Nonlinear impact and chaotic response of slender rocking objects
Nonlinear impact and chaotic response of slender rocking objects
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细长摇摆物体的非线性冲击和混沌响应
DOI：
10.1061/(asce)0733-9399(1991)117:9(2079
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
Huan Lin
中科院分区：
文献类型：
--
作者：
S. Yim;Huan Lin
本研究的重点是与冲击相关的非线性对受水平基础激励的独立刚性物体的摇摆响应行为的影响。其目的是确定使摇摆响应难以预测的原因，以及使过去具有相同设置和激励的实验无法重复的原因。研究的影响非线性包括：(1)控制方程的过渡；(2)角速度的突然减小与底部的撞击有关。除了周期响应和翻转响应外，本研究还发现了两种新的（有界）响应类型——拟周期响应和混沌响应。提出了一种基于Melnikov函数解析预测混沌响应存在性的近似方法。采用现代几何和数字识别技术。数值结果验证了该方法的准确性。这种关系是……
This investigation focuses on the influence of nonlinearities associated with impact on the behavior of the rocking response of free‐standing rigid objects subjected to horizontal base excitations. The object is to identify the causes that make the rocking response difficult to predict and that have made past experiments with identical setups and excitations unrepeatable. The impact nonlinearities examined are: (1) The transition of governing equations; and (2) the abrupt reduction in angular velocity associated with impact at the base. In addition to the periodic and overturning responses, the existence of two new types of (bounded) response not previously revealed in literature—quasi‐periodic and chaotic are discovered in this study. An approximate method based on the Melnikov function to analytically predict the existence of chaotic response is derived. Modern geometric and numerical identification techniques are employed. The accuracy of the method is assessed by numerical results. The relationship be...