PERIOD-INFINITY PERIODIC MOTIONS, CHAOS, AND SPATIAL COHERENCE IN A 10 DEGREE-OF-FREEDOM IMPACT OSCILLATOR
PERIOD-INFINITY PERIODIC MOTIONS, CHAOS, AND SPATIAL COHERENCE IN A 10 DEGREE-OF-FREEDOM IMPACT OSCILLATOR
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DOI：
10.1016/0960-0779(93)90003-j
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发表时间：
1993-09-01
影响因子：
7.8
通讯作者：
BAI, BY
中科院分区：
文献类型：
--
作者：
CUSUMANO, JP;BAI, BY
对一个10自由度的碰撞振子进行了数值研究。该数学模型由线性质量阵列组成，其中每个质量通过相同的弹簧和阻尼器连接到其最近的邻居。一端质量连接到刚性支撑，而另一端自由地撞击正弦振动的刚性台。基于冲击庞加莱映射的分叉图得到了整个固有频率范围内，表频率作为分叉参数。图中显示了许多混沌带以及各种各样的周期-（n，m）（P（n，m））轨道，其中n是相对于撞击庞加莱映射的周期，m是表周期的数目。也许最有趣的解是P（无穷大，m）解（其中m是有限的）。这些都是由于碰撞之间的时间在有限时间内接近于零的粘附事件引起的。在卡事件的影响时间序列的收敛特性示出的影响法律的恢复系数控制。的运动的空间复杂性进行了研究，通过寻找适当的正交模式为各种稳定状态，和激励的自由度的数量估计通过找到超过99%的信号功率所需的模式的数量。这些结果相比，分形维数理论的预测。
The numerical study of a 10 degree of freedom impact oscillator is presented. The mathematical model consists of a linear array of masses in which each mass is connected to its nearest neighbor by identical springs and dashpots. One end mass is attached to a rigid support while the other is free to impact a sinusoidally vibrating rigid table. Bifurcation diagrams based on the impact Poincare map are obtained over the entire range of natural frequencies, taking the table frequency as the bifurcation parameter. The diagrams reveal many chaotic bands as well as a wide variety of period-(n,m) (P(n,m)) orbits, where n is the period with respect to the impact Poincare map and m is the number of table periods. Perhaps the most interesting solutions are P(infinity,m) solutions (where m is finite). These arise from sticking events in which the time between impacts approaches zero in finite time. The convergence properties of the impact time sequence during a sticking event is shown to be controlled by the coefficient of restitution of the impact law. The spatial complexity of the motions is studied by finding proper orthogonal modes for various steady states, and the number of excited degrees of freedom is estimated by finding the number of modes needed to exceed 99% of the signal power. These results are compared to the predictions of fractal dimension theory.