite

Static and dynamic behavior of highly-deformed risers and pipelines

Journal Article Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE · December 21, 2007 This paper models flexible risers and pipelines as slender elastica structures. The theoretical formulation leads to a type of nonlinear boundary value problem that can be solved numerically given appropriate boundary conditions. The offsetting effects of ... Full text Cite

An experimental nonlinear oscillator subject to two-frequency excitation

Journal Article Conference Proceedings of the Society for Experimental Mechanics Series · December 1, 2007 This paper describes some interesting nonlinear behavior in the response of an experimental mechanical oscillator. The focusis on the characterization of nonlinear response (subharmonic, quasiperiodic and chaotic) of a discrete mechanical oscillator subjec ... Cite

Non-linear behavior in a discretely forced oscillator

Journal Article International Journal of Non-Linear Mechanics · June 1, 2007 The simulated and experimental responses of a rigid-arm pendulum driven by an external impactor are considered. Here, impact occurs if the trajectory of a rotating impactor intersects that of the pendulum. Using the rotation rate of the impactor as the con ... Full text Cite

Effect of gravity on the vibration of vertical cantilevers

Journal Article Mechanics Research Communications · April 1, 2007 The free vibration of a vertically-oriented, thin, prismatic cantilever is influenced by weight. That is, the natural frequencies (and to a lesser extent, mode shapes) are affected by the application of a linearly varying axial load. A beam with an "upward ... Full text Cite

Bragg grating-based fibre optic sensors in structural health monitoring.

Journal Article Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · February 2007 This work first considers a review of the dominant current methods for fibre Bragg grating wavelength interrogation. These methods include WDM interferometry, tunable filter (both Fabry-Perot and acousto-optic) demultiplexing, CCD/prism technique and a new ... Full text Cite

Vibration of axially loaded structures

Book · January 1, 2007 This book concerns the vibration and the stability of slender structural components. The loss of stability of structures is an important aspect of structural mechanics and is presented here in terms of dynamic behavior. A variety of structural components a ... Full text Cite

Finite element analysis of a slender isogrid structure

Journal Article Journal of Spacecraft and Rockets · 2007 Cite

Slender solar sail booms: Finite element analysis

Journal Article Journal of Spacecraft and Rockets · January 1, 2007 Various aspects related to the numerical (finite element) analysis of the support structure for solar sails are analyzed. Static analyses of single booms (simple beam and isogrid configurations) are presented and dynamic properties are extracted before and ... Full text Cite

Cylindrical shell submerged in bounded acoustic media: A modal approach

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · January 1, 2007 The dynamics of a simply-supported cylindrical shell submerged in liquid hydrogen (LH2) and liquid oxygen (LOX) are considered. The shell itself is bounded by a rigid outer cylinder with closed rigid ends. This configuration gives rise to two fluid-filled ... Full text Cite

Post-buckling and vibration of heavy beam on horizontal or inclined rigid foundation

Journal Article Journal of Applied Mechanics, Transactions ASME · July 1, 2006 A slender, straight beam resting on a flat, rigid foundation does not buckle when subjected to a compressive load, since the load cannot overcome the effect of the beam's weight. However, it buckles if its ends are moved toward each other. Post-buckling of ... Full text Cite

Vibration and large deflection of cantilevered elastica compressed by angled cable

Journal Article AIAA Journal · July 1, 2006 A thin cantilevered beam is compressed by a cable attached to the tip of the beam and terminating near the base. Large-deflection equilibrium configurations and small vibrations about equilibrium are investigated. This system has a direct application to so ... Full text Cite

Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach

Journal Article International Journal of Solids and Structures · June 1, 2006 Various static and dynamic aspects of post-buckled thin plates, including the transition of buckled patterns, post-buckling dynamics, secondary bifurcation, and dynamic snapping (mode jumping phenomenon), are investigated systematically using asymptotical ... Full text Cite

Finite element analysis of post-buckling dynamics in plates. Part II: A non-stationary analysis

Journal Article International Journal of Solids and Structures · June 1, 2006 With the secondary bifurcation and the local post-secondary buckling behavior being analyzed in Part I, Part II of this study consists of developing an adaptive non-stationary load sweeping algorithm to investigate post-buckling dynamics and mode jumping p ... Full text Cite

Postbuckling of elastic columns with second-mode imperfection

Journal Article Journal of Engineering Mechanics · 2006 Initial imperfections of columns are often assumed to have the shape of the first buckling mode. In this technical note, the imperfection has the shape of the second mode. An elastica analysis is performed, and numerical results are obtained for two cases ... Full text Link to item Cite

A reflection on nonlinear oscillations, dynamical systems, and bifurcations of vector fields

Journal Article Journal of Computational and Nonlinear Dynamics · January 1, 2006 Full text Cite

Vibration and large deflection of a beam-cable system

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · December 19, 2005 This paper studies the large-deflection static and dynamic characteristics of a slender prismatic cantilevered beam loaded by a cable attached at the tip and terminating near the base. This system has a direct application to square solar-sail structures wh ... Cite

Equilibria and vibration of a heavy pinched loop

Journal Article Journal of Sound and Vibration · November 22, 2005 A thin strip is bent such that the two ends are brought together and clamped (pinched) to form a teardrop shape. The clamped end is held at various angles with the loop either upright, horizontal, downward, or halfway between these positions. The length of ... Full text Cite

Hopf-flip bifurcation of high dimensional maps and application to vibro-impact systems

Journal Article Acta Mechanica Sinica/Lixue Xuebao · August 1, 2005 This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form w ... Full text Cite

Analysis of buckled and pre-bent fixed-end columns used as vibration isolators

Journal Article Journal of Sound and Vibration · May 20, 2005 The use of a buckled or pre-bent column with fixed ends as a vibration isolator is analyzed. The column is designed to have a high axial stiffness under the weight that it supports, so that the static displacement of the weight is not excessive, and then t ... Full text Cite

