Skip to main content
Journal cover image

Iterative techniques for analyzing nonlinear vibrating dynamical systems in the frequency domain

Publication ,  Journal Article
Culver, D; Dowell, E
Published in: Nonlinear Dynamics
March 1, 2018

The nonlinear response of prototypical structures experiencing harmonic excitation is studied using novel techniques called iterative harmonic analysis (IHA) and iterative modal analysis (IMA). First, a simple damped oscillator with a cubic hardening stiffness nonlinearity is studied, and IHA is used in this single-degree-of-freedom system. In this first section, a high-order harmonic balance is applied, and IHA is employed in order to find the amplitude coefficients for different harmonics and their codependence. Additionally, a set of nested sums are identified that describe the harmonic coupling explicitly. Secondly, a pinned–pinned nonlinear beam of rectangular cross-section is studied, and IMA is applied to find the amplitude coefficients for different modes and their codependence. The nonlinearity is introduced through the membrane effect, where axial strain due to transverse deflection becomes a significant contributor to the system behavior. Typical frequency-domain methods cannot be easily applied to these systems as the solutions of the differential equations lead to intricate coupling between coefficients of the solution, and no analytical expression exists for those coefficients. Based upon these examples, other nonlinear systems may also be considered in future work using either a modal-based or finite element model. Finally, the advantages of the new method (reduced computational cost) as well as the limitations (effectively the same as those of an nth-order harmonic balance) are emphasized.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

EISSN

1573-269X

ISSN

0924-090X

Publication Date

March 1, 2018

Volume

91

Issue

4

Start / End Page

2113 / 2140

Related Subject Headings

  • Acoustics
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Culver, D., & Dowell, E. (2018). Iterative techniques for analyzing nonlinear vibrating dynamical systems in the frequency domain. Nonlinear Dynamics, 91(4), 2113–2140. https://doi.org/10.1007/s11071-017-4005-0
Culver, D., and E. Dowell. “Iterative techniques for analyzing nonlinear vibrating dynamical systems in the frequency domain.” Nonlinear Dynamics 91, no. 4 (March 1, 2018): 2113–40. https://doi.org/10.1007/s11071-017-4005-0.
Culver D, Dowell E. Iterative techniques for analyzing nonlinear vibrating dynamical systems in the frequency domain. Nonlinear Dynamics. 2018 Mar 1;91(4):2113–40.
Culver, D., and E. Dowell. “Iterative techniques for analyzing nonlinear vibrating dynamical systems in the frequency domain.” Nonlinear Dynamics, vol. 91, no. 4, Mar. 2018, pp. 2113–40. Scopus, doi:10.1007/s11071-017-4005-0.
Culver D, Dowell E. Iterative techniques for analyzing nonlinear vibrating dynamical systems in the frequency domain. Nonlinear Dynamics. 2018 Mar 1;91(4):2113–2140.
Journal cover image

Published In

Nonlinear Dynamics

DOI

EISSN

1573-269X

ISSN

0924-090X

Publication Date

March 1, 2018

Volume

91

Issue

4

Start / End Page

2113 / 2140

Related Subject Headings

  • Acoustics
  • 09 Engineering
  • 01 Mathematical Sciences