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Abstract: By adopting the thought of Adomian's decomposition method,
the three-degree-of-freedom non-linear models of the gear system with
clearances are transformed into a standard
first-order-differential-equations, and then the A-operator method (AOM)
for the approximate analytic solution of the system is developed based
on the exact solution in form. The symbolic-numeric (S-N) method on the
basis of the AOM is proposed for the first time in this paper. By using
the AOM, the bifurcation and chaotic behavior of the gear system with
clearances is investigated. It shows that under a certain condition the
system will become chaotic through the route of period-doubling
bifurcation or crisis, which is illustrated by the damping bifurcation
diagram and frequency bifurcation diagram. It also follows that the
method presented in this paper is of practical significance in nonlinear
dynamic analysis of mechanical system.
Key words: Bifurcation Chaos A-operator method (AOM) Gear system
CLC No: TH113
O322
国家自然科学基金(50075070)和博士后基金资助项目.
Received 20010521, received in revised form 20010930
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