A multivariate, attractor-based approach to structural health monitoring

Journal Article Journal of Sound and Vibration · May 6, 2005 In this work, recent advances in the use of nonlinear time-series analysis for structural health monitoring are extended to incorporate multivariate data. Structural response data recorded at multiple locations are combined using a multivariate time delay ... Full text Cite

Finite element analysis of slender solar sail booms

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · January 1, 2005 Full text Cite

Nonlinear oscillations of a buckled mechanism used as a vibration isolator

Journal Article Solid Mechanics and its Applications · January 1, 2005 Various devices have been used to reduce the dynamic response of mechanical and structural systems connected to moving sources. A vibration isolator can be inserted between a system and source to absorb energy and reduce the system's motion. The applicatio ... Full text Cite

Dynamic analysis of modal shifting and mode jumping in thermally buckled plates

Journal Article Journal of Sound and Vibration · November 22, 2004 Both analytical and finite element investigations are performed for the various static and dynamic aspects of the mode jumping phenomenon of a simply-supported rectangular plate heated deeply into the post-buckling regime. For the analytical method, the vo ... Full text Cite

An assessment of modal property effectiveness in detecting bolted joint degradation: Theory and experiment

Journal Article Journal of Sound and Vibration · August 23, 2004 An experiment and a corresponding simple model were constructed to explore whether modal analysis is an appropriate tool for detecting bolted joint degradation. For the study, a beam is bolted to supports at its edges, and the spring encase the bolts such ... Full text Cite

Chaos and period-adding; experimental and numerical verification of the grazing bifurcation

Journal Article Journal of Nonlinear Science · August 1, 2004 Experimental results are presented for a single-degree-of-freedom horizontally excited pendulum that is allowed to impact with a rigid stop at a fixed angle θ to the vertical. By inclining the apparatus, the pendulum is allowed to swing in an effectively r ... Full text Cite

Use of data-driven phase space models in assessing the strength of a bolted connection in a composite beam

Journal Article Smart Materials and Structures · April 1, 2004 This work explores the role of empirical dynamical models in deducing the level of preload loss in a bolted connection. Specifically, we examine the functional relationship between data gleaned from locations on either side of the connection using nonlinea ... Full text Cite

Postbuckling and vibration of linearly elastic and softening columns under self-weight

Journal Article International Journal of Solids and Structures · January 1, 2004 The critical height for buckling of a linearly elastic cantilevered column due to its self-weight was determined by Greenhill in 1881. Postbuckling behavior also has been studied, often assuming that the column is an elastica (inextensible, with its bendin ... Full text Cite

Three-dimensional postbuckling and vibration of vertical half-loop under self-weight

Journal Article International Journal of Solids and Structures · January 1, 2004 The stability and vibration characteristics of a flexible and inextensible half-loop are investigated. The loop is fixed at two base points, which are separated by a specified distance, and is only subjected to gravity loading. If the length of the loop is ... Full text Cite

Investigation of structural dynamics in a 2-meter square solar sail model including axial load effects

Journal Article 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference · December 1, 2003 This paper presents a parameter study of the effect of boom axial loading on the global dynamics of a 2-meter solar sail scale model. The experimental model used is meant for building expertise in finite element analysis and experimental execution, not as ... Cite

Development and application of chaotic attractor property analysis for vibration-based structural damage assessment

Conference AIP Conference Proceedings · August 19, 2003 Long-term, high-level performance demands on a variety of structures and equipment have stimulated significant research in the field of structural health monitoring. The primary goals of this field are to provide information regarding structural performanc ... Full text Cite

Structural health monitoring through chaotic interrogation

Journal Article Meccanica · April 16, 2003 The field of vibration based structural health monitoring involves extracting a 'feature' which robustly quantifies damage induced changes to the structure in the presence of ambient variation, that is, changes in ambient temperature, varying moisture leve ... Full text Cite

Vibration isolation using buckled struts [3]

Journal Article Journal of Sound and Vibration · March 6, 2003 Post-buckled struts were used as spring components in a vibration isolation system. Vibration isolation is concerned with the minimization of the force or motion transmitted to a device from a source of vibration. The approach was shown to have promise in ... Full text Cite

Detection of fastener preload loss in a hybrid composite-to-metal bolted joint

Conference Structural Health Monitoring 2003: From Diagnostics and Prognostics to Structural Health Management - Proceedings of the 4th International Workshop on Structural Health Monitoring, IWSHM 2003 · January 1, 2003 In this work we present two novel nonlinear time series analysis techniques-nonlinear cross prediction error and chaotic amplification of attractor distortion-for detecting preload loss in a hybrid metal-to-composite bolted joint. The two techniques involv ... Cite

On the use of attractor dimension as a feature in structural health monitoring

Journal Article Mechanical Systems and Signal Processing · January 1, 2003 Recent works in the vibration-based structural health monitoring community have emphasised the use of correlation dimension as a discriminating statistic in separating a damaged from undamaged response. This paper explores the utility of attractor dimensio ... Full text Cite

A note on the response spectrum map

Journal Article International Journal of Bifurcation and Chaos in Applied Sciences and Engineering · January 1, 2003 A study was performed on the response spectrum map. A plot of frequency, or spectral, content versus a system parameter was a useful alternative to bifurcation diagrams in nonlinear dynamics. The spectrum map was based on the data taken from two experiment ... Full text Cite

Use of chaotic excitation and attractor property analysis in structural health monitoring.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · January 2003 This work explores the utility of attractor-based approaches in the field of vibration-based structural health monitoring. The technique utilizes the unique properties of chaotic signals by driving the structure directly with the output of a chaotic oscill ... Full text Cite

System identification through chaotic interrogation

Journal Article Mechanical Systems and Signal Processing · January 1, 2003 We introduce a method by which the coefficient of viscous damping for a linear ndof system may be estimated. The technique utilises the unique properties of chaos by driving the system with the output of a non-linear oscillator. By tuning the Lyapunov expo ... Full text Cite

Investigation of structural dynamics in a 2-meter square solar sail model including axial load effects

