Free Vibration Analysis of a Nonlinear Beam Using Homotopy and Modified Lindstedt-Poincare Methods

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  • M.T Ahmadian*1,
  • M Mojahedi2,
  • H Moeenfard2,
  1. Center of Excellence in Design, Robotics and Automation, School of Mechanical Engineering, Sharif University of Technology
  2. School of Mechanical Engineering, Sharif University of Technology

Revised: 2009-03-20

Accepted: 2009-04-24

Published in Issue 2009-04-30

How to Cite

Ahmadian, M., Mojahedi, M., & Moeenfard, H. (2009). Free Vibration Analysis of a Nonlinear Beam Using Homotopy and Modified Lindstedt-Poincare Methods. Journal of Solid Mechanics, 1(1), 29-36. https://oiccpress.com/jsm/article/view/12004

PDF views: 164

Abstract

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational 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 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.
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