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Numeric Research of Chaotic Vibration for a Hard Stiffness Nonlinear Rod

In: Computational Mechanics

Author

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  • J. W. Gao

    (North University of China, Department of Mechanics)

  • Z. M. Cai

    (Taiyuan University of Technology, Institute of Applied Mechanics)

Abstract

In this paper, longitudinal vibration of a nonlinear viscoelastic rod system with one end fixed and another end subjected to an axial periodical excitation was studied under the consideration of transverse inertia. By using Galerkin method and for hard stiffness nonlinear material, a combined Parametric and Forcing Excited hard nonlinear dynamic system is derived. Because of no homoclinic or heteroclinic orbits existing in such a case, Melnikov method can’t be used as a bifurcation or chaotic criteria. So numerical computing becomes an important approach to research such a system. Here, arc-length method is used for an accurate integral procedure; the process of the system evolved from stable periodic motion to chaos is given in period-doubling bifurcation graph in the parameter space. While the Lyapunov exponent spectrum is also presented that is perfectly consistent with bifurcation process. The strange attractor obtained from Poincaré Map has different fractal dimension from Duffing’s one, so it may be a new chaotic attractor.

Suggested Citation

  • J. W. Gao & Z. M. Cai, 2007. "Numeric Research of Chaotic Vibration for a Hard Stiffness Nonlinear Rod," Springer Books, in: Computational Mechanics, pages 418-418, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75999-7_218
    DOI: 10.1007/978-3-540-75999-7_218
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