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · January 1, 2003 This paper presents a parameter study of the effect of boom axial loading on the global dynamics of a 2-meter solar sail scale model. The experimental model used is meant for building expertise in finite element analysis and experimental execution, not as ... Full text Cite

Use of chaotic excitation and attractor property analysis in structural health monitoring

Journal Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics · January 1, 2003 The utility of attractor based approaches in the field of vibration based structural health monitoring (SHM) was discussed. The technique utilized the properties of chaotic signals by driving the structure directly with the output of a chaotic oscillator. ... Cite

The stability of limit-cycle oscillations in a nonlinear aeroelastic system

Journal Article Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · September 8, 2002 The effects of a freeplay structural nonlinearity on an aeroelastic system are studied experimentally. Particular attention is paid to the stability of a periodic nonlinear aeroelastic response, known as limit-cycle oscillations (LCOs). The major thrust of ... Full text Cite

Use of frequency data to predict secondary bifurcation

Journal Article Journal of Sound and Vibration · April 11, 2002 Full text Cite

Structural damage assessment using chaotic dynamic interrogation

Journal Article ASME International Mechanical Engineering Congress and Exposition, Proceedings · January 1, 2002 This work considers a new technique for damage detection in vibration-based structural health monitoring. The technique involves exciting a structure with a low-dimensional chaotic input, reconstructing the attractor, and analyzing certain properties of th ... Full text Cite

The use of a high-performance fiber optic measurement system in structural damage assessment

Journal Article Proceedings of SPIE - The International Society for Optical Engineering · January 1, 2002 We have developed and tested a fiber optic system that relies on Fiber Bragg Gratings (FBGs) as strain gages for structural monitoring. FBGs reflect a narrow (< 0.2 nm) band of light whose center wavelength changes as the fiber is stretched or compressed. ... Cite

Structural damage assessment using chaotic dynamic interrogation

Journal Article American Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC · 2002 Cite

Geometric scaling properties of inflatable structures for use in space solar power generation

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · January 1, 2002 Investigation of the geometric scaling properties of polyimide film inflatable booms is described. These structures have considerable potential for use in space with solar concentrators, solar sails, and space solar power systems including solar arrays. Mu ... Full text Cite

An investigation of a rocking-sliding block

Journal Article Proceedings of the ASME Design Engineering Technical Conference · December 1, 2001 The short end of a rigid rectangular block with a 2:1 aspect ratio is placed on a flat horizontal surface. The surface exhibits a horizontal harmonic motion, and two-dimensional motions of the block are investigated numerically and experimentally. A variet ... Cite

On the response of a shaken cable-suspended mass

Journal Article Proceedings of the ASME Design Engineering Technical Conference · December 1, 2001 A small mass is suspended by two cables which are attached at angles to a rigid frame. The frame is shaken harmonically in the horizontal direction, causing the mass to respond typically in an erratic manner as the cables alternately become taut and slack. ... Cite

Mode splitting in an inflated polyimide cylinder with circumferential asymmetry

Journal Article 19th AIAA Applied Aerodynamics Conference · December 1, 2001 In the past, a good deal of the research on the feasibility of inflatable structures for space applications has focused on the behavior of inflated cylinders. In many cases, especially in theoretical and numerical studies, the cylinder has been assumed to ... Cite

Damping estimates from experimental non-linear time-series

Journal Article Journal of Sound and Vibration · October 4, 2001 This paper seeks to illustrate the utility of the Lyapunov spectrum in estimating the damping of an experimental non-linear system. A mechanical model of Duffing's equation operating in the chaotic regime is used to generate a single observable. Using stan ... Full text Cite

Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio

Journal Article Smart Materials and Structures · October 1, 2001 A novel feature extracted from a nonlinear time series is presented within the context of vibration-based damage detection in a system. An eight-degree-of-freedom spring-mass-damper 'structure' is considered with damage incurred by a stiffness degradation ... Full text Cite

Practical evaluation of invariant measures for the chaotic response of a two-frequency excited mechanical oscillator

Journal Article Nonlinear Dynamics · September 1, 2001 This paper presents results which characterize the chaotic response of a low-dimensional mechanical oscillator. An experimental system based on a cart rolling on a two-well potential surface has been shown to closely approximate a modified form of Duffing' ... Full text Cite

Vibration-based damage assessment using local attractor variance

Journal Article Proceedings of SPIE - The International Society for Optical Engineering · July 30, 2001 Recently proposed methodologies in the field of vibration-based structural health monitoring have focused on the incorporation of statistical-based analysis. The structure in question is dynamically excited, some feature is identified for extraction from a ... Full text Cite

An implicit boundary element solution with consistent linearization for free surface flows and non-linear fluid-structure interaction of floating bodies

Journal Article International Journal for Numerical Methods in Engineering · June 10, 2001 In this work, a new comprehensive method has been developed which enables the solution of large, non-linear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian-Lagrangian approach has been translated into an impli ... Full text Cite

STABILITY TRANSITIONS IN A NONLINEAR AIRFOIL

Conference Proceedings of the 5th Experimental Chaos Conference · April 2001 Full text Cite

Mode splitting in an inflated polyimide cylinder with circumferential asymmetry

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · January 1, 2001 In the past, a good deal of the research on the feasibility of inflatable structures for space applications has focused on the behavior of inflated cylinders. In many cases, especially in theoretical and numerical studies, the cylinder has been assumed to ... Cite

Mode splitting in an inflated polyimide cylinder with circumferential asymmetry

Conference 19th AIAA Applied Aerodynamics Conference · January 1, 2001 In the past, a good deal of the research on the feasibility of inflatable structures for space applications has focused on the behavior of inflated cylinders. In many cases, especially in theoretical and numerical studies, the cylinder has been assumed to ... Full text Cite

On the OGY control of an impact-friction oscillator

Journal Article JVC/Journal of Vibration and Control · January 1, 2001 An earlier paper by the same authors examined the dynamic behavior of an impact-friction oscillator. It was shown that a variety of highly complex behavior was possible including chaos, and the results of numerical simulation were verified experimentally. ... Full text Cite

