Nonlinear Rocking Motions. II: Overturning under Random Excitations
Nonlinear Rocking Motions. II: Overturning under Random Excitations
复制标题
非线性摇摆运动。
DOI：
10.1061/(asce)0733-9399(1996)122:8(728
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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
作者从完全概率的角度研究了刚性物体在任意相对强度的确定性和随机性联合激励下的摇摆响应。推导了相应的Fokker-Planck方程，并用路径积分解技术对其进行数值求解，得到了联合概率密度函数。JPDF的演化和稳态被用来阐明摇摆响应的全局行为。如文中所述，数值结果验证了随机激励的存在跨越了共存响应的吸引域，并且倾覆吸引子具有最大的相对稳定性。因此，在随机激励的影响下，所有靠近异宿轨道的摇摆响应轨迹最终都会发生翻转。概率从“安全”域迅速泄漏到倾覆区域意味着混沌吸引子的弱稳定性。以平均首次通过时间为性能指标，考察了摇摆响应对系统参数的敏感性和随机激励的(非)平稳性。
The authors examine the rocking responses of rigid objects under combined deterministic and stochastic excitations of arbitrary relative intensities from a fully probabilistic viewpoint. The associated Fokker-Planck equation is derived and solved numerically by a path-integral solution technique to obtain the joint probability density functions (JPDFs). The evolutions and the steady states of the JPDFs are used to clarify the global behavior of the rocking responses. As noted in a companion paper, numerical results verify that the presence of stochastic excitation bridges the domains of attraction of coexisting responses, and that overturning attractors are of the greatest relative stability. Thus, all rocking response trajectories that come near the heteroclinic orbit eventually overturn under the influence of stochastic excitation. A rapid leakage of the probability out of the "safe" domain to the overturning regime implies weak stability of the chaotic attractor. Sensitivity of rocking responses to system parameters and (non)stationarity of the stochastic excitation, based on mean first-passage time as a performance index, are also examined.