具界面损伤压电智能层合板的非线性自由振动分析  

Non-Linear Free Vibration Analysis of Piezoelastic Laminated Plates With Interfacial Damage

作　　者：傅衣铭[1] 李升[1] 姜叶洁[1] 

机构地区：[1]湖南大学力学与航空航天学院,长沙410082

出　　处：《应用数学和力学》2009年第2期127-141,共15页Applied Mathematics and Mechanics

基　　金：国家自然科学基金重点资助项目(10572049)

摘　　要：基于广义6自由度板理论、应变等效原理和Hamilton变分原理,通过引入三维弹性平衡方程和静电平衡方程的通解来构造满足界面间力电耦合关系和各类连续条件的位移、电势分布形函数,建立了具铺设层内和层间界面处损伤效应的压电智能层合板的非线性运动控制方程组,并运用Galerkin方法进行求解.数值算例中,分别讨论了,不同损伤程度、压电层厚度、厚跨比及长宽比对四边简支非理想界面压电智能层合板线性自由振动频率和非线性幅频响应曲线的影响.A nonlinear model for piezoelastic laminated plates containing the damage effect of the intra-layers and inter-laminar interface is presented, and the discontinuity of displacement and electric potential on the interfaces were depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect were derived. Then, using the Galerldn method, a mathematical solution was presented. In numerical results, the effects of different damage models, the thickness of piezoelectric layer, the side-to-thickness ratio and the length-to-width ratio on the natural frequencies and non-linear amplitude-frequency response characteristics of the simply-supported piezoelastic laminated plates with inteffacial imperfections were discussed.

关 键 词：压电智能层合板 非线性振动分析 界面损伤 损伤演化 GALERKIN方法 

分 类 号：O343[理学—固体力学]