Novel nonlinear feature identification in vibration-based damage detection using local attractor variance

Journal Article Proceedings of the International Modal Analysis Conference - IMAC · January 1, 2001 Recent research in the broad scope of structural health monitoring has introduced a somewhat new paradigm within the context of vibration-based damage detection. The incorporation of statistical-based analysis has shown great promise in more accurately ass ... Cite

Characterizing stability of responses in a nonlinear aeroelastic system

Journal Article 41st Structures, Structural Dynamics, and Materials Conference and Exhibit · December 1, 2000 A method for investigating the degree of stability of nonlinear limit cycle oscillations (LCO) observed in an aeroelastic system is presented. The system considered is a typical section airfoil model with a free-play nonlinear-ity in the control surface st ... Cite

Characterizing stability of responses in a nonlinear aeroelastic system

Journal Article Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · January 1, 2000 A method for investigating the degree of stability of nonlinear limit cycle oscillations (LCO) observed in an aeroelastic system is presented. The system considered is a typical section airfoil model with a free-play nonlinearity in the control surface sti ... Cite

Characterizing stability of responses in a nonlinear aeroelastic system

Conference 41st Structures, Structural Dynamics, and Materials Conference and Exhibit · January 1, 2000 A method for investigating the degree of stability of nonlinear limit cycle oscillations (LCO) observed in an aeroelastic system is presented. The system considered is a typical section airfoil model with a free-play nonlinear-ity in the control surface st ... Full text Cite

Nonlinear features in the dynamics of an impact-friction oscillator

Conference STOCHASTIC AND CHAOTIC DYNAMICS IN THE LAKES · January 1, 2000 Link to item Cite

Grazing bifurcations and basins of attraction in an impact-friction oscillator

Journal Article Physica D: Nonlinear Phenomena · June 1, 1999 This paper describes some interesting global dynamic behavior in the response of a double-sided, harmonically-forced, impact oscillator including the influence of Coulomb damping. The system under study is modeled as piecewise linear in both its force-defl ... Full text Cite

On the evolution of deterministic non-periodic behavior of an airfoil

Journal Article International Journal of Non-Linear Mechanics · January 1, 1999 This paper describes some interesting transitional behavior in the limit cycle response of a typical section airfoil with a loosely connected flap subject to a fluid flow. The freeplay non-linearity associated with the flap connection has considerable prac ... Full text Cite

Grazing bifurcations and basins of attraction in an impact-friction oscillator

Journal Article Physica D: Nonlinear Phenomena · 1999 This paper describes some interesting global dynamic behavior in the response of a double-sided, harmonically-forced, impact oscillator including the influence of Coulomb damping. The system under study is modeled as piecewise linear in both its force-defl ... Cite

Bottlenecking phenomenon near a saddle-node remnant in a Duffing oscillator

Journal Article Physics Letters, Section A: General, Atomic and Solid State Physics · November 9, 1998 The bottlenecking phenomenon near a saddle-node remnant or ghost is discussed for an electronic circuit modeling Duffing's equation. Numerical simulation and a useful experimental perturbation method, stochastic interrogation, are used to confirm the analy ... Full text Cite

Stability estimation of high dimensional vibrating systems under state delay feedback control

Journal Article Journal of Sound and Vibration · July 16, 1998 The paper presents a method of assessing the stability of high dimensional vibrating systems under state feedback control with a short time delay. It is first proved that if the time delay is sufficiently short, an n -degree-of-freedom system with feedback ... Full text Cite

Impact response and the influence of friction

Journal Article Journal of Sound and Vibration · April 16, 1998 Non-smooth stiffness and damping characteristics are commonly encountered in mechanical systems. The specific physical contacts considered in this paper are impact and friction. Although these individual effects have been the subject of quite intensive res ... Full text Cite

Basins of attraction in experimental nonlinear oscillators

Journal Article International Journal of Bifurcation and Chaos in Applied Sciences and Engineering · January 1, 1998 This paper addresses two relatively simple but fundamental questions in nonlinear oscillations: Given an arbitrary initial condition where will the trajectory go, and how long will it take to get there? These related questions are addressed from an experim ... Full text Cite

Basins of attraction in experimental nonlinear oscillators

Journal Article International Journal of Bifurcation and Chaos in Applied Sciences and Engineering · 1998 This paper addresses two relatively simple but fundamental questions in nonlinear oscillations: Given an arbitrary initial condition where will the trajectory go, and how long will it take to get there? These related questions are addressed from an experim ... Cite

Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback

Journal Article Nonlinear Dynamics · January 1, 1998 The paper presents analytical and numerical studies of the primary resonance and the 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under state feedback control with a time delay. By using the method of multiple scales, the first ord ... Full text Cite

Limit cycle behavior of an airfoil with a control surface

Journal Article Journal of Fluids and Structures · January 1, 1998 A three-degree-of-freedom aeroelastic model with freeplay is modeled theoretically using a small number of aerodynamic eigenmodes (i.e. a reduced order model) based upon Peters' finite-state model for two-dimensional aerodynamic flow. The limit cycle behav ... Full text Cite

Nonlinear aeroelasticity of an airfoil with control surface freeplay

Conference 35th Aerospace Sciences Meeting and Exhibit · January 1, 1997 © 1997, American Institute of Aeronautics and Astronautics, Inc.This paper presents a correlation study between numerical and experimental results for the response of a typical section airfoil with freeplay in the control surface. Since this is an inherent ... Cite

Nonlinear aeroelasticity of an airfoil with control surface freeplay

Conference 35th Aerospace Sciences Meeting and Exhibit · January 1, 1997 This paper presents a correlation study between numerical and experimental results for the response of a typical section airfoil with freeplay in the control surface. Since this is an inherently nonlinear system the equations of motion are integrated numer ... Cite

The effect of thermal prestress on the free vibration characteristics of clamped rectangular plates: theory and experiment

