An analytical study on the nonlinear vibration of functionally graded beams
An analytical study on the nonlinear vibration of functionally graded beams
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DOI：
10.1007/s11012-009-9276-1
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发表时间：
2010-12-01
期刊：
影响因子：
2.7
通讯作者：
Kitipornchai, Sritawat
中科院分区：
文献类型：
--
作者：
Ke, Liao-Liang;Yang, Jie;Kitipornchai, Sritawat
本文基于欧拉-伯努利梁理论和冯卡门几何非线性，研究了功能梯度材料（FGM）梁的非线性振动。假设材料属性在厚度方向上遵循指数分布或幂律分布。伽辽金程序用于获得具有二次和三次非线性项的二阶非线性常方程。采用直接数值积分法和龙格-库塔法求解不同端部支撑的FGM梁的非线性振动响应。讨论了材料属性分布和端部支撑对 FGM 梁非线性动态行为的影响。研究发现，与均质梁不同，由于弯曲-拉伸耦合效应产生的二次非线性项，FGM 梁在正振幅和负振幅下表现出不同的振动行为。
Nonlinear vibration of beams made of functionally graded materials (FGMs) is studied in this paper based on Euler-Bernoulli beam theory and von Karman geometric nonlinearity. It is assumed that material properties follow either exponential or power law distributions through thickness direction. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. The direct numerical integration method and Runge-Kutta method are employed to find the nonlinear vibration response of FGM beams with different end supports. The effects of material property distribution and end supports on the nonlinear dynamic behavior of FGM beams are discussed. It is found that unlike homogeneous beams, FGM beams show different vibration behavior at positive and negative amplitudes due to the presence of quadratic nonlinear term arising from bending-stretching coupling effect.