随机干扰下碰撞振动系统运动解的Chebyshev多项式逼近

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。

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

A three degree of freedom vibro-impact system is established according to the hydraulic impact breaker. The system perturbation solution is approximated by the second Chebyshev polynomial. Under the different disturbance intensities, the approximation properties between approximated solutions and perturbation solutions are analyzed by the numerical simulation. The results show that the system approximated by the second Chebyshev polynomial presents good approximating characteristics under some small degree of disturbance intensity, and there are variety of forms of the 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.