Journal Article Trans. ASME. J. Vib. Acoust. (USA) · 1997 In a combined theoretical and experimental approach, the free vibration characteristics of a uniformly heated, fully clamped (out-of-plane), rectangular plate are considered. Specifically, this work focuses on the behavior of the small amplitude natural fr ... Cite

An experimental verification of basin metamorphoses in a nonlinear mechanical system

Journal Article International Journal of Bifurcation and Chaos in Applied Sciences and Engineering · January 1, 1997 This paper describes bifurcations and the basin boundary metamorphoses that give rise to post-fold outcome indeterminacy from a primarily experimental perspective. A gravity-loaded cart-and-track system is constrained to mimic the twin-well, single-degree- ... Full text Cite

Experiments and simulation of overturning of an asymmetric rocking block on an oscillating foundation

Journal Article European Journal of Mechanics, A/Solids · January 1, 1997 This paper describes what happens when the base upon which a relatively slender rigid block rests is subjected to a horizontal harmonic acceleration. The force transmitted to the block may be sufficient to initiate rocking or even cause overturning. The nu ... Cite

Nonlinear behavior of a typical airfoil section with control surface freeplay: A numerical and experimental study

Journal Article Journal of Fluids and Structures · January 1, 1997 A three degree-of-freedom aeroelastic typical section with control surface freeplay is modeled theoretically as a system of piecewise linear state-space models. The system response is determined by time marching of the governing equations using a standard ... Full text Cite

Extracting information from interimpact intervals in a mechanical oscillator

Journal Article Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics · January 1, 1997 Monitoring all the state variables in dynamic experiments may be difficult or even impossible. It is also desirable to reduce the coupling between the system under study and the measuring device to as low a level as possible. To these ends, we investigated ... Full text Cite

A detailed study of the low-frequency periodic beliavior of a dry friction oscillator

Journal Article Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME · January 1, 1997 This work examines the periodic stopping motion present in the low-frequency response of a dry friction oscillator, excited harmonically through a base spring. Piecewise linear solution methods are used to compare two simple friction models, to consider th ... Full text Cite

An experimental impact oscillator

Journal Article Chaos, Solitons and Fractals · January 1, 1997 The present work considers the impacting behavior of a piecewise linear experimental system, a previous version of which has successfully displayed a wide variety of non-linear, including chaotic, behavior in other previous experiments [1-3]; making use of ... Full text Cite

Monitoring the behavior of an experimental impacting system

Journal Article American Society of Mechanical Engineers, Design Engineering Division (Publication) DE · December 1, 1996 Since monitoring all the state variables in dynamic experiments may be difficult or even impossible, and since it is desirable to reduce the coupling between the system under study and the measuring device to as low a level as possible, it is useful to ass ... Cite

Free surface flow computation using a fully consistent method

Journal Article American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED · December 1, 1996 Free surface flows described by nonlinear equations due to nonlinear boundary conditions written for unknown boundary position are solved using a new implicit, fully consistent method. The proposed algorithm is tested for a couple of hydrodynamic free surf ... Cite

Natural frequency considerations of an impact oscillator

Journal Article Journal of Sound and Vibration · July 18, 1996 Full text Cite

Periodic solutions of an unsymmetric oscillator including a comprehensive study of their stability characteristics

Journal Article Journal of Sound and Vibration · May 23, 1996 The periodic solutions of a non-linear oscillator with unsymmetric restoring force and harmonic excitation are studied by means of harmonic balance using an arbitrary number of modes in the assumed solution. Comparisons between the approximate solution for ... Full text Cite

Transient motion and overturning of a rocking block on a seesawing foundation

Journal Article Journal of Sound and Vibration · March 21, 1996 Full text Cite

MONITORING THE BEHAVIOR OF AN EXPERIMENTAL IMPACTING SYSTEM

Conference ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) · January 1, 1996 Since monitoring all the state variables in dynamic experiments may be difficult or even impossible, and since it is desirable to reduce the coupling between the system under study and the measuring device to as low a level as possible, it is useful to ass ... Full text Cite

Experimental snap-through boundaries for acoustically excited, thermally buckled plates

Journal Article Experimental Mechanics · 1996 This paper presents some recent experimental results on the dynamic snap-through behavior of a clamped, rectangular plate subject to thermal loading and intense acoustic excitation. The likelihood of snap-through oscillations is characterized in terms of b ... Cite

Characterizing the dynamic response of a thermally loaded, acoustically excited plate

Journal Article Journal of Sound and Vibration · 1996 In this work the dynamic response is considered of a homogeneous, fully clamped rectangular plate subject to spatially uniform thermal loads and narrow-band acoustic excitation. In both the pre- and post-buckled regimes, the small amplitude, linear respons ... Full text Link to item Cite

Fractal Behavior of an Asymmetric Rigid Block Overturning Due to Harmonic Motion of a Tilted Foundation

Journal Article Chaos, Solitons and Fractals · January 1, 1996 The motion of a slender rigid block with a flat or concave base resting on a rigid and flat foundation is analyzed. The block may be symmetric or asymmetric, and the foundation may be horizontal or tilted. The foundation oscillates harmonically for a finit ... Full text Cite

The nonstationary transition through resonance

Journal Article Nonlinear Dynamics · January 1, 1996 This paper considers the resonant behavior of a mechanical oscillator during a linear frequency sweep. Both numerical and experimental results are presented. The experimental system consisting of a track in the shape of a potential energy surfaces has been ... Full text Cite

Efficient determination of higher-order periodic solutions using n-mode harmonic balance

Journal Article IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) · January 1, 1996 This paper presents a systematic procedure to explicitly determine the algebraic equations arising from the method of harmonic balance with an arbitrary number of modes in the assumed solutions. The technique can be used for a wide variety of nonlinear osc ... Full text Cite

On the global convergence characteristics of numerically evaluated jacobian matrices: Technical note

