OSCILLATIONS OF THE INTERACTING SYSTEMS DISTRIBUTED PARAMETERS

Motions of interacting oscillating systems are analyzed. These motions are governed by an initialboundary value problem for a system of hyperbolic equations with variable coefficients and nonhomogeneous boundary conditions of the first kind. A technique of constructing the forced motions of the system is presented. This technique is based on the solution of the corresponding vector boundary value problem of the Sturm-Liouville type for eigenvalues and eigenfunctions. An efficient numerical-analytical method of accelerated (quadratic) convergence is developed for high-accuracy construction of natural frequencies and modes of the system. The algorithm is tested by the numerical solution of some example problems. A modification of the method for wider classes of multidimensional oscillating systems with variable distributed parameters is suggested.