碰撞-渐进振动系统的亚谐振动与分岔分析

Subharmonic Vibrations and Bifurcations of Vibro-impact Systems with Progression

建立了碰撞-渐进振动系统的力学模型。分析了激振器和缓冲垫发生碰撞的类型,以及滑块渐进运动的条件。给出了系统可能呈现的4种运动状态的判断条件和运动微分方程。通过二维参数分岔分析,得到系统的各类周期振动在激振频率和预压量参数平面内的存在域及其分布规律。详细分析了1/n亚谐振动的分岔过程。当激振频率增大时,由于发生周期振动的实擦边分岔、虚擦边分岔或鞍结分岔等非光滑分岔,使得1/n亚谐振动的分岔过程变得更加复杂,而且受预压量的影响比较大。

A mechanics model of the vibro-impact systems with progressive motions was established.Types of impacts between the vibration exciter and the cushion,and conditions of progressive motions of the slider were analyzed.Judgment conditions and motion equations of four probable motion states presented by the systems were put forward.Based on bifurcation analysis of two-dimensional parameters,existence regions and distribution laws of different types of periodic motions of the systems were obtained in the exciting frequencies and precompression parameter planes.Bifurcation processes of 1/n subharmonic vibrations were analyzed in detail.When the exciting frequencies increase,bifurcation processes of 1/n subharmonic vibrations become more complicated due to the occurrence of non-smooth bifurcations of the periodic motions,incuding real-grazing bifurcations,baregrazing bifurcations,or saddle-node bifurcations.Moreover,the effects of precompression are relatively large.