Journal Article Nonlinear Dynamics · January 1, 1996 Since locating all the fixed points of a nonlinear oscillator involves the numerical solution of simultaneous equations, it is useful to observe some of the global convergence characteristics of these techniques. Specifically, the popular Newton or quasi-N ... Full text Cite

Experiments on a rocking block

Journal Article American Society of Mechanical Engineers, Design Engineering Division (Publication) DE · December 1, 1995 A rigid, slender, rectangular block is an apparently simple example of a stability problem. In a static sense, the upright position remains stable providing the restoring moment due to gravity is sufficient to offset any applied overturning moment. Rotated ... Cite

Experimental study of the forced response of pre- and post-critical plates

Journal Article American Society of Mechanical Engineers, Design Engineering Division (Publication) DE · December 1, 1995 Experimental results are presented which characterize the dynamic response of homogeneous, fully clamped, rectangular plates to narrow band acoustic excitation and uniform thermal loads. Using time series, pseudo-phase projections, power spectra and auto-c ... Cite

Routes to escape from an energy well

Journal Article Journal of Sound and Vibration · October 19, 1995 Dynamical systems characterized by the possibility of escape from a local potential energy well occur in a great many physical problems, including a rigid-arm pendulum passing over its inverted equilibrium position, snap-through buckling in arch and shell ... Full text Cite

An experimental study of the forced response of pre- And post-critical plates

Conference Proceedings of the ASME Design Engineering Technical Conference · January 1, 1995 Experimental results are presented which characterize the dynamic response of homogeneous, fully clamped, rectangular plates to narrow band acoustic excitation and uniform thermal loads. Using time series, pseudo-phase projections, power spectra and auto-c ... Full text Cite

Experiments on a rocking block

Conference Proceedings of the ASME Design Engineering Technical Conference · January 1, 1995 A rigid, slender, rectangular block is an apparently simple example of a stability problem. In a static sense, the upright position remains stable providing the restoring moment due to gravity is sufficient to offset any applied overturning moment. Rotated ... Full text Cite

A comparison of piecewise linear and continuous approximating models

Journal Article Mechanics Research Communications · January 1, 1995 Full text Cite

Curve and surface veering for a braced column

Journal Article J. Sound Vib. (UK) · 1995 Curve veering arises naturally in a wide variety of eigenvalue problems in structural mechanics, such as vibration of beams, rotors, plates and shells, and buckling of columns and plates. Previous work on curve veering is extended with the consideration of ... Full text Link to item Cite

Nonlinear behavior of a magnetic bearing system

Journal Article Trans. ASME, J. Eng. Gas Turbines Power (USA) · 1995 This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bear ... Cite

Overturning of a rigid block under horizontal base excitation

Journal Article Proceedings of Engineering Mechanics · January 1, 1995 Overturning conditions for a rigid, rectangular block on a rigid, horizontal, vibrating base are investigated. The base moves with a simple-harmonic horizontal acceleration over a finite period of time, and the block can rotate about either of its bottom c ... Cite

Practical considerations in the control of chaos.

Journal Article Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · July 1994 Full text Cite

Nonlinear behavior of a magnetic bearing system

Journal Article American Society of Mechanical Engineers (Paper) · January 1, 1994 This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bear ... Cite

On the behavior of characteristic multipliers through a period-doubling sequence

Journal Article Journal of Sound and Vibration · 1994 Initial work along these lines by the present authors has focused attention on how these ideas can be used to infer and predict the loss of stability of an n = 1 solution. Here, the algorithm is applied through a series of period-doubling bifurcations, but ... Full text Link to item Cite

A new approach to the overturning stability of floating structures

Journal Article Ocean Engineering · January 1, 1994 The increasingly widespread use of floating offshore production facilities has led to a need for a better understanding and accurate prediction of dynamic behavior. The approach described in this paper uses an approximate criterion for safe, forced, roll o ... Full text Cite

Measuring the stability of periodic attractors using perturbation-induced transients: applications to two non-linear oscillators

Journal Article Journal of Sound and Vibration · 1994 In this paper a combined analytical, numerical and experimental approach is used to study the behavior of small, perturbation-induced transients superimposed on a periodic steady state. The behavior of these transients is monitored in terms of characterist ... Full text Link to item Cite

Nonlinear behavior of a magnetic bearing system

Journal Article Proceedings of the ASME Turbo Expo · January 1, 1994 This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bear ... Full text Cite

STABILITY MEASUREMENTS IN NONLINEAR MECHANICAL EXPERIMENTS GUIDED BY DYNAMICAL SYSTEMS THEORY

Conference NONLINEARITY AND CHAOS IN ENGINEERING DYNAMICS · January 1, 1994 Link to item Cite

FREE VIBRATION OF THERMALLY LOADED PANELS INCLUDING INITIAL IMPERFECTIONS AND POST-BUCKLING EFFECTS

Conference STRUCTURAL DYNAMICS: RECENT ADVANCES - PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE, VOLS I AND II · January 1, 1994 Link to item Cite

Effect Of Axial Load On Forced Vibrations Of Beams

Journal Article Journal of Sound and Vibration · December 22, 1993 The steady state linear response of beams subjected to a distributed, harmonically varying, transverse force is considered. A static axial load, either tensile or compressive, is also applied to the beam, and damping is included in the analysis. Four stand ... Full text Cite

On the stability of forced radial oscillations of an experimental spring pendulum

Journal Article American Society of Mechanical Engineers, Design Engineering Division (Publication) DE · December 1, 1993 The elastic pendulum is a 2-degree-of-freedom, non-linear device in which the pendulum bob may slide up and down the pendulum arm subject to the restoring force of a linear spring. In this study, radial motion (motion along the arm) is excited directly. Re ... Cite

Nonlinear behavior of low aspect ratio panels in subsonic flow: a preliminary study

Journal Article American Society of Mechanical Engineers, Aerospace Division (Publication) AD · December 1, 1993 We describe an experimental investigation into the nonlinear behavior of thin elastic panels in subsonic flow. Specially, an apparatus is detailed that supports a low aspect ratio panel by clamping it along the spanwise edges while leaving its leading and ... Cite

