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.

中文翻译：

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具有多个刚性挡块的机械振动系统的周期性冲击运动的多样性和规律性

建立了具有多个刚性挡块的两自由度振动系统的力学模型，研究了多个刚性挡块对系统两个质量块动力学特性的影响。分析了系统质量对刚性挡块的影响的判断条件和运动微分方程。基于多参数多目标协同仿真分析，研究了振动系统动力学特性与模型参数之间的相关性。分析了基本的周期和次谐波冲击运动，重点研究了动力学参数对模态多样性和分布特性的影响，揭示了各种周期性冲击运动在参数平面上的出现和竞争规律。奇点 分析了磁滞过渡域以及由低频域中相邻基本周期性冲击运动之间的过渡的不可逆性所引起的伴随的二维维分叉。确定与系统动态特性优化相关的合理参数匹配范围。