Introduction

The theoretical model for studying dynamic response of composite plates are available in literature, however, analytical solutions are obtainable only for simple geometric and boundary conditions due to the difficulties in solving partial differential equations of motion for arbitrary initial and boundary conditions. Finite Element technique is used often to deal with complex geometry and boundary conditions. However, instead of using 3-D elements like hexahedral or brick element, one can use 2-D high precision elements (generally 9-12 degrees of freedom per node) for solving the plate problems. The advantage of using 2-D high precision element is that it is simpler than 3-D element and also it is computationally less intensive for dynamic analysis of plate structure. These elements are used for modal analysis (eigen frequencies and mode shape) of passive plate structures. But the refinement of mesh for accurate estimation of modal frequencies and shape is limited due to computational burden generated by large degrees of freedom.

To reduce the computational burden of numerical integration, symbolic manipulation has been carried out by using MATHEMATICA. The closed form expressions of stiffness and mass matrices are used wherever required to reduce the computational burden. Static condensation is used to further reduce the size of the eigen value problem.