冲击渐进振动系统相邻基本振动的转迁规律

冲击振动现象广泛存在于动力机械系统中,使得系统表现出复杂的动力学响应.目前对冲击振动系统的p/1类基本振动的稳定性及分岔研究报道较少,而且已有的对冲击振动系统动力学的研究基本都是基于单参数分岔进行分析的.研究以小型振动冲击式打桩机为工程背景,建立了冲击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四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在(ω,l)参数平面内存在的各类周期振动的参数域和分布规律.详细分析了相邻p/1类基本振动的转迁规律.在5/1基本振动的参数域的右边区域,相邻p/1基本振动的参数域临界线上存在一个奇异点X_p,相邻p/1类基本振动的分岔特点以奇异点X_p为临界点.在l小于l_X_p的区域内,相邻p/1基本振动经实擦边分岔和鞍结分岔相互转迁,实擦边分岔线和鞍结分岔线之间存在迟滞域,迟滞域内,系统存在两个周期吸引子共存的现象.在l大于l_X_p的区域内,相邻p/l类基本振动的参数域之间存在一个中间过渡区域.中间过渡区域内,系统呈现(2p+2)/2和(2p+1)/2周期振动等.在5/1基本振动的参数域的左边区域,p/1基本振动经多重滑移分岔产生(P+1)/1基本振动.

TRANSITION LAW OF ADJACENT FUNDAMENTAL MOTIONS IN VIBRO-IMPACT SYSTEM WITH PROGRESSION

The vibro-impact phenomena which widely exists in power mechanical system will make the system exhibit complex dynamic response. So far the research on stability and bifurcation of p/1 fundamental motions of vibro-impact system is still rare, and most studies of vibro-impact dynamics are based on single-parameter bifurcation analysis. In this paper, taking a small vibro-impact driver as engineering background, a mechanical model of a vibro-impact system with progressive motions is established. Types of impact between the vibration exciter and the cushion, and conditions of progressive motions of the slider are analyzed. Judgment conditions and motion equations of four probable motion states presented by the system are put forward. Based on bifurcation analysis of two-dimensional parameters, existence regions and distribution laws of different types of periodic motions of the system are obtained in the (ω, l) parameter plane. Transition laws of adjacent p/1 fundamental motions are analyzed in detail. In the right region of the existence region of 5/1 fundamental motion, there exists a singular point X p on the boundary between adjacent regions of p/1 fundamental motions, which is the critical point of bifurcation characteristics of adjacent p/1 fundamental motions. In the region with l less than lXp, adjacent p/1 fundamental motions are transited mutually by real-grazing bifurcation and saddle-node bifurcation. Two periodic attractors can coexist in the hysteresis region, which exists between real-grazing bifurcation boundary and saddle-node bifurcation boundary. In the region with l more than lXp, there exists a transition region between adjacent regions of p/1 fundamental motions. The system exhibits (2 p+2)/2 and (2 p+1)/2 motions in the transition region. In the left region of the existence region of 5/1 fundamental motion, p/1 fundamental motion transits to ( p+1)/1 fundamental motion via multi-sliding bifurcation.