Optimal control of the dynamic response of an anisotropic plate with various boundary conditions

The problem of minimising the dynamic response of an anisotropic rectangular plate 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. This orientation angle has been taken as an optimisation design parameter. The control problem is formulated as an optimisation problem by using a performance index, which comprises a weight sum of the control objective and penalty function of the control force. The explicit solutions for the closed-loop distributed control function is obtained by means of Liapunov-Bellman theory. To assess the present solution, numerical results are presented to illustrate the effect of anisotropy ratio, orientation angle, aspect ratio and boundary conditions on the control process.