This article is cited in 1 paper

Numerical-analytical method for studying the dynamics of hinged elastic plate

M. A. Ankilov, A. S. Andreev

Ulyanovsk State University

Abstract: Based on the simplest mathematical model of free oscillations of an elastic plate, a numerical-analytical method for studying its dynamics in the case of hinged fastening of the ends has been developed. The model is described by a partial differential equation; we search for a solution by the Bubnov–Galerkin method. The purpose of the study is to determine the error of the obtained approximate solution using a Lyapunov-type functional. Numerical experiments have been conducted to confirm the reliability of the proposed method.

Keywords: mathematical modeling, dynamics, elastic plate, Bubnov–Galerkin method, partial differential equation, Lyapunov functional

UDC: 519.63

MSC: 35Q74

DOI: 10.36535/2782-4438-2025-242-3-10