Diversity and Regularity of Periodic Impact Motions of a Mechanical Vibration System with Multiple Rigid Stops

The mechanical model of a two-degree-of-freedom vibration system with multiple rigid stops was established, and the effects of the multiple rigid stops to dynamic characteristics of two mass blocks of the system were studied. The judgment conditions and differential equations of motion of the system masses impacting rigid stops were analyzed. Based on the multiparameter and multiobjective collaborative simulation analysis, the correlation between the dynamic characteristics of the vibration system and the model parameters is studied. The basic periodic and subharmonic impact motions are analyzed with emphasis on the influences of dynamical parameters on the mode diversity and the distribution characteristics, and the law of emergence and competition of various periodic impact motions on the parametric plane is revealed. The singular points, the hysteresis transition domains, and the accompanying codimension-two bifurcations, caused by the irreversibility of the transition between adjacent basic periodic impact motions in the low-frequency domain, are analyzed. The reasonable parameter matching range, associated with dynamic characteristic optimization of the system, is determined.