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Dynamical reliability of internally resonant or non-resonant strongly nonlinear system under random excitations

机译：随机激励下内部共振或非共振强非线性系统的动力可靠性

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摘要

The dynamical reliability of multi-degrees-of-freedom (MDOF) strongly nonlinear system under Gaussian white noise excitations is studied, including resonance and nonresonance. Firstly, the equations of motion of the original system with or without internal resonance are reduced to a set of Ito stochastic differential equations after stochastic averaging. Then, the backward Kolmogorov equation and the Pontryagin equation associated with the resonantly or non-resonantly averaged Ito stochastic differential equations, which determine the conditional reliability function and the mean first-passage time of the original random system, are constructed under appropriate boundary and (or) initial conditions, respectively. In particular, if the non-resonantly averaged system is completely decoupled, the conditional reliability function and the mean first-passage time of the original nonresonant system can be obtained by solving a set of simplified backward Kolmogorov equations. A system comprising two weakly coupled and strongly nonlinear mechanical oscillators is given as a concrete example to show the application of the proposed method. The 1:1 internal resonance or non-resonance is discussed. The corresponding high-dimensional backward Kolmogorov equation and Pontryagin equation are established and solved numerically. All theoretical results are validated by a Monte Carlo digital simulation. (C) 2018 Elsevier Ltd. All rights reserved.
机译：研究了高斯白噪声激励下的多自由度（MDOF）强非线性系统的动力可靠性，包括共振和非共振。首先，经过随机平均后，带有或不带有内部共振的原始系统的运动方程都简化为一组伊藤随机微分方程。然后，在适当的边界下构造与共振或非共振平均Ito随机微分方程相关的反向Kolmogorov方程和Pontryagin方程，它们确定了原始随机系统的条件可靠性函数和平均首次通过时间，并且（或）初始条件。特别是，如果非共振平均系统完全解耦，则可以通过求解一组简化的后向Kolmogorov方程来获得原始非共振系统的条件可靠性函数和平均首次通过时间。作为一个具体示例，给出了一个包含两个弱耦合和强非线性机械振荡器的系统，以说明所提出方法的应用。讨论了1：1内部共振或非共振。建立并求解了相应的高维向后Kolmogorov方程和Pontryagin方程。所有的理论结果均由Monte Carlo数字仿真验证。 （C）2018 Elsevier Ltd.保留所有权利。

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