Introduction

The active control of dynamic structural systems has been extensively studied for last 30 years. Leipholz and others have obtained closed-form solutions for vibration in beams and plates subjected to a distributed control force. The analytical solutions have gained renewed and practical utility with the advent of smart materials as truly distributed sensing and actuation layers could be developed from these materials. To site a few important milestones in this direction, Burke and Hubbard have designed distributed controller for vibration suppression in cantilever beam using PVDF film. Crawley and Rogers have brought out the role of important parameters like thickness ratio of smart and passive elements, the distance of smart actuating layer from the neutral axis etc. required for efficient vibration control. All these analysis are performed on Euler Bernoulli beam model. Reddy et al [1991] have extended it to models in which shear deformation and rotary inertia are included. Finite elements are used to bring out the importance of higher order terms on vibration suppression. Cowper has earlier developed a triangular thin plate element with transverse deflection and their first and second derivatives as DOF and the displacement function in the form of constrained quintic polynomial. Finite element proposed by Reddy et al [1991] is based on this Cowper element. Tzou have developed iso-parametric finite element for the analysis of smart plates and shells.