含间隙弹簧振动系统的非线性模态特性

针对含间隙的两自由度弹簧-质量分段振动系统的非线性模态开展了研究.首先,解析确定了分段保守自治系统发生同相和反相模态运动的初始位移,并采用加权平均方法确定了分段振动系统的模态频率,及其在位形空间模态曲线.然后,采用数值方法求解了系统的非线性模态曲线和模态频率,与本文获得的解析模态频率比较,说明本文的结果较等效模态频率有更好的精度.研究结果表明:在一定的参数条件下,系统的非线性模态个数会高于系统的自由度数目,系统可能发生内共振,而产生多余模态.多余模态运动是两振子同向振动中含有异向振动,说明多余模态是在同相模态运动和反相模态运动之间转换的模态.

Nonlinearnormal modes of a vibrational system with clearance springs

The nonlinear normal mode of a 2 DOF piecewise linear system was investigated. First, the initial conditions of the in phase and the anti phase nonlinear normal mode motions as well as their curves in configuration space were studied theoretically, and the modal frequencies were obtained by weighted average method. Then, numerical method was adopted in order to determine the curves of nonlinear normal modes in the configuration space and the corresponding modal frequencies. The comparison between the theoretical and the numerical results shows that the proposal formulae of modal frequencies in this paper are more accurate than the one proposed previously in the literature. It is demonstrated that the system may own the so called superabundant modes beside the in phase and the anti phase modes, namely, the number of modes may exceed the number of the degree of freedom of the system. The appearance of the superabundant modes indicates the internal resonance between the in phase and the anti phase modes.