冲击渐进振动系统的双参数分岔分析

Two-parameter bifurcation analysis for an impact progressive vibration system

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在(ω,l)-参数平面内各点处,系统呈现的周期振动的类型。详细分析了1/1和2/1基本碰撞运动的分岔特点,以及系统参数、冲击速度和滑块渐进率之间的关联关系。1/1基本碰撞运动经周期倍化分岔产生2/2周期振动,经虚擦边分岔或多重滑移分岔产生2/1基本碰撞运动。2/1基本碰撞运动经实擦边分岔,虚擦边分岔或多重滑移分岔产生3/1基本碰撞运动。由于p/1(p=1, 2)基本碰撞运动的虚擦边分岔,使得p/1基本碰撞运动在向稳定的(p+1)/1基本碰撞运动转迁的过程中出现一个中间过渡区域。此外,在一定参数条件下,系统呈现1/1基本碰撞运动的概周期运动和周期泡现象。

The mechanical model of an impact progressive vibration system was established. Impact types between a vibration exciter and a cushion, and progressive motion conditions of a slider were analyzed. Judgment conditions and dynamic equations for 4 possible motion states of the system were derived. Based on bifurcation analysis in a 2-D parametric plane, periodic vibration types of the system were obtained at all points in the parametric plane of(ω, l). The bifurcation characteristics of the fundamental impact motions of 1/1 and 2/1 were analyzed in detail. The relations among system parameters, impact velocity and slider’s progressive motion rate were studied. It was shown that the fundamental impact motion of 1/1 produces the periodic vibration of 2/2 through period-doubling bifurcation, and it produces the fundamental impact motion of 2/1 through virtual erasure bifurcation or multi-slip one;the fundamental impact motion of 2/1 produces the fundamental impact motion of 3/1 through real erasure bifurcation, virtual erasure one or multi-slip one;due to virtual erasure bifurcation of the fundamental impact motion of p/1(p=1, 2), an intermediate transition region appears in the transition process from the fundamental impact motion of p/1 to the stable fundamental impact motion of(p+1)/1;the system exhibits a quasi-periodic motion and a periodic bubble phenomenon of the fundamental impact motion of 1/1 under certain parametric conditions.