, Volume 47, Issue 4, pp 969–984 | Cite as

Chaotic vibration and resonance phenomena in a parametrically excited string-beam coupled system

  • Y. A. Amer
  • Usama H. HegazyEmail author


The nonlinear behavior of a string-beam coupled system subjected to parametric excitation is investigated in this paper. Using the method of multiple scales, a set of first order nonlinear differential equations are obtained. A numerical simulation is carried out to verify analytic predictions and to study the steady-state response, stable solutions and chaotic motions. The numerical results show that the system behavior includes multiple solutions, and jump phenomenon in the resonant frequency response curves. It is also shown that chaotic motions occur and the system parameters have different effects on the nonlinear response of the string-beam coupled system. Results are compared to previously published work.


Parametric excitation Hardening and softening nonlinearities Chaotic motion 


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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt
  2. 2.Department of Mathematics, Faculty of ScienceAlAzhar University-GazaGazaPalestine

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