Dynamical behavior of an elastic beam in large-amplitude vibrations (Q1104153)

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.