Nonlinear Rocking Motions. I: Chaos under Noisy Periodic Excitations
Nonlinear Rocking Motions. I: Chaos under Noisy Periodic Excitations
复制标题
非线性摇摆运动。
DOI：
10.1061/(asce)0733-9399(1996)122:8(719
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
S. Yim
中科院分区：
文献类型：
--
作者：
H. Lin;S. Yim
分析和仿真研究了低强度随机扰动对摇摆物体在周期激励下混沌响应稳定性的影响。一个随机Melnikov过程的开发，以确定可能的混沌域的下限。平均相通量率的计算，以证明从混沌到翻转的过渡噪声的影响。利用平均Poincare映射技术在Poincare截面上重构了随机噪声下的嵌入混沌吸引子。大量的模拟研究混沌行为从合奏的角度来看。分析预测，随机扰动的存在扩大了可能的混沌域和桥梁共存吸引子的吸引域。数值结果表明，在共存吸引子中，翻转吸引子的强度最大;由于混沌吸引子的稳定性较弱，随机噪声的存在最终会导致翻转的混沌摇摆响应.嵌入的奇怪吸引子（重建使用平均庞加莱映射）的存在表明，摇摆对象可能会经历短暂的混乱之前推翻。
The effects of low-intensity random perturbations on the stability of chaotic response of rocking objects under otherwise periodic excitations are examined analytically and via simulations. A stochastic Melnikov process is developed to identify a lower bound for the domain of possible chaos. An average phase-flux rate is computed to demonstrate noise effects on transitions from chaos to overturning. A mean Poincare mapping technique is employed to reconstruct embedded chaotic attractors under random noise on Poincare sections. Extensive simulations are employed to examine chaotic behaviors from an ensemble perspective. Analysis predicts that the presence of random perturbations enlarges the possible chaotic domain and bridges the domains of attraction of coexisting attractors. Numerical results indicate that overturning attractors are of the greatest strength among coexisting ones; and, because of the weak stability of chaotic attractors, the presence of random noise will eventually lead chaotic rocking responses to overturning. Existence of embedded strange attractors (reconstructed using mean Poincare maps) indicates that rocking objects may experience transient chaos prior to overturn.