有限长压电层合简支板自由振动的三维精确解

基于三维弹性理论和压电理论，导出了有限长矩形压电层合简支板的动力学方程及相应的边界条件，给出了一种求解压电层合板自由振动三维精确解的方法；分析了正、逆向压电效应对层合板振动频率的影响．本文所述的方法和结果对于求解其他三维动态问题，验证、比较其他简化模型、有限元计算结果以及工程应用都有指导意义．

THREE DIMENSIONAL EXACT ANALYSIS FOR FREE VIBRATION OF SIMPLY SUPPORTED PIEZOELECTRIC COMPOSITE LAMINATES 1)

In recent years, piezoelectric materials have been widely used as sensors and actuators in structural shape control, vibration suppression,noise attenuation and damage monitoring. Exact study can provide better understanding of the mechanical and electric behaviors of piezoelectric structures. An analysis for the three dimensional solutions of piezoelectric laminated plates has been conducted by several researchers. The exact solution methods, used in the papers before, mostly follow the strategy of Pagano. This approach has been proven effective to static problems, but it is very complicated for the three dimension dynamic problems of finite long piezoelectric laminated plates. In this paper, free vibration of a finite long simply supported rectangular piezoelectric composite laminates has been studied on the basis of three dimensional linear elasticity and piezoelectricity without any simplification. The laminates can be composed of an arbitrary number of elastic and piezoelectric layers of orthotropic materials. The solution to the derived governing differential equations is obtained by the power series expansion method. The results show that the present approach is more effective than Pagan method mentioned above. Different boundary conditions are investigated to model the direct and inverse piezoelectric effects. The natural frequencies of free vibration are investigated, also. The obtained results can not only be used to assess various approximate theories, but also enhance the understanding of the dynamic behavior of piezoelectric structures.