Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force

Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

مقاله 6، دوره 5، شماره 2، آذر 2012، صفحه 61-72   

نوع مقاله: Persian

نویسندگان

A. Mamandi^{* 1}؛ M.H. Kargarnovin²

¹Assistant Professor, Mechanical and Aerospace Engineering, Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Tehran, Iran.

²Professor, Mechanical Engineering, Department of Mechanical Engineering, Sharif university of Technology, Tehran, Iran

چکیده

This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time Scales. Under three to-one-internal resonance condition applying nonlinear normal modes the steady state stability analysis of the beam’s vibrations is performed. Then the effect of changing the value of different parameters on the beam’s dynamic response and the steady state stability analysis is investigated.

کلیدواژه‌ها

Nonlinear vibrations؛ Euler-Bernoulli beam؛ Nonlinear elastic foundation؛ The 3:1

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