关键词: 倍周期分岔, 非线性齿轮系统, 分频采样, 混沌, 频谱分析

Abstract: Based on the dynamic model of strongly nonlinear gear system with clearance and time-variable mesh stiffness, the period-doubling bifurcation phenomena are researched, and the problem of hiberarchy in chaotic zones is discussed. By using the frequency analysis method the periodic motions and chaotic motions are judged, and the periodic orbits embedded in different chaotic bands are distinguished. The first period- doubling bifurcation sequence and merged sequence of chaotic bands are obtained by means of the stroboscopic sampling method. The chaos hiberarchy problem in the coexistence area of period-window and chaos-window are also researched. Results show that complex bifurcation structure and some commonly suited rules are existed in the strongly nonlinear gear system. These conclusions can provide some references for deeply researching the characters of nonlinear dynamic behaviors in mechanical systems.

Key words: Chaos, Frequency analysis, Non-linear gear system, Period-doubling bifurcation, Stroboscopic sampling