两自由度混合非线性系统非线性模态的叠加性

Modal Superposition of a Nonlinear System of Two Degrees of Freedom

通过对某一两自由度混合非线性系统非线性模态的研究 ,获知非线性模态叠加解在许多模态产生静态分岔和内共振情形下仍然有效 ,同时也存在许多模态产生静态分岔情形下失效的现象 ,故可以认为非线性模态叠加解的有效性是一个复杂的问题 。

The nonlinear normal modes and their superposition of a nonlinear system of two degrees of freedom are analyzed theoretically and numerically.It is found that the modal superposition can effectively simulate the system's direct solutions not only in many cases of non-static-bifurcation, but also in many cases with the modal static bifurcation and internal resonance occurring, so there are no simple tests to determing the modal superposition can or can't effectively simulate the system's direct solutions for a general problem.