Analysis of infinite systems of linear equations in the problem of flexible vibrations of a clamped rectangular plate

Abstract

Analysis of infinite systems of linear equations in the problem of flexible vibrations of a clamped rectangular plate

Papkov S.O., Papkova Yu.I., Pasechnik V.A.

Incoming article date: 29.12.2023

The problem of flexible vibrations of a rectangular orthotorque plate clamped along the contour is considered. The general solution of the problem, which satisfies the vibartion equation identically, is constructed on the basis of the superposition method in the form of two Fourier series. Clamped boundary conditions lead to a homogeneous infinite system of linear algebraic equations with respect to unknown coefficients in the general solution. The uniqueness of a bounded non-trivial solution of an infinite system for the natural frequency is proved, the asymptotics of the unknowns are found, and an effective solution algorithm is constructed. Examples of the numerical implementation of the developed algorithm for calculating the natural frequencies and natural modes of the plate vibrations are given.

Keywords: plate, vibrations, natural frequencies, planar forces, superposition method, infinite system of linear equations, asymptotics