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Nonlinear Responses of Inextensible Cantilever and Free-Free Beams Undergoing Large Deflections

Publication ,  Journal Article
McHugh, K; Dowell, E
Published in: Journal of Applied Mechanics, Transactions ASME
May 1, 2018

A theoretical and computational model has been developed for the nonlinear motion of an inextensible beam undergoing large deflections for cantilevered and free-free boundary conditions. The inextensibility condition was enforced through a Lagrange multiplier which acted as a constraint force. The Rayleigh-Ritz method was used by expanding the deflections and the constraint force in modal series. Lagrange's equations were used to derive the equations of motion of the system, and a fourth-order Runge-Kutta solver was used to solve them. Comparisons for the cantilevered beam were drawn to experimental and computational results previously published and show good agreement for responses to both static and dynamic point forces. Some physical insights into the cantilevered beam response at the first and second resonant modes were obtained. The free-free beam condition was investigated at the first and third resonant modes, and the nonlinearity (primarily inertia) was shown to shift the resonant frequency significantly from the linear natural frequency and lead to hysteresis in both modes.

Duke Scholars

Published In

Journal of Applied Mechanics, Transactions ASME

DOI

EISSN

1528-9036

ISSN

0021-8936

Publication Date

May 1, 2018

Volume

85

Issue

5

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 4001 Aerospace engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0901 Aerospace Engineering
 

Citation

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McHugh, K., & Dowell, E. (2018). Nonlinear Responses of Inextensible Cantilever and Free-Free Beams Undergoing Large Deflections. Journal of Applied Mechanics, Transactions ASME, 85(5). https://doi.org/10.1115/1.4039478
McHugh, K., and E. Dowell. “Nonlinear Responses of Inextensible Cantilever and Free-Free Beams Undergoing Large Deflections.” Journal of Applied Mechanics, Transactions ASME 85, no. 5 (May 1, 2018). https://doi.org/10.1115/1.4039478.
McHugh K, Dowell E. Nonlinear Responses of Inextensible Cantilever and Free-Free Beams Undergoing Large Deflections. Journal of Applied Mechanics, Transactions ASME. 2018 May 1;85(5).
McHugh, K., and E. Dowell. “Nonlinear Responses of Inextensible Cantilever and Free-Free Beams Undergoing Large Deflections.” Journal of Applied Mechanics, Transactions ASME, vol. 85, no. 5, May 2018. Scopus, doi:10.1115/1.4039478.
McHugh K, Dowell E. Nonlinear Responses of Inextensible Cantilever and Free-Free Beams Undergoing Large Deflections. Journal of Applied Mechanics, Transactions ASME. 2018 May 1;85(5).

Published In

Journal of Applied Mechanics, Transactions ASME

DOI

EISSN

1528-9036

ISSN

0021-8936

Publication Date

May 1, 2018

Volume

85

Issue

5

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 4001 Aerospace engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0901 Aerospace Engineering