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Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria

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submitted on 2023-11-07, 06:30 and posted on 2023-11-07, 11:57 authored by Raed Ali Mara'Beh, Ahmad Y. Al-Dweik, B.S. Yilbas, M. Sunar

A mechanical system, in general, undergoes vibrational motion when the system is subjected to a tension or an external force. One of the examples of such a system is a cantilever beam when it is exposed to a bending action. When the tension is released, the cantilever beam suffers from the oscillations until the strain energy is totally released through the damping characteristics of the cantilever beam. Depending on the stiffness and damping factors of the beam, the vibrational motion can be non-linear; in which case, the analytical solution becomes challenging formulating the flexural characteristics of the beam. Although numerical solution for the non-linear problem is possible, the analytical solution provides useful information between the mechanical response and the cantilever beam characteristics. In the present study, the analytical solution of the non-linear equations governing the motion of the cantilever beam is presented. The governing equation is linearized incorporating the Lie-Tresse linearization method. The closed form solution for the displacement of the cantilever beam is reduced to a linear solution after introducing the appropriate beam characteristics. The dynamic behavior of the flexural motion due to non-linear and linear cantilever beams are compared.

Other Information

Published in: Heliyon
License: http://creativecommons.org/licenses/by/4.0/
See article on publisher's website: https://dx.doi.org/10.1016/j.heliyon.2022.e11673

Funding

Open Access funding provided by the Qatar National Library

History

Language

  • English

Publisher

Cell Press

Publication Year

  • 2022

License statement

This Item is licensed under the Creative Commons Attribution 4.0 International License

Institution affiliated with

  • Qatar University
  • Deanship of General Studies - QU
  • College of Arts and Sciences - QU