FGM梁考虑纵向振动的动力学分析

基于Euler-Bernoulli梁理论并且考虑几何非线性和纵向振动的影响,研究了纵向和横向振动的FGM梁非线性动力学问题。假设材料的性质沿梁的厚度方向按幂指函数形式连续变化,利用Hamilton变分原理建立了梁的非线性动力学控制微分方程。采用打靶法对方程进行数值求解,结果表明:横向振动的过程中存在着纵向振动,且纵向振动削弱了横向振动,但其影响较小。在此基础上分析了考虑纵向振动时梯度指数、长细比、载荷等对梁的动力响应特性的影响。

Dynamic Analysis of FGM Beam Considering Longitudinal Vibration

Based on Euler-Bernoulli beam theory and considering the effects of geometric nonlinearity and longitudinal vibration,the nonlinear dynamic problems of FGM beams with longitudinal and transverse vi-brations were studied.The material properties were assumed to vary continuously along the thickness direc-tion of the beam in the form of power exponential function,the nonlinear dynamic governing differential e-quation of the beam was established by using the Hamilton variational principle.The numerical solution of the equation was carried out by shooting method,the results showed that there existed longitudinal vibra-tion in the process of transverse vibration,and the longitudinal vibration weakened the transverse vibra-tion,but its impact was small.On this basis,considering longitudinal vibration,the influence of the gradient index,slenderness ratio and load on the dynamic response features of the beam was analyzed.