Nonlinear Vibration Analysis of the Beam Carrying a Moving Mass Using Modified Homotopy

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  • M Poorjamshidian1,
  • J Sheikhi2,
  • S Mahjoub-Moghadas*1,
  • M Nakhaie1,
  1. Department of Mechanical Engineering, Imam Hossein University
  2. Civil Engineering, Imam Hossein University

Revised: 2014-07-21

Accepted: 2014-09-24

Published in Issue 2014-12-30

How to Cite

Poorjamshidian, M., Sheikhi, J., Mahjoub-Moghadas, S., & Nakhaie, M. (2014). Nonlinear Vibration Analysis of the Beam Carrying a Moving Mass Using Modified Homotopy. Journal of Solid Mechanics, 6(5), 389-396. https://oiccpress.com/jsm/article/view/12476

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Abstract

In the present study, the analysis of nonlinear vibration for a simply-supported flexible beam with a constant velocity carrying a moving mass is studied. The amplitude of vibration assumed high and its deformation rate is assumed slow. Due to the high amplitude of vibrations, stretching is created in mid-plane, resulting in, the nonlinear strain-displacement relations is obtained, Thus, Nonlinear terms governing the vibrations equation is revealed. Modified homotopy equation is employed for solving the motion equations. The results shown that this method has high accuracy. In the following, analytical expressions for nonlinear natural frequencies of the beams have been achieved. Parametric studies indicated that, due to increasing of the velocity concentrated mass, the nonlinear vibration frequency is reduced. On the other hand, whatever the mass moves into the middle of beam, beam frequency decreases.
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