Using the Kantorovich–Galerkin approach to analyze the resonant characteristics of damped systems

Abstract

The Kantorovich–Galerkin method is extended to solve a wider range of problems related to oscillations of mechanical systems with moving boundaries. We take bending rigidity, environmental resistance, and foundation rigidity into account. The main attention is paid to studying the resonance characteristics of the solutions obtained. Quadrature expressions for the amplitudes of dynamical modes of different orders are derived. As an illustration, the problem of forced oscillations of a string with a uniformly moving boundary is considered. The error of the Kantorovich–Galerkin method is estimated depending on the velocity of the boundaries.