旗帜型滞迟系统的首次穿越失效研究

First-passage failure of SDOF flag-shaped self-centering system

自复位结构作为一种新型的抗震结构模型受到广泛关注,但这类结构的随机振动问题是技术上的难点,而首次穿越失效作为结构可靠性分析的一个重要模型,则属于非线性随机振动研究中最为困难的问题之一。本文针对随机地震激励下旗帜型滞迟系统的首次穿越失效问题。将旗帜型自复位恢复力在广义谐波平衡技术下应用,近似为幅值相关的等效阻尼和等效刚度组合,从而推导出系统运动方程的等效系统;利用随机平均原理导出关于幅值的平均It?微分方程;采用有限差分法并结合适当的边界条件和初始条件,求解与上述方程对应的后向Kolmogorov(BK)方程,得到首次穿越时间的条件概率密度函数和条件可靠度函数。作为算例,分别讨论了两种随机地震激励模型作用时,系统参数对条件可靠性函数与首次穿越时间的条件概率密度函数的影响。另外,通过与对原方程的蒙特卡罗模拟数据的对比,验证了理论解的有效性。

The self-centering structure is a new type of seismic structural model in recent years, while the corresponding random vibration problem of this kind of structures has been fallen into some technical challenges.The first-passage failure, as an important model of structural reliability analysis, belongs to one of the most difficult problems in the field of nonlinear random vibration. In this paper, the first-passage failure of flag-shaped hysteresis structure under stochastic earthquake excitation is investigated. By applying the technique of generalized harmonic balance, the self-centering restoring force is approximated as the combination of amplitude dependent equivalent damping and equivalent stiffness, and the equivalent random system of motion equation is obtained. Based on the principle of stochastic averaging, the averaged It?equation for amplitude is derived. The Backward Kolmogorov(BK) equation associated with the averaged It?equation is established, and then solved to obtain the conditional probability density function of first-passage time and the conditional reliability function by the finite difference method together with suitable initial and boundary conditions. For illustration, the influence of parameters in case of the system subjected to two different models of random seismic excitations is examined,respectively. In addition, the data obtained with Monte Carlo simulation is applied to validate the theoretical solutions.