Nonlinear Dynamics

, Volume 67, Issue 3, pp 1969–1984 | Cite as

Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances

  • M. H. Wei
  • Y. Q. Xiao
  • H. T. Liu
Original Paper


The bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances are investigated. The combined effects of the nonlinear term due to the cable’s geometric and coupled behavior between the modes of the beam and the cable are considered. The nonlinear partial-differential equations are derived by the Hamiltonian principle. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. The bifurcation diagrams in three separate loading cases, namely, excitation acting on the cable, on the beam and simultaneously on the beam and cable, are analyzed with changing forcing amplitude. Based on careful numerical simulations, bifurcations and possible chaotic motions are represented to reveal the combined effects of nonlinearities on the dynamics of the beam and the cable when they act as an overall structure.


Cable–beam coupled system Internal resonant External resonant Bifurcation Chaos 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Shenzhen Graduate SchoolHarbin Institute of TechnologyShenzhenChina

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