14 th Annual (International) Mechanical Engineering Conference – May 2006 Isfahan University of Technology, Isfahan, Iran THEORETICAL ANALYSIS OF PIEZOELECTRIC HYBRID PLATES M. Tahani 1 , A.M. Naserian-Nik 2 Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran mtahani@ferdowsi.um.ac.ir Abstract An analytical method is devlopteded to analyze piezoelectric hybrid laminated composite plates with arbitrary lamination and boundary conditions subjected to electromechanical loads. The method is based on separation of spatial variables of displacement field components. Within the displacement field of a first-order shear deformation plate theory and using the principle of minimum total potential energy, two systems of coupled ordinary differential equations with constant coefficients are obtained. These equations may be solved analytically with the help of state-space approach. Also a Levy-type solution is employed for verification the validity and accuracy of the proposed method. It is seen that the present results have close agreements with those obtained by Levy-type method. Keywords: Analytical solution- Piezoelectric- Laminated plate- Boundary conditions. Introduction Hybrid composite plates consisting of fiber- reinforced and piezoelectric layers are important components of smart or intelligent structures2([1]- [3]). For the analytical solution of laminated composite plates, Pagano [4] firstly presented the exact solution of the laminated plate with simply supppted edges. Ray et al. [5,6] and Brooks and Heyliger [7] extended this methodology to develop a three-dimensional, exact, plane strain piezoelastic solution for simply supported single-layer and laminated piezoelectric plates with distributed and patched actuators. Three-dimensional, exact piezoelastic solutions for simply supported rectangular plates coupled to distributed sensors and actuators have been presented by Ray et al. [8], Heyliger [9,10] and Lee and Jiang [11]. Tauchert [12] applied the classical lamination theory (CLT) to obtain an analytical solution for a smart composite plate. Jonnalagadda et al. [13] employed first-order shear deformation theory (FSDT) to solve the piezothermoelastic response of hybrid plates with a known thermoelectric field. They presented a 1-Assistant professor 2- M.S. student Navier-type solution for rectangular plates with all edges simply supported, and a finite element solution by using nine-noded Lagrangian elements, for plates with various edge support conditions. Huang and wu [14] have given a coupled, first-order shear deformation theory for the piezoelectric response of hybrid plates and a post-processing technique to obtain the accurate response of transverse stresses, transverse displacement, electric potential and electric displacement. A Levy-type solution for the bending of cross-ply, hybrid, rectangular plates with two opposite edges simply supported by using a mixed formulation of first- order shear deformation and classical lamination theories was presented by Kapuria et al. [15]. Senthil and Batra [16] provided the analytical solutions of piezoelectric laminated plates via Eshelby–Stroh formalism. It can be seen most of avaiable analytical solution techniques for deformation of piezoelectric plates are restricted to whose edges are simply supported. Here, a new analytical method is developed to analyze laminated composite plates with arbitrary lamination and boundary conditions subjected to mechanical and electrical loads. Using the principle of minimum total potential energy and first-order shear deformation theory simultaneously, two