Optimal Design and Control for Minimizing the Dynamic Response of an Anisotropic Plate with Variable Thickness

Abstract

The problem of minimizing the dynamic response of an anisotropic rectangular plate of variable thickness with minimum possible expenditure of force is presented for various cases of boundary conditions. The plate has a principal direction of anisotropy rotated at an arbitrary angle relative to the coordinate axes. The orientation angle and thickness parameter have been taken as optimization design parameters. The control problem is formulated as an optimization problem by using a performance index, which comprises a weight sum of the control objective and penalty function of the control force. Explicit solutions for the surface shape, the total elastic energy of the plate and the closed-loop distributed control force are obtained by means of Liapunov-Bellman theory. To assess the present solutions, numerical results are presented to illustrate the effect of various thickness parameters, orientation angles, aspect ratios and boundary conditions on the control process.