具界面损伤压电智能层合板的非线性自由振动分析

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.     

Nonlinear free vibration analysis of piezoelastic laminated plates with interface damage

This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness ratio, and length-to-width ratio.