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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: Non-linear gear system Period-doubling bifurcation
Chaos Stroboscopic sampling Frequency analysis
CLC No: TH113
国家自然科学基金资助项目(50075070).
Received 20040707, received in revised form 20041215
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