微型压电层合板结构的振动特性研究  

VIBRATION ANALYSIS OF THE MICRO PIEZOELECTRIC LAMINATED PLATE BASED ON THE STRAIN GRADIENT THEORY

作　　者：张霄峙[1] 陈丽华[1] 张伟 

机构地区：[1]北京工业大学机械工程与应用电子技术学院机械结构非线性振动与强度北京市重点实验室,北京100124

出　　处：《动力学与控制学报》2016年第5期429-437,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11472019)~~

摘　　要：从经典薄板理论出发,基于应变梯度理论,综合考虑尺寸效应和压电效应的影响,利用哈密顿原理建立了微型压电层合板结构的动力学模型及其边界条件.在选取符合其边界条件的模态函数后,利用Ritz法分别研究四边简支和悬臂条件下的微型压电层合板的振动特性,求解了前五阶固有频率并绘制了3D模态图.分析了微尺度带来的尺寸效应对于固有频率的影响,最后研究了外加电压对于系统固有频率的影响.The dynamic model of the micro laminated plates is developed with its boundary conditions through Hamilton~ principle, based on the classical thin plate theory and taken into consideration of the size effect caused by the micro scale using the strain gradient theory. After choosing the proper mode functions for the boundary conditions of both simple-support and cantilever, the first five orders of natural frequencies and the corresponding 3D mode shapes are achieved by the Ritz method, respectively. The effect of size effect on natural frequencies is studied. Eventually, the influence of the external voltage on the natural frequency is also examined.

关 键 词：应变梯度理论 RITZ法 微型压电层合板 固有频率 振型 

分 类 号：O327[理学—一般力学与力学基础]