强电场作用下简支压电层合梁的非线性动力分析  

THE NONLINEAR DYNAMIC ANALYSIS OF SIMPLY SUPPORTED PIEZOELECTRIC LAMINATED BEAM UNDER STRONG ELECTRIC FIELD

作　　者：姚林泉[1] 王伟[2] 

机构地区：[1]苏州大学数学科学学院,苏州215006 [2]南京铁道职业技术学院苏州校区,苏州215031

出　　处：《固体力学学报》2008年第4期341-347,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10672111);江苏省自然科学基金(BK2006725);暨南大学重点实验室开放课题基金资助

摘　　要：研究可移简支压电弯曲层合梁在交变强电场作用下的非线性动力学行为.考虑材料的电致伸缩和电致弹性压电效应以及几何非线性导出压电层合梁的数学模型.导出简支压电执行器的弯曲振动控制方程,并得到它的刚度是关于时间的慢变函数关系.利用非定常振动的渐近理论和Galerkin方法对具有慢变系数的非线性动力方程进行求解,得到了可移简支压电层合梁的动力特征.最后得到了可移压电简支梁的共振频率、固有频率和电场频率三者之间的变化关系以及谐振幅度与作用电场强度的关系.Nonlinear dynamic characteristics of slip simply supported piezoelectric bending actuators under strong electric field is studied. Considering nonlinear geometrical relationship and nonlinear piezoelectric effect of the electrostriction and electroelasticity,the math model and vibration governing equations of piezoelectric laminated beam are derived. And, it is obtained that the stiffness is slowly varying function with regard to time. Using the asymptotic theory of nonstationary vibrations and Galerkin method,the nonlinear dynamic equation with slowly varying coefficient is solved. The dynamic characteristics of the lami- nated beam are obtained. Finally the relations among the resonant frequency, fundamental natural frequency and electric frequency are obtained. The relations between the resonance amplitude of max deflections for the piezoelectric actuators and the electric field are also gotten.

关 键 词：压电结构 强电场 层合梁 渐进理论 非线性动力分析 

分 类 号：O322[理学—一般力学与力学基础]