内共振平方非线性系统的非线性模态及其分岔

利用多足度方法研究了一类1：2内共振平方非线性系统的非线性模态的近似解及其分叉特性．研究表明，此类系统除存在非耦合模态外还存在耦合模态，且后者有分岔现象，这可导致非线性模态的数目合超过系统的自由度数．耦合非线性模态的分叉既与调谐参数有关又与模态振幅有关，但与非耦合弹簧的非线性刚度无关．

Bifurcation of Nonlinear Internal Resonant Normal Modes of Systems with Quadric Nonlinearity

The construction of nonlinear normal modes of a system with 1: 2 internal resonance is presented for the case of quadric nonlinearity. Approximate solutions for the nonlinear normal modes are determined by applying the method of multiple scales. It is shown that there exist coupled as well as uncoupled nonlinear normal modes. Different from the uncoupled nonlinear normal modes, the coupled nonlinear normal mode has bifurcation behavior, which can directly result in the number of nonlinear normal modes being more than the degrees of freedom. The bifurcation behavior of the coupled nonlinear normal mode is associated with detuning parameter and mode amplitude, but not with the nonlinear stiffness of uncoupling spring.