This article is cited in 1 paper

Asymptotic analysis of geometrically nonlinear vibrations of long plates

B. Affane, A. G. Egorov

Kazan Federal University, Kazan, 420008 Russia

Abstract: In this paper, we performed an asymptotic analysis for equations of the classical plate theory with the von Kármán strains under the assumption that the width of the plate is small compared with its length. A system of one-dimensional equations, which describes the nonlinear interaction of flexural and torsional vibrations of beams, was derived. This enables the possibility of exciting torsional vibrations by flexural vibrations. This possibility was analyzed for a model problem, when flexural vibrations occur in normal modes.

Keywords: asymptotic analysis, flexural vibrations, torsional vibrations, parametric resonance, resonance gaps, Mathieu equation.

UDC: 534.121

Received: 16.10.2020

DOI: 10.26907/2541-7746.2020.4.396-410

Bibliographic databases:

•