基于多步恢复力反馈的实时混合试验Runge-Kutta算法

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英文篇名：Runge-Kutta algorithm behind real-time hybrid test based on multistep restoring forces feedback 作者：孟丽岩 ; 王涛 ; 韩木逸 ; 曾聪 英文作者：Meng Liyan;Wang Tao;Han Muyi;Zeng Cong;School of Civil Engineering,Heilongjiang University of Science & Technology;Institute of Engineering Mechanics,China Earthquake Administration;Architectural Design & Research Institute of HIT;Institute of Civil Engineering & Architecture,Northeast Electrical Power University; 关键词：混合试验 ; Runge-Kutta算法 ; 稳定性 ; 精度 ; 多步恢复力反馈 英文关键词：hybrid testing;;Runge-Kutta algorithm;;stability;;accuracy;;multistep restoring forces feedback 中文刊名：HLJI 英文刊名：Journal of Heilongjiang University of Science and Technology 机构：黑龙江科技大学建筑工程学院;中国地震局工程力学研究所;哈尔滨工业大学建筑设计研究院;东北电力大学建筑工程学院; 出版日期：2019-03-30 出版单位：黑龙江科技大学学报 年：2019 期：v.29;No.130 基金：黑龙江省省属高等学校基本科研业务费科研项目(2017);; 黑龙江省青年科学基金项目(QC2013C055) 语种：中文; 页：HLJI201902020 页数：9 CN：02 ISSN：23-1588/TD 分类号：112-120

摘要

为提高显式数值积分在慢速及实时混合试验中的精度,采用经典Runge-Kutta(RK)算法求解结构运动方程。针对单自由度线性体系,采用放大矩阵谱半径的方法分析RK算法的稳定性和精度。提出单步恢复力反馈法(SRK)和多步恢复力反馈法(MRK)两种RK算法在实时混合试验中的实现方法,并分别对单自由度线性结构和多自由非线性结构开展混合试验数值仿真。结果表明,与传统中心差分法和实时中心差分法相比,RK算法具有更高的稳定性界限和精度。随着阻尼比的增大,RK算法稳定界限呈波动变化趋势,整体稳定界限保持在2.6~3.0;当Ω为0~0.75时,算法数值阻尼比和周期失真率接近于零。随着试验子结构刚度增加,单步恢复力反馈法计算精度急剧降低,多步恢复力反馈法继承了经典RK算法优良的数值性能,具有较高的计算精度。
        This paper seeks to achieve a higher accuracy of explicit numerical integration in the slow and real-time hybrid test by solving structural motion equations using the classical Runge-Kutta( RK) algorithm. The study describes the analysis of the stability and the accuracy of the RK algorithm for a linear single-degree-of-freedom system using the method of amplifying the spectral radius of matrix,the proposed application of the two algorithms,single restoring force feedback method( SRK) and multi-step restoring force feedback method( MRK),in real-time hybrid experiments,and the subsequent numerical simulation of hybrid experiment involving single-degree-of-freedom linear structure and multi-degree-offreedom non-linear structure. The results show that the RK algorithm features a higher stability boundary and accuracy than both the conventional center difference method( CDM) and the real-time center difference method( RCDM). The RK algorithm exhibits a more volatile stability boundary due to an increasing damping ratio,with the whole stability boundary ranging from 2. 6 to 3. 0 In the case Ω ranging between0 and 0. 75,both numerical damping ratios and period distortion of the RK algorithm are close to zero.Along with an increase in the stiffness of the substructure comes a sharp decrease in the calculation accuracy of the single restoring force feedback method and the MRK method owes its higher accuracy to the inheritance of the excellent numerical performance of the classic RK algorithm.

引文

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