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Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force

Publication ,  Journal Article
McHugh, KA; Dowell, EH
Published in: Journal of Computational and Nonlinear Dynamics
March 1, 2019

The dynamic stability of a cantilevered beam actuated by a nonconservative follower force has previously been studied for its interesting dynamical properties and its applications to engineering designs such as thrusters. However, most of the literature considers a linear model. A modest number of papers consider a nonlinear model. Here, a system of nonlinear equations is derived from a new energy approach for an inextensible cantilevered beam with a follower force acting upon it. The equations are solved in time, and the agreement is shown with published results for the critical force including the effects of damping (as determined by a linear model). This model readily allows the determination of both in-plane and out-of-plane deflections as well as the constraint force. With this novel transparency into the system dynamics, the nonlinear postcritical limit cycle oscillations (LCO) are studied including a concentration on the force which enforces the inextensibility constraint.

Duke Scholars

Published In

Journal of Computational and Nonlinear Dynamics

DOI

EISSN

1555-1423

ISSN

1555-1415

Publication Date

March 1, 2019

Volume

14

Issue

3

Related Subject Headings

  • Acoustics
  • 4903 Numerical and computational mathematics
  • 4017 Mechanical engineering
  • 0913 Mechanical Engineering
  • 0103 Numerical and Computational Mathematics
 

Citation

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McHugh, K. A., & Dowell, E. H. (2019). Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force. Journal of Computational and Nonlinear Dynamics, 14(3). https://doi.org/10.1115/1.4042324
McHugh, K. A., and E. H. Dowell. “Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force.” Journal of Computational and Nonlinear Dynamics 14, no. 3 (March 1, 2019). https://doi.org/10.1115/1.4042324.
McHugh KA, Dowell EH. Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force. Journal of Computational and Nonlinear Dynamics. 2019 Mar 1;14(3).
McHugh, K. A., and E. H. Dowell. “Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force.” Journal of Computational and Nonlinear Dynamics, vol. 14, no. 3, Mar. 2019. Scopus, doi:10.1115/1.4042324.
McHugh KA, Dowell EH. Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force. Journal of Computational and Nonlinear Dynamics. 2019 Mar 1;14(3).

Published In

Journal of Computational and Nonlinear Dynamics

DOI

EISSN

1555-1423

ISSN

1555-1415

Publication Date

March 1, 2019

Volume

14

Issue

3

Related Subject Headings

  • Acoustics
  • 4903 Numerical and computational mathematics
  • 4017 Mechanical engineering
  • 0913 Mechanical Engineering
  • 0103 Numerical and Computational Mathematics