基于Clough-Penzien谱激励的指数型非黏滞阻尼结构随机地震动响应简明封闭解

A Simple Closed Response Solution to Random Ground Motion for Exponential Non-Viscous-Damping Structures Based on the Clough-Penzien Spectrum Excitation

非黏滞阻尼模型相比传统黏滞阻尼模型能更准确描述结构材料的耗能行为,其本构关系常用核函数为指数函数的卷积形式表示.针对目前非黏滞阻尼结构的随机地震动响应分析方法所得结果较为复杂,该文提出了一种基于Clough-Penzien(C-P)谱的结构响应0~2阶谱矩分析的简明封闭解法.该方法首先提出非黏滞阻尼结构的精确等效微分本构关系式,并利用其与C-P谱滤波微分方程重构了结构的地震动方程;再基于随机振动理论获得了结构随机响应0~2阶谱矩的简明封闭解,并基于得到的0~2阶谱矩采用首次超越破坏准则和Markov分布规则进行了结构动力可靠度分析;最后通过算例论证了该简明封闭解的准确性及高效性.

Compared with the traditional viscous damping model,the non-viscous-damping model can more accurately describe the energy dissipation behavior of structural materials,and its constitutive relationship is usually expressed in the form of convolution of exponential functions.In view of the complexity of the response to random ground motion obtained with the existent methods for structures with non-viscous damping,a simple closed-solution method for the analysis of 0~2nd-order spectral moments of structural responses was proposed based on the Clough-Penzien(C-P)spectrum.With this method,the exact equivalent differential constitutive relation of non-viscous-damping structures was first proposed and the ground motion equation of the structure was reconstructed with the C-P spectrum filtering differential equation.Then,based on the random vibration theory,the concise closed solution of the 0~2nd-order spectral moments of the structural random responses was obtained.Accordingly,the dynamic reliability of the structure was analyzed under the first excursion criterion and the Markov distribution rule.Finally,an example was given to demonstrate the accuracy and efficiency of the closed solution.