An analysis for the three-dimensional solutions of piezoelectric laminated plates has been conducted by several researchers. For example, Ray and Rao [1] and Ray and Samanta [2] have studied the exact static analysis of piezoelectric plates under cylindrical bending and finite dimension piezoelectric plates. Free vibration exact solutions of infinite-length piezoelectric plates under cylindrical bending were studied by Heyliger and Brooks [3]. Recently, Batra and Liang [4] have studied the forced vibration of piezoelectric laminates using the three-dimensional elasticity theory, but the piezoelectric layers have been modelled as thin surface films in this paper, so it is not strictly speaking a three-dimensional solution.
The three-dimensional methods used in the papers mentioned above mostly follow the strategy of Pagano [5,6]. This method has proved effective for static problems, but it is very complicated for the three-dimensional dynamic problems of piezoelectric laminated plates of finite-length. Laura [7] used some simple polynomial approximations and a variational approach to study the piezoelectric flexural plate hydrophone. In this paper, free vibration of a finite length rectangular piezoelectric composite laminates has been investigated based on 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 of the derived governing differential equations is obtained using the power series expansion method. The results show that the method is more effective than the Pagano's method mentioned above. Different boundary conditions are studied to model the direct and inverse piezoelectric effects. The natural frequencies and the shapes of modal distribution for free vibration are investigated. The results obtained can be used not only to assess various approximate theories, but also enhance the understanding of the dynamic behavior of piezoelectric structures.