High-dimensional chaos can lead to weak turbulence

Journal Article Nonlinear Dynamics · December 1, 1993 One of the outstanding unresolved questions of nonlinear dynamics is the relationship between chaos and turbulence. This is a deep and difficult question, not the least reason being that the definitions of "chaos" and "turbulence" are not universally agree ... Full text Cite

Nonlinear coupled heave and roll oscillations of a ship in beam seas

Journal Article American Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC · December 1, 1993 The coupled (heave and roll) oscillations of a ship in transverse sinusoidal waves are considered. Extensive simulation studies show that resonance conditions may lead to large amplitude roll angles with the possibility of capsize. In contrast to much of t ... Cite

An empirical study of the stability of periodic motion in the forced spring-pendulum

Journal Article Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences · November 8, 1993 The elastic pendulum is a two-degree-of-freedom, nonlinear device in which the primary mass slides up and down the pendulum arm subject to the restoring force of a linear spring. In this study, radial motion (motion along the arm) is excited direct ... Full text Cite

An experimental study of an impacting pendulum

Journal Article Journal of Sound and Vibration · June 22, 1993 Full text Cite

On the stability of forced radial oscillations of an experimental spring pendulum

Conference Proceedings of the ASME Design Engineering Technical Conference · January 1, 1993 The elastic pendulum is a 2-degree-of-freedom, nonlinear device in which the pendulum bob may slide up and down the pendulum arm subject to the restoring force of a linear spring. In this study, radial motion (motion along the arm) is excited directly. Res ... Full text Cite

Dynamic characteristics of deteriorating engineering structures

Journal Article Applied Mechanics Reviews · 1993 The monitoring of energy production and distribution systems with a view to predicting their future performance and service life is a difficult but increasingly important exercise. Specific interest here concerns the behavior of aging offshore oil and gas ... Cite

Experimental mimicry of Duffing's equation

Journal Article Journal of Sound and Vibration · November 8, 1992 Extensive analytical and numerical investigations have focused on Duffing's equation. However, experimental work, in a mechanics context, has been limited to studying systems the stiffness characteristics of which can be approximated by a non-linear (cubic ... Full text Cite

Experimental evidence of diffusive dynamics and `random walking' in a simple deterministic mechanical system: the shaken pendulum

Journal Article Int. J. Bifurcation Chaos Appl. Sci. Eng. (Singapore) · 1992 An experimental model of a simple pendulum, harmonically shaken, displays chaotic dynamics. Moreover, in strongly excited chaotic regimes the time series of total angular displacement, which is rarely examined, wanders unboundedly, displaying a power spect ... Cite

Prediction of escape from a potential well under harmonic excitation

Journal Article International Journal of Non-Linear Mechanics · January 1, 1992 Non-linear dynamical systems are considered which are conservative except for the presence of viscous damping. The systems are initially at rest in a potential well. Harmonic excitation is applied, and approximate conditions for escape from the potential w ... Full text Cite

Chaotic rattling of a piecewise nonlinear oscillator

Journal Article American Society of Mechanical Engineers (Paper) · December 1, 1991 Loosely connected sructures may rattle: free play due to design tolerances, wear, or manufacturing error causes drastic force discontinuities (impacts) in periodically driven mechanisms. Previous investigators have examined impact oscillators described by ... Cite

A note on the escape from a potential well

Journal Article International Journal of Non-Linear Mechanics · January 1, 1991 This brief note compares analytical results pertaining to the escape from a potential well. The system studied is the classical Duffing's equation with positive linear and negative cubic stiffness terms, i.e. a softening spring characteristic. Under gradua ... Full text Cite

Catchment Regions of Multiple Dynamic Responses in Nonlinear Problems of Offshore Mechanics

Journal Article Journal of Offshore Mechanics and Arctic Engineering · January 1, 1990 Consideration of nonlinear effects in the dynamic analysis of offshore structures leads to complex phenomena even for relatively simple deterministic mathematical models. Nonlinearity in the stiffness or restoring force of a structure can be conveniently i ... Full text Cite

On spatial chaos, asymptotic modal analysis, and turbulence

Journal Article Journal of Applied Mechanics, Transactions ASME · January 1, 1990 Full text Cite

Use of frequency data to predict buckling

Journal Article Journal of Engineering Mechanics · January 1, 1990 Full text Cite

Approximate criterion for capsize based on deterministic dynamics

Journal Article Dynamics and Stability of Systems · January 1, 1989 An approach to studying the critical forcing parameters of an oscillator with a softening spring characteristic is developed. The harmonic response of the system is limited within a region of the phase plane, the boundary of which corresponds to a level of ... Full text Cite

Approximate criterion for capsize based on deterministic dynamics

Journal Article Dynamics and Stability of Systems · 1989 An approach to studying the critical forcing parameters of an oscillator with a softening spring characteristic is developed. The harmonic response of the system is limited within a region of the phase plane, the boundary of which corresponds to a level of ... Cite

On the harmonic response of an oscillator with unsymmetric restoring force

Journal Article Journal of Sound and Vibration · October 8, 1988 The approximate fundamental response of a driven mechanical oscillator with a quadratic stiffness characteristic is studied by using the method of harmonic balance.The accuracy of the periodic solutions based on first approximation theory, and their stabil ... Full text Cite

Spatial chaos and localization phenomena in nonlinear elasticity

Journal Article Physics Letters A · January 25, 1988 Classical static-dynamic analogies are invoked to demonstrate spatial chaos and localization of deformations in the elastica of a post-buckled strut. Some conjectures are then made relating homoclinic events in the dynamic analogy of a strut on a nonlinear ... Full text Cite

The onset of chaotic motions of a moored semi-submersible

Journal Article Journal of Offshore Mechanics and Arctic Engineering · January 1, 1988 This paper describes a combined numerical and geometric approach to study the dynamic behavior of a moored semi-submersible based on solutions of the nonlinear differential equation used to model the system. Complex features including competing steady stat ... Full text Cite

Complex dynamics and chaotic responses in the time domain simulations of a floating structure

Journal Article Ocean Engineering · January 1, 1988 The motion of a moored semi-submersible is modelled using a semi-empirical nonlinear ordinary differential equation. Time domain simulations, guided by the qualitative theory of dynamical systems, illustrate the extremely complex nature of typical response ... Full text Cite

On the computation of domains of attraction during the dynamic modelling of oscillating systems

Journal Article Applied Mathematical Modelling · January 1, 1988 A particular feature of nonlinear differential equations is that they may have competing steady-state solutions. This paper describes some multiple dynamic responses typically found when modelling nonlinear systems with particular reference to the catchmen ... Full text Cite

Catchment regions of multiple dynamic responses in nonlinear problems of offshore mechanics.

