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Nonlinear Vibration and Buckling Analysis of Beams Using Homotopy Perturbation Method

[+] Author Affiliations
Mahdi Mojahedi, Hamid Moeenfard, Mohammad Taghi Ahmadian

Sharif University of Technology, Tehran, Iran

Paper No. IMECE2010-39592, pp. 463-469; 7 pages
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 10: Micro and Nano Systems
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4447-2
  • Copyright © 2010 by ASME


In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational and buckling analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin’s decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies and critical axial loads of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions are valid for a wide range of vibration amplitudes. Comparing the semi-analytic solutions with numerical results, presented in the literature, indicates good agreement. The results signify the fact that HPM is a powerful tool for analyzing dynamic and vibrational behavior of structures analytically.

Copyright © 2010 by ASME



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