一类单自由度多频激励滞后非线性系统的亚组合共振

Sub-combination Resonance in a Single DOF Hysteretic Nonlinear System with Multiple Frequency Excitations

利用平均法研究了一类单自由度滞后非线性系统在多频激励作用下的亚组合共振，得到了该系统产生的亚组合共振响应的解析解，研究表明亚组合共振的幅频曲线具有又型分叉（PitchforkBifurcation）特性，而且亚组合共振的响应比相应的线性系统的振幅大很多，所以，必须充分考虑非线性的影响。还研究了系统参数对亚组合共振幅频特性的影响，研究发现多频激励使得系统的亚组合共振曲线发生偏移。最后，用数值仿真计算验证了结论的正确性。

This paper presents the investigation of the subcombination resonance in a single DOF hysteretic nonlinear system with multiple frequency excitations. The amplitude-frequency response is obtained by using the averaging method. It is found that the subcombination resonance is a kind of pitchfork bifurcation. The effect of system parameters on the subcombination resonance is studied,and the results are verified by digital simulation.