两自由度非对称三次系统非奇异时的非线性模态及叠加性<sup>*</sup>

两自由度非对称三次系统非奇异时的非线性模态及叠加性^*

基金项目: 国家自然科学基金(19602003);中国博士后基金

Department of Applied Mathematics and Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

摘要: 本文利用非线性模态子空间的不变性研究两自由度非对称三次系统在非奇异条件下的非线性模态及其模态叠加解有效性,重点考虑这种有效性与模态动力学方程静态分岔之间的关系.大量的数值结果表明,非线性模态解的有效性不仅与其局部性的限制有关,而且与模态动力学方程静态解分岔有关.
- 非线性模态 /
- 非对称系统 /
- 静态分岔 /
- 非线性振动 /
- 非线性动力学
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 nonlinear 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 results show that the validity has something to do not only with its local restriction,but also with the static bifurcation of modal dynamics.
- nonlinear normal mode /
- asymmetric system /
- nonlinear vibration /
- nonlinear dynamics /

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