含分数阶阻尼器结构地震响应的直接数值求解  

Direct Numerical Solution of Seismic Response of Structures with Fractional Dampers

作　　者：廖宁 陈太聪[1,2] LIAO Ning;CHEN Taicong(South China University of Technology,School of Civil Engineering and Transportation,Guangzhou 510640,China;State Key Laboratory of Subtropical Building Science,Guangzhou 510640,China)

机构地区：[1]华南理工大学土木与交通学院,广州510640 [2]亚热带建筑科学国家重点实验室,广州510640

出　　处：《华南地震》2021年第2期105-112,共8页South China Journal of Seismology

基　　金：亚热带建筑科学国家重点实验项目(2017KB13)。

摘　　要：分数阶导数模型可以全面地反映粘弹性阻尼器的力学性能和变化机制,但其中的Riemann-Liouville积分复杂,给减震结构的动力响应求解带来一定的困难。传统分析方法仅考虑结构基频的影响,通过等效刚度和等效阻尼简化结构响应计算,计算结果精度有限。针对含分数阶导数粘弹性阻尼器的减震结构,通过引入Caputo分数阶导数及相关高阶预估-校正技术,提出一种高精度的动力响应直接数值解法。通过多层结构算例,检验本文算法的有效性,对比考察了传统等效方法在不同简谐激励及El Centro地震波作用下的相关计算偏差。The fractional derivative model can fully represent the mechanical properties and the changing mechanism of viscoelastic dampers,however,the Riemann-Liouville integral involved is complex,which brings difficulties to the solution of dynamic structural responses.The conventional method often takes the fundamental natural frequency of the structure into account to obtain the equivalent stiffness and damping provided by the damper,which can simplify the solution while provides results with limited accuracy.In this paper,a high-precision numerical method to directly solve dynamic responses is proposed by introducing the Caputo fractional derivative and a corresponding high-order predictor-corrector algorithm.The effectiveness of the proposed method is verified via a numerical example of a multi-story structure,and comparisons with the conventional equivalent method are carried out to identify the relative errors of dynamic responses under different harmonic excitations and the EI Centro seismic wave.

关 键 词：粘弹性阻尼器 分数阶导数 Riemann-Liouville积分 CAPUTO导数 预估-校正法 

分 类 号：O328[理学—一般力学与力学基础]