Periodic Motion Transition and Driving Characteristics of Collision and Stick-Slip Vibration-Driven System
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摘要:
为研究碰撞振动系统的动力学演化规律和驱动性能，首先，考虑外部环境不连续力与内部非光滑碰撞，建立一类碰撞与黏滑振动驱动系统；其次，基于不连续动力系统的流转换理论与映射动力学理论，刻画系统相空间内的不连续边界和子区域映射关系，采用分段分析法描绘系统相空间运行轨迹；最后，通过数值协同仿真研究参数域内系统周期运动分布转迁机理和平均速度分布规律. 研究表明：在激励频率 、间隙双参数平面内，系统正反向最大平均驱动速度集中于主共振区，呈现周期1-1-1（或1-1-2）运动类型；结合参数域内系统驱动方向和驱动速度与系统参数的关联关系，可通过调控系统参数与外激励频率实现宽速驱动；低频小间隙区存在2种序列擦边分岔，一种在低频区随着激励频率减小，右侧擦边分岔诱导系统碰撞次数依次增加，另一种在超低频区围绕碰撞子空间内的平衡点衍生出序列相轨迹，泛延过程中出现左侧擦边分岔，系统呈现出簇发振荡的现象.
Abstract:To study the dynamic evolution laws and driving performance of collision vibration-driven systems, firstly, Considering the discontinuous resistance of the external environment and the internal non-smooth collision were considered, and a type of mobile system driven by collision and stick-slip vibration-driven system is was established. The evolution law of system dynamics and driving performance are two key issues in the study of vibration-driven system. This article first considers external environmental discontinuous forces and internal non-smooth collisions, and establishes a type of collision and stick-slip vibration-driven system. Secondly, based on the flow conversion theory and mapping dynamics theory of discontinuous dynamical systems, the mapping relationship between discontinuous boundaries and subregions in the phase space of the system is was characterized, and the segmented analysis method is was used to depict the motion trajectory of the system's system’s phase space operation. The segmented analysis method is used to describe the trajectory of the system in the phase space. Study the mechanism of periodic motion distribution transition and average velocity distribution in the parameter domain were studied through numerical collaborative simulation. Research has shown that in the two-parameter plane of excitation frequency w and gap δ, the maximum average driving velocityspeed of the system in the forward and reverse directions is concentrated in the main resonance region, exhibiting a period of 1-1-1 (or 1-1-2) motion type. By combining the correlation between the driving direction and velocityspeed of the system within the parameter domain and the system parameters, widely velocityspeed driving can be achieved by adjusting the system parameters and external excitation frequency. There are two types of sequence edge scraping bifurcations in the low-frequency small gap region. One is that in the low-frequency region, as the excitation frequency decreases, the right edge scraping bifurcation induces an increase in the number of collisions in the system. Another method is to derive sequence phase trajectories around equilibrium points in the collision subspace in the ultra-low frequency region. During the generalization process, there is a left edge scraping bifurcation, and the system exhibits a phenomenon of cluster oscillation.
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图 3 碰撞与黏滑振动驱动系统映射关系
Figure 3. Mapping relationship between collision and stick-slip vibration-driven system
图 10 1-1最大平均驱动速度颜色编码像素
Figure 10. Color coded pixel map of maximum average driving velocity for 1-1 system
图 11 1-2型系统平均驱动速度颜色编码像素图
Figure 11. Color coded pixel map of average driving velocity for 1-2 system
图 12 周期1-1下$ w {\text{-}}v $分布
Figure 12. Distribution of$ w {\text{-}}v $under cycle 1-1
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