轴对称压电圆板的非线性动力响应  

Nonlinear Dynamic Response of Transversely Isotropic Axisymmetric Piezoelectric Plate

作　　者：傅衣铭[1] 张普[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467-472,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10572049)

摘　　要：基于Von Kármán板理论和压电材料力学,考虑横向剪切变形,建立了轴对称压电圆板的非线性运动方程,提出了相应的力学与电学边界条件。求解时,首先应用Galerkin方法,将非线性偏微分运动方程转化为仅含时间变量的非线性常微分方程。然后,应用Newmark-β方法将时间函数离散,整个问题应用Newton迭代法求解。算例中,求得了压电圆板线性振动基频,验证了方程和求解方法的可靠性,讨论了压电效应、几何非线性、结构尺寸、力学和电学荷载等因素对板非线性动力响应的影响。Following the Von Kármán’s plate theory and the piezoelectric material mechanics, considering the transverse shear deformation, the nonlinear dynamic equations of transversely isotropic axisymmetric piezoelectric plates and the corresponding boundary conditions are derived. And these nonlinear motion equations are solved with the Galerkin method by Newton iteration. The resonant frequencies to the piezoelectric circular plates are represented. The factors affecting nonlinear dynamic response, such as the piezoelectric effect, geometric nonlinearity, plate size, mechanical and electrical loads, are discussed.

关 键 词：轴对称压电圆板 横观各向同性 非线性动力响应 

分 类 号：O344[理学—固体力学]