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

LI Chuangdi; CHEN Mingjie; GE Xinguang

doi:10.21656/1000-0887.410151

Volume 42 Issue 3

Mar. 2021

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LI Chuangdi, CHEN Mingjie, GE Xinguang. A Simple Closed Response Solution to Random Ground Motion for Exponential Non-Viscous-Damping Structures Based on the Clough-Penzien Spectrum Excitation[J]. Applied Mathematics and Mechanics, 2021, 42(3): 282-291. doi: 10.21656/1000-0887.410151

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

doi: 10.21656/1000-0887.410151

School of Civil Engineering & Architecture, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, P.R.China

Funds: The National Natural Science Foundation of China（51468005）

Received Date: 2020-05-26
Rev Recd Date: 2020-06-14
Publish Date: 2021-03-01

Abstract

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.
- non-viscous damping,
- filtering equation,
- convolution,
- spectral moment,
- concise closed solution

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References(19)

References

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