非线性振动理论中的非线性模态对应原理探讨

Nonlinear Mode Correspondence Principle in Nonlinear Vibration Theory

提出了非线性振动理论中的非线性模态对应原理 ,并给出了该原理的证明。非线性模态对应原理指出 :无论非线性振动系统具有相似模态还是具有非相似模态 ,n个自由度的非线性振动系统至少具有n个非线性模态 ,且这n个非线性模态形式上对应于该非线性振动系统对应的线性振动系统的n个线性模态。

In this paper, the nonlinear mode correspondence principle in nonlinear vibration theory is proposed and proved. The principle suggests that a nonlinear vibration system with n degrees of freedom has no less than n nonlinear modes that correspond to n linear modes of the corresponding linear vibration system, no matter the nonlinear vibration system possesses either similar normal modes or dissimilar ones. The calculation example shows that the proposed principle can be applied to seeking the nonlinear modes that are corresponding to the linear mode of the corresponding linear system of the nonlinear one.