About one problem of the optimal stabilization of rectangular orthotropic plate vibrations

It is studied the optimal stabilization problem for thin, homogeneus, orthotropic rectangular hinged-supported plate vibrations, having constant thickness. On the plate edges is acted an uniformly distributed force. The problem is solved by means of Fourie method and the infinite system of ordinary differential equations are obtained with separable variables. The optimal control reaction is obtained which stabilised the motion, under condition of minimal value of total energy.