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本文用振型分解法提出了一种分析线性串联多自由度体系在任意(可分离和不可分离的)非平稳随机地震干扰下的动力可靠性的解析方法。文中首先对受任意非平稳随机干扰的线性串联多自由度体系利用振型分解法求出了体系质点相对位移和速度反应的联合概率密度函数。在首通机制下,利用随机点理论和级数解法导出了各质点相对位移的可靠性函数级数解的一般表达式;在Poisson界限交差假设下,简化了可靠性函数的一般表达式。进一步,以“最弱链环”模型为基础,提出了串联多自由度体系受任意非平稳随机干扰的动力可靠性计算的理论方法。其次,通过把地震地面运动加速度模拟为Iyengar型可分离非平稳高斯随机过程,分析了受这种非平稳随机地震干扰的线性串联多自由度体系的反应,求出了计算体系可靠性所需要的反应统计量的半解析表达式。最后,利用忽奈姆港和加里福尼亚韦尔农的地震随机模型,对两层剪切型框架求出了动力可靠性的数字结果,并与模拟结果进行了比较。
In this paper, an analytical method for analyzing the dynamic reliability of a linear series multi-degree-of-freedom system under arbitrary (separable and inseparable) non-stationary random seismic disturbances is proposed using the mode-decomposition method. In this paper, we first use the mode decomposition method to determine the joint probability density function of relative displacement and velocity response of a system of linearly concatenated multi-degrees of freedom subjected to any non-stationary random disturbance. Under the first-pass mechanism, the general expressions of the series of reliability function relative to the displacement of each particle are derived using the random point theory and the series solution method. Under the Poisson boundary intersection assumption, the general expression of the reliability function is simplified. Further, based on the “weakest link” model, a theoretical method for calculating the dynamic reliability of series multi-degree-of-freedom systems subjected to arbitrary non-stationary random disturbances is proposed. Secondly, by simulating the seismic ground motion acceleration as a Iyengar-type separable nonstationary Gaussian stochastic process, the response of the linear series multi-degree-of-freedom system subjected to this non-stationary random seismic disturbance is analyzed, and the required reliability of the computational system is obtained. Semi-analytic expression of response statistics. Finally, using the seismic random model of Port Hunerm and Vernon, California, the numerical results of dynamic reliability were obtained for the two-layer shear frame and compared with the simulation results.