This article is cited in 1 paper

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

V. L. Litvinov^a, K. V. Litvinova<sup>b

a</sup> Samara State Technical University, Samara, Russia
^b Lomonosov Moscow State University

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.

Keywords: oscillations of systems with moving boundaries, resonant properties, laws of boundary motion, resistance of the medium, oscillation amplitude.

Received: 07.02.2025
Revised: 07.02.2025

DOI: 10.4213/tmf10930

 English version: Theoretical and Mathematical Physics, 2025, 224:1, 1211–1219

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