随机干扰下碰撞振动系统运动解的Chebyshev多项式逼近

The Chebyshev Polynomial Approximation of Vibro-impact System Motion Solution under Stochastic Disturbances

建立一类破碎锤的3自由度碰撞振动系统模型,运用第二类Chebyshev多项式逼近随机干扰下系统的随机扰动解,通过数值仿真,对比分析不同扰动强度下逼近系统的逼近解和随机干扰下扰动解的接近程度。结果表明:低强度扰动下,运用第二类Chebyshev多项式能够较好地逼近随机干扰下系统的扰动解,在一定系统参数下系统存在周期倍化分岔、逆周期倍化分岔序列的缺失、Hopf分岔、环面倍化分岔,经锁相系统进入混沌等多种分岔向混沌的演化形式。

A 3-DOF vibro-impact system of a hydraulic impact breaker is established.The perturbation solution of the system under stochastic excitations is obtained by using the second-kind Chebyshev polynomial approximation.Under the different disturbance intensities,the approximation properties between the approximated solutions and the perturbation solutions are analyzed and compared by numerical simulation.The results show that the system approximated by the secondkind Chebyshev polynomial presents good approximation characteristics under small disturbance intensity,and there are variety of forms of evolutions from periodic motion to chaos,such as the periodic doubling bifurcation,the loss of sequence in inverse periodic doubling bifurcation,Hopf bifurcation and torus doubling bifurcation,phase lock etc.