Optimal shapes of PZT actuators for laminated structures subjected to displacement or eigenfrequency constraints

In this paper, dynamics, electromechanical couplings, and control of piezoelectric laminated cylindrical shells and rectangular plates are investigated. It is assumed that the piezoelectric layers are distributed on the top and bottom surfaces of the structures. First of all the governing equations and boundary conditions including elastic and piezoelectric couplings are formulated and solutions are derived. Then control of the plate/shells deflections and natural frequencies using high control voltages are studied in order to optimize the structural response. The present formulation of optimal design introduces boundaries of piezoelectric patches as new class of design variables. In addition, classical design variables in the form of ply orientation angles of orthotropic layers are also taken into account. For the actuator/actuator configuration, it was shown that the piezoelectric actuators can significantly reduce deformations/eigenfrequencies of the composite plate. Those effects were dependent on the value of the applied voltage. It was demonstrated that the proper choice of the actuator area is more efficient in reducing deflections/eigenfrequencies. The accuracy of optimal design are verified both with the aid of the FE package ABAQUS and using the standard Rayleigh–Ritz method. The results concerning active vibration control for axisymmetric cylindrical shells are also discussed.