Chaotic vibrations in nonlinear problems of bar structures

Abstract

In the response of nonlinear mathematical models which describe vibrations of structural elements one could observe an irregular behaviour which is called chaos. Loss of the information on initial states in deterministic dynamical systems after a short time of theirs evolution, increasing amplitudes of displacements, velocities and accelerations, sensitive dependency on initial conditions makes chaos dangerous phenomenon in mechanics of construction. In this article quantitative (bifurcation diagrams, Poincare sections and Fourier power spectrum analysis) identication methods of the chaotic dynamics in geometrically nonlinear model of one DOF Mises truss are shown. Main goal of this article is to show and verify dangerous influence of chaos (in the engineering sense) on the analyzed structure. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)