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Energy Method for Computing Periodic Solutions of Strongly Nonlinear Autonomous Systems with Multi-Degree-of-Freedom

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Abstract

In this paper with the use of conservation of average energy, a newmethod for computing the periodic solutions of strongly nonlinearautonomous systems with multi-degree-of-freedom is suggested. Thismethod cannot only decide the existence, but also give the approximateexpressions of the periodic solutions.

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References

  1. Nayfeh, A. H., Perturbation Methods, Wiley, New York, 1973.

    Google Scholar 

  2. Nayfeh, A. H., Introduction to Perturbation Techniques, Wiley, New York, 1981.

    Google Scholar 

  3. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.

    Google Scholar 

  4. He Ji-huan, ‘A review on some recently developed nonlinear analytical techniques’, International Journal of Nonlinear Sciences and Numerical Simulation 1(1), 2000, 51–70.

    Google Scholar 

  5. Resenberg, R. M., ‘The normal modes of nonlinear n-degree-of-freedom system’, Journal of Applied Mechanics, 29, 1962, 7–14.

    Google Scholar 

  6. Chechin, G. M., Sakhnenko, V. P., and Stokes, H. T., ‘Non-linear normal modes for systems with discrete symmetry’, International Journal of Non-Linear Mechanics 35(3), 2000, 497–513.

    Google Scholar 

  7. Xu Jian, Lu Qi-shao and Huang Ke-lei, ‘Singular characteristics of nonlinear normal modes in a two degrees of freedom asymmetric system with cubic non-linearity’, Applied Mathematics and Mechanics 22(8), 2001, 972–980.

    Google Scholar 

  8. Chen, S. H. and Cheung, Y. K., ‘A modified Lindstedt–Poincaré method for a strongly non-linear two degrees of freedom system’, Journal of Sound and Vibration 193(4), 1996, 751–762.

    Google Scholar 

  9. Qaisi, M. I. and Kilani, A. W., ‘Power-series solution for a strongly nonlinear two-dof system’, Journal of Sound and Vibration 233(3), 2000, 489–494.

    Google Scholar 

  10. Luo, G. W., ‘Hopf bifurcation of two-dof vibro-impact system’, Journal of Sound and Vibration 213(3), 1998, 391–408.

    Google Scholar 

  11. Chen, S. H., Cheung, Y. K., and Lau, S. L., ‘On the internal resonance of multi-degree-of-freedom systems with cubic non-linearity’, Journal of Sound and Vibration 128(1), 1989, 13–24.

    Google Scholar 

  12. Cheung, Y. K. and Xu Zhao, ‘Internal resonance of strongly non-linear autonomous vibrating systems with many degrees of freedom’, Journal of Sound and Vibration 180(1), 1995, 229–238.

    Google Scholar 

  13. Lau, S. L. and Xu Zhao, ‘On internal resonance of non-linear vibrating system with many degrees of freedom’, Applied Mathematics and Mechanics 113, 1992, 29–37.

    Google Scholar 

  14. Li, L., ‘Energy method for approximate periodic solution of strongly nonlinear nonautonomous systems’, Nonlinear Dynamics 19, 1999, 237–260.

    Google Scholar 

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Li, L., Hongling, Y. Energy Method for Computing Periodic Solutions of Strongly Nonlinear Autonomous Systems with Multi-Degree-of-Freedom. Nonlinear Dynamics 31, 23–47 (2003). https://doi.org/10.1023/A:1022116423164

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  • DOI: https://doi.org/10.1023/A:1022116423164

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