《Chaotic vibration and resonance phenomena in a parametrically excited string-beam coupled》.pdf

Meccanica DOI 10.1007/s11012-011-9490-5 Chaotic vibration and resonance phenomena in a parametrically excited string-beam coupled system Y.A. Amer · Usama H. Hegazy Received: 20 August 2010 / Accepted: 4 October 2011 © Springer Science+Business Media B.V. 2011 Abstract The nonlinear behavior of a string-beam 1 Introduction coupled system subjected to parametric excitation is investigated in this paper. Using the method of mul- Different kinds of Beam and string models have been tiple scales, a set of first order nonlinear differential investigated by many researchers [ 1–6]. There are many engineering systems which can be reduced equations are obtained. A numerical simulation is car- to a string-beam coupled model, such as the opti- ried out to verify analytic predictions and to study cal fiber coupler used in telecommunications, cable- the steady-state response, stable solutions and chaotic stayed bridges and tower cranes. They are used in motions. The numerical results show that the system many engineering applications, like satellite antenna, behavior includes multiple solutions, and jump phe- spacecraft, automobiles, mechanisms and others. Al- nomenon in the resonant frequency response curves. It though, the beam and string are two essential structural is also shown that chaotic motions occur and the sys- elements and very significant models in engineering, tem parameters have different effects on the nonlinear limited research has been conducted for the analysis response of the stri