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

Abstract

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.