压电层合圆杆中的几何非线性波  

Geometrically Nonlinear Waves in Layered Piezoelectric rod

作　　者：邓庆田[1] 罗松南[1] 彭亮[1] 王立喆[1] 

机构地区：[1]湖南大学,长沙410082

出　　处：《应用力学学报》2009年第3期519-523,共5页Chinese Journal of Applied Mechanics

基　　金：高等学校博士学科点专项科研基金(20050532002);湖南省自然科学基金(06JJ2058)

摘　　要：利用有限变形理论,导出了描述压电层合杆中几何非线性波的传播方程。在端部作用有限振幅位移函数的边界条件下,用逐步近似法对位移函数进行了假设,推导出了一维压电杆中位移函数与电势函数之间的关系式,并应用变动参数法求解了变换得到的非齐次波动方程,得到了位移和电势的响应。数值分析表明:初始频率的改变对位移和电势的非线性特性影响不大;而初始振幅的增加会使非线性波形畸变特性明显增强。The nonlinear equation of wave propagation in layered piezoelectric rod was derived according to finite deformation theory. Considering the boundary condition of finite displacement function acting on the end of the rod, the approximation is used to describe the displacement function step by step and the relation between displacement and electric displacement in one dimensional rod is obtained. The transformed inhomogeneous wave equation is solved parameter perturbation method, and the responses of displacement and electric potential are obtained. The numerical results show that the effects of initial frequency on the nonlinear characteristics of displacement and electric potential are not significant and aberration characteristics of nonlinear wave shape become more obvious with increasing initial amplitude.

关 键 词：有限变形 压电层合杆 非线性波 

分 类 号：O347.41[理学—固体力学]