THE OPTIMAL CONTROL OF MOTION OF ELASTIC SYSTEMS

Vibration of a rectangular membrane with substantially varying surface density is considered. An efficient accelerated convergence algorithm is developed for solving the corresponding self-adjoint boundaryvalue problem to determine eigenvalues and eigenfunctions in the cases admitting the separation of the spatial variables. The results are generalized to the cases of nonuniform surface tension of the membrane and the interaction of the membrane with an external elastic medium. An algorithm taking into account perturbations is suggested. To illustrate the efficiency of the accelerated convergence method, we present the computational results for some specific distributions of the membrane mass.