On the solution of an optimal stabilization problem of highly sloping shell

The optimal stabilization problem of the oscillations of an orthotropic rectangular highly sloping shell which is fixed at the edges by hinges has been considered. The shell becomes stable by means of supplementary control action on its upper surface. The problem has been solved by Fourier’s method, after which an infinite system of a second-order ordinary differential equations was received with separable variables. The optimal control action for each equation was formed.