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Multi-pulse orbits and chaotic dynamics in a nonlinear forced dynamics of suspended cables

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Abstract

The global bifurcations in mode of a nonlinear forced dynamics of suspended cables are investigated with the case of the 1:1 internal resonance. After determining the equations of motion in a suitable form, the energy phase method proposed by Haller and Wiggins is employed to show the existence of the Silnikov-type multi-pulse orbits homoclinic to certain invariant sets for the two cases of Hamiltonian and dissipative perturbation. Furthermore, some complex chaos behaviors are revealed for this class of systems.

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References

  1. Tong X., Tabarrok B.: Melnikovsmethod for rigid bodies subject to small perturbation torques. Arch. Appl. Mech. 66, 215–230 (1996)

    Article  MATH  Google Scholar 

  2. Ravindra B., Zhu W.D.: Low-dimensional chaotic response of axially accelerating continuum in the supercritical regime. Arch. Appl. Mech. 68, 195–205 (1998)

    Article  MATH  Google Scholar 

  3. Wiggins S.: Global Bifurcations and Chaos. Springer, New York (1988)

    MATH  Google Scholar 

  4. Kovačič G., Wiggins S.: Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation. Phys. D 57, 185–225 (1992)

  5. Kaper T.J., Kovačič G.: Multi-bump orbits homoclinic to resonance bands. Trans. Am. Math. Soc. 348, 3835–3887 (1996)

    Google Scholar 

  6. Camassa R., Kovačič G., Tin S.K.: A Melnikov method for homoclinic orbits with many pulse. Arch. Ration. Mech. Anal. 143, 105–193 (1998)

  7. Haller G., Wiggins S.: Orbits homoclinic to resonances: the Hamiltonian case. Phys. D 66, 298–346 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Haller G., Wiggins S.: N-pulse homoclinic orbits in perturbations of resonant Hamiltonian system. Arch. Ration. Mech. Anal. 130, 25–101 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Haller G., Wiggins S.: Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation. Phys. D 85, 311–347 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mcdonald R.J., Sri Namachchivaya N.: Pipes conveying pulsating fluid near a 0:1 resonance: global bifurcations. J. Fluids Struct. 21, 665–687 (2005)

    Google Scholar 

  11. Feng Z.C., Wiggins S.: On the existence of chaos in a class of two-degree-of-freedom, damped parametrically forced mechanical systems with broken O(2) symmetry. ZAMP 44, 201–248 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Feng Z.C., Sethna PR.: Global bifurcation in motions of parametricaliy excited thin plates. Nonlinear Dyn. 4, 398–408 (1993)

    Article  Google Scholar 

  13. Feng Z.C., Liew K.M.: Global bifurcations in parametrically excited systems with zero-to-one internal resonance. Nonlinear Dyn. 21, 249–263 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wei Z., Minghui Y.: Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt. Chaos Solitons Fractals 28, 42–66 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wei Z., Wang F.X., Minghui Y.: Global bifurcations and chaotic dynamics in nonlinear nonplanar oscillations of a parametrically excited cantilever beam. Nonlinear Dyn. 40, 251–279 (2005)

    Article  MATH  Google Scholar 

  16. Narakorn S., Giuseppe R.: The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables. Int. J. Nonlinear Mech. 42, 180–195 (2007)

    Article  MATH  Google Scholar 

  17. Narakorn S., Giuseppe R.: Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables. J. Sound Vib. 310, 230–242 (2008)

    Article  Google Scholar 

  18. Narakorn S., Giuseppe R.: Space-time numerical simulation and validation of analytical predictons for nonlinear forced dynamics of suspended cables. J. Sound Vib. 310, 230–242 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, People’s Republic of China

    Yugao Huangfu & Fangqi Chen

  2. College of Mathematics and Information Science, Henan Polytechnic University, 454000, Jiaozuo, People’s Republic of China

    Yugao Huangfu

  3. Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, 300072, Tianjin, People’s Republic of China

    Fangqi Chen

Authors
  1. Yugao Huangfu
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  2. Fangqi Chen
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Correspondence to Yugao Huangfu.

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Huangfu, Y., Chen, F. Multi-pulse orbits and chaotic dynamics in a nonlinear forced dynamics of suspended cables. Arch Appl Mech 81, 1231–1252 (2011). https://doi.org/10.1007/s00419-010-0482-z

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  • DOI: https://doi.org/10.1007/s00419-010-0482-z

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