Journal Article IN: OMAE 1988 HOUSTON, PROC. 7TH INT. CONF. ON OFFSHORE MECHANICS AND ARCTIC ENGINEERING, (HOUSTON, U.S.A.: FEB. 7-12, 1988), · January 1, 1988 This paper concentrates on the computation of the domains of attraction or catchment regions using numerical techniques based on Poincare mapping ideas. The three specific examples illustrated are the roll motion of a ship, the oscillations of an articulat ... Cite

CATCHMENT REGIONS OF MULTIPLE DYNAMIC RESPONSES IN NONLINEAR PROBLEMS OF OFFSHORE MECHANICS.

Journal Article Proceedings of the International Offshore Mechanics and Arctic Engineering Symposium · January 1, 1988 Consideration of nonlinear effects in the dynamic analysis of offshore structures leads to complex phenomena even for relatively simple deterministic mathematical models. Nonlinearity in the stiffness or restoring force of a structure can be conveniently i ... Cite

Free vibrations of imperfect cantilever bars under self-weight loading

Journal Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science · January 1, 1987 This brief study examines the relationship between the natural frequency of small oscillations and the length of vertical cantilever struts in a gravitational field. The analysis uses a Rayleigh approach and includes post-buckled equilibrium states and emp ... Full text Cite

The onset of chaotic motions of a moored semi-submersible.

Journal Article IN: PROC. ASME SIXTH (1987) INT. OFFSHORE MECHANICS AND ARCTIC ENGINEERING SYMP., (HOUSTON, U.S.A.: MAR. 1-6, 1987) · January 1, 1987 This paper describes a combined numerical and geometric approach to study the dynamic behaviour of a moored semi-submersible based on solutions of the non-linear differential equation used to model the system. Complex features including competing steady st ... Cite

Predicting incipient jumps to resonance of compliant marine structures in an evolving sea-state

Journal Article Journal of Offshore Mechanics and Arctic Engineering · January 1, 1987 When monitoring the wave-driven motions of a compliant offshore facility, be it an articulated mooring tower or a vessel, the engineer would like to be able to predict, in real time, any incipient jump to resonance that might be imminent due to the slowly ... Full text Cite

FREE VIBRATIONS OF IMPERFECT CANTILEVER BARS UNDER SELF-WEIGHT LOADING.

Journal Article Proceedings of the Institution of Mechanical Engineers. Part C. Mechanical engineering science · 1987 This brief study examines the relationship between the natural frequency of small oscillations and the length of vertical cantilever struts in a gravitational field. The analysis uses a Rayleigh approach and includes post-buckled equilibrium states and emp ... Cite

The nonlinear rolling response of a vessel including chaotic motions leading to capsize in regular seas

Journal Article Applied Ocean Research · January 1, 1987 The rolling motion of a ship has been successfully modelled using a semi-empirical nonlinear differential equation by a number of researchers. Experimental data has been used to model nonlinear damping and righting lever characteristics and comparison with ... Full text Cite

ONSET OF CHAOTIC MOTIONS OF A MOORED SEMI-SUBMERSIBLE.

Journal Article Proceedings of the International Offshore Mechanics and Arctic Engineering Symposium · January 1, 1987 This paper describes a combined numerical and geometric approach to study the dynamic behaviour of a moored semi-submersible based on solutions of the nonlinear differential equation used to model the system. Complex features including competing steady-sta ... Cite

Parametric studies of the dynamic evolution through a fold

Journal Article Journal of Sound and Vibration · October 8, 1986 A brief study is presented of the dynamic behaviour of a system approaching a fold (also known in the literature as a limit point or saddle-node bifurcation). A study of the transient dynamics shows that it is possible to predict the incipient loss of stab ... Full text Cite

Postbuckling dynamics of struts as related to their loading devices

Journal Article Engineering Structures · January 1, 1986 This paper examines the linear dynamics of axially compressed pin-ended 'perfect' inextensional struts. Relationships are established between the natural frequencies of small oscillations about any equilibrium configuration (unbuckled and postbuckled) and ... Full text Cite

Predicting a jump to resonance using transient maps and beats

Journal Article International Journal of Non-Linear Mechanics · January 1, 1986 In this paper it is shown how the transient frequencies can be used to predict an incipient jump to resonance of a lightly damped non-linear oscillator. The appropriate frequency ω can be determined from the rotation number of a Poincaré map, or measured d ... Full text Cite

The dynamics of symmetric post-buckling

Journal Article International Journal of Mechanical Sciences · January 1, 1985 This work examines the relationship between natural frequency and compressive load for a conservative elastic mechanical system characterised by symmetric buckling. Application of some general theory shows that for a perfect system, exhibiting a stable-sym ... Full text Cite

The onset of chaotic motions of a moored semi-submersible.

Journal Article IN: PROC. ASME SIXTH (1987) INT. OFFSHORE MECHANICS AND ARCTIC ENGINEERING SYMP., (HOUSTON, U.S.A.: MAR. 1-6, 1987) This paper describes a combined numerical and geometric approach to study the dynamic behaviour of a moored semi-submersible based on solutions of the non-linear differential equation used to model the system. Complex features including competing steady st ... Cite