Dynamical behavior of an elastic beam in large-amplitude vibrations
type: Item
instance of: scholarly article
title: Dynamical behavior of an elastic beam in large-amplitude vibrations
zbMATH Open document ID: 0646.73025
DOI: 10.1016/0093-6413(88)90012-2
author: Chingzhen Fong
published in: Mechanics Research Communications
publication date: 1988-01-01T00:00:00Z
review text: There are many papers in which nonlinear vibrations of an elastic beam are studied. The beam is supported in a way that restricts the movement of its ends, so that the source of the nonlinearity is caused by the nonlinear stretching of the midplane. \textit{P. J. Holmes} [Philos. Trans. R. Soc. Lond., A 292, 419-448 (1979; Zbl 0423.34049)] studied the chaotic behavior of a beam in this case. In the present paper, we investigate the effects of the nonlinear curvature on the large-amplitude vibrations of an elastic beam. By making use of a Galerkin approximation, a set of nonlinear integro-differential equations is derived. Computational results show that this nonlinear system models an interesting dynamical behavior involving cusp catastrophe and chaos.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 4055161
zbMATH Keywords: nonlinear stretching of the midplane
zbMATH Keywords: effects of the nonlinear curvature
zbMATH Keywords: Galerkin approximation
zbMATH Keywords: set of nonlinear integro-differential equations
zbMATH Keywords: cusp catastrophe
zbMATH Keywords: chaos
MaRDI profile type: Publication
full work available at URL: 0093-6413(88)90012-2
OpenAlex ID: W1985828702
description: scientific article; zbMATH DE number 4055161