Applied Mathematics and Mechanics (English Edition) ›› 1998, Vol. 19 ›› Issue (12): 1167-1177.

• 论文 • 上一篇    下一篇

NONLINEAR NORMAL MODES AND THEIR SUPERPOSITION IN A TWO DEGREES OF FREEDOM ASYMMETRIC SYSTEM WITH CUBIC NONLINEARITIES

徐鉴, 陆启韵, 黄克累   

  1. Department of Applied Mathematics and Physics, Peking University of Aeronautics and Astronautics, Beijing 100083, P. R. China
  • 收稿日期:1996-09-02 修回日期:1997-03-20 出版日期:1998-12-18 发布日期:2012-06-18
  • 基金资助:

    Project Supported by the National Natural Science Foundation and PSF of China

NONLINEAR NORMAL MODES AND THEIR SUPERPOSITION IN A TWO DEGREES OF FREEDOM ASYMMETRIC SYSTEM WITH CUBIC NONLINEARITIES

Xu Jian, Lu Qishao, Huang Kelei   

  1. Department of Applied Mathematics and Physics, Peking University of Aeronautics and Astronautics, Beijing 100083, P. R. China
  • Received:1996-09-02 Revised:1997-03-20 Online:1998-12-18 Published:2012-06-18
  • Supported by:

    Project Supported by the National Natural Science Foundation and PSF of China

摘要: This paper investigates nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities for all nonsingular conditions,based on the invariant subspace in nonlinear normal modes for the nonlhTear equations of motion.The focus of attention is to consider relation between the validity of superposition and the static bifurcation of modal dynamics.The numerical resuhs show that the validity has something to do not only with its local restriction,but also with the static bifurcation of modal dynamics.

关键词: super noalinear velocity, relative nonsymmetry, twin paradox, μmeson, followed body, nonlinear normal mode, asymmetric system, nonlinear vibration, nonlinear dynamics

Abstract: This paper investigates nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities for all nonsingular conditions,based on the invariant subspace in nonlinear normal modes for the nonlhTear equations of motion.The focus of attention is to consider relation between the validity of superposition and the static bifurcation of modal dynamics.The numerical resuhs show that the validity has something to do not only with its local restriction,but also with the static bifurcation of modal dynamics.

Key words: super noalinear velocity, relative nonsymmetry, twin paradox, μmeson, followed body

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