受电压激励的复合材料悬臂板的分叉分析

摘要

以飞行器机翼作为工程背景,将机翼简化为悬臂板模型,研究了受横向电压激励、基础激励、面内激励联合作用下复合材料层合悬臂板的非线性动力学问题.首先建立其动力学模型,考虑冯-卡门大变形理论,利用Hamilton原理建立复合材料层合悬臂板的非线性动力学方程;选择符合边界条件的模态函数,利用Galerkin方法对系统进行四阶离散,得到四自由度非线性常微分方程;代入系统实际物理参数,应用MATLAB软件数值模拟得到系统振动幅值随电压激励变化的分叉图,由图可知,电压激励使系统从混沌运动变为倍周期运动,降低了系统振幅,保持系统的稳定.%The bifurcations of a composite laminated cantilevered plate are studied, which is simultaneously forced by the voltage, base and in-plane excitations. The nonlinear partial differential governing equations of the system motion are established by using the Hamilton's principle. The Galerkin approach is used to discretize the partial differential equations to the ordinary differential equations with four degree of freedom. Numerical simulations are also carried out to investigate the effects of the voltage excitation on the steady-state responses of the cantilevered piezoelectric plate. The bifurcation diagram of the system is then obtained. The system motions can be shown as follows: the chaotic motion to the multiple periodic motion. The results show that the amplitude of the system can reduce effectively and keep the stability by adjusting the voltage excitation.