Abstract：A mechanical impact oscillator with a pre-compressed spring is considered. The Poincaré map composed of smooth flow map and discontinuous map is constructed, and a numerical calculation method of Floquet multipliers is given. The periodic attractor patterns and their parameter regions of the system in the two-parameter plane are obtained by numerical simulation. The bifurcation characteristics of period-1 attractors and the discontinuous bifurcation behaviors, such as discontinuous grazing bifurcation, bifurcations induced by grazing and period-doubling, subcritical period-doubling bifurcation and crisis, are studied by applying continuation shooting method and cell mapping method, and the formation mechanism of hysteresis and subharmonic inclusions regions is revealed. In the transition between adjacent 1–m and 1–(m+1) attractors, the hysteresis and subharmonic inclusions regions are created by discontinuous grazing bifurcations. However, they are respectively created by grazing induced saddle-node and period-doubling bifurcations as the pre-compression is equal to 0. The results can provide guidance for the parameter design and optimization of mechanical impact system with a pre-compressed spring.
吕小红，王继培，张锦涛. 含预紧弹簧碰撞系统的两参数动力学[J]. 振动与冲击, 2024, 43(4): 12-19.
Lv Xiaohong，WANG Jipei，ZHANG Jintao. Two-parameter dynamics of an impact oscillator with a pre-compressed spring. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(4): 12-19.
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