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

Journal of Solid Mechanics

مقاله 4، دوره 1، شماره 1، خرداد 2009، صفحه 29-36   

نوع مقاله: Research Paper

نویسندگان

M.T Ahmadian^{* 1}؛ M Mojahedi²؛ H Moeenfard²

¹Center of Excellence in Design, Robotics and Automation, School of Mechanical Engineering, Sharif University of Technology

²School of Mechanical Engineering, Sharif University of Technology

چکیده

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.

کلیدواژه‌ها

Free vibration؛ Nonlinear beam؛ Homotopy Perturbation method؛ Lindstedt-Poincare method؛ Axial load

مراجع

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