非一致地震激励的改进位移输入法：误差分析与应用

PDF(1502 KB)

振动与冲击 ›› 2022, Vol. 41 ›› Issue (16) : 85-92.

论文

李宁1,2，陈浩1，李忠献1,2

作者信息 +

An improved displacement input method for non-uniform seismic excitation: error analysis and application

LI Ning1,2，CHEN Hao1，LI Zhongxian1,2

Author information +

文章历史 +

摘要

非一致激励其破坏性效应复杂，大跨结构地震反应计算时应合理考虑其影响。本文针对位移输入法（displacement input method ,DIM）计算大跨结构非一致地震响应时存在的误差和来源展开研究。采用Rayleigh阻尼假定，分析了某长跨桥梁结构的地震反应及误差，指出了DIM对不同地震动效应的适用性和误差产生的原因。而后讨论了差动激励的常用算法和模拟理论的差异，最后提出了改进的位移输入法（improved displacement input method ,IDIM），并进行了验证。结果表明：DIM用于求解大跨结构的非一致地震响应时存在不可忽略的误差，其大小与输入的地震动特性和刚度比例阻尼系数β相关，且随着β的增大而增大。DIM误差来源于忽略了阻尼项（与地震动增量速度和β相关）；通过2种IDIM与已有方法对比可知，DIM对于脉冲地震动作用和β较大的情形（较长自振周期）不再适用；本文提出的IDIM对于多点激励结构反应计算精度好、算法易用且可靠。最后建议了通用的非一致地震激励结构反应分析流程，考虑了近断层效应、残余位移等并最小化了大刚度、大质量法的舍入误差，研究成果可推广用于大型结构非一致激励的动力响应计算。
关键词：非一致激励；位移输入法；多维多点；误差分析；Rayleigh阻尼

Abstract

The potential damage effects of spatial seismic ground motions are leading to complicated structure response. They should be considered reasonably in seismic response calculation. In this study, the errors and sources of the displacement input method (DIM) in the calculation of non-uniform seismic response of long-span structures are studied. Considering Rayleigh damping, the seismic responses and errors from different calculation methods for the long-span bridge structure are analyzed. The applicability of DIM under the influence of different types of ground motions were tested, and the reasons for the errors are given. Then, the difference between commonly used multi-point excitation input algorithms and simulation theory is discussed. Finally, the improved displacement input method (IDIM) is proposed and verified. The results showed that when DIM is used to solve the non-uniform seismic response of long-span structures, there is an error that cannot be ignored. The magnitude of error is related to the characteristics of input ground motion and the stiffness proportional damping coefficient, β. And it increases with the increase of β. DIM error comes from neglecting the damping term of (which is related to the incremental velocity of ground motion and β). By comparing with the existing methods, DIM is no longer suitable for the cases of pulse-like ground motions and large β (long natural period). Further, the IDIM proposed are of good accuracy, easy to implemented and reliable for structure analysis subjected to multi-support excitation. At last, a general flow chart of structural response analysis under non-uniform seismic excitation is proposed, which takes pulse effect and residual displacement into account and avoids the rounding error of large stiffness and large mass methods. The research results can be applied to dynamic response analysis of large structures subjected to non-uniform seismic excitations.
Keywords: non-uniform excitation; displacement input method; multi-point multi-dimension; error analysis; Ray-leigh damping

导出引用

李宁1,2，陈浩1，李忠献1,2. 非一致地震激励的改进位移输入法：误差分析与应用[J]. 振动与冲击, 2022, 41(16): 85-92

LI Ning1,2，CHEN Hao1，LI Zhongxian1,2. An improved displacement input method for non-uniform seismic excitation: error analysis and application[J]. Journal of Vibration and Shock, 2022, 41(16): 85-92

参考文献

[1] 李忠献, 黄信. 行波效应对深水连续刚构桥地震响应的影响[J]. 工程力学, 2013, 30(3): 120-125.
Li Zhongxian, Huang Xin. Influence of traveling wave effect on seismic responses of continuous rigid-frame bridge in deep water[J]. Engineering Mechanics, 2013, 30(3): 120-125. (in Chinese)
[2] Wilson E L. Static and Dynamic Analysis of Structures: A physical Approach with Emphasis on Earthquake Engineering [M]. Berkley, California: Computers and Structures, Inc, 2004.
[3] 田玉基，杨庆山. 地震地面运动作用下结构反应的分析模型[J]. 工程力学，2005，22(6): 170-174.
Tian Yuji, Yang Qingshan. Analysis models and methods for structure seismic responses [J]. Engineering Mechanics, 2005, 22(6): 170-174. (in Chinese)
[4] 杜宪亭, 夏禾, 余竹. 桥梁抗震分析中的激励输入模式研究[J]. 铁道学报, 2011, 33(10): 86-90.
Du Xianting, Xia He, Yu Zhu. Study on input patterns of ex-citation in bridge aseismatic analysis[J]. Journal of the China railway society, 2011, 33(10): 86-90. (in Chinese)
[5] 柳国环, 李宏男, 国巍. 求解结构地震响应位移输入模型存在的问题及其AMCE实效对策[J]. 计算力学学报, 2009, 26(6): 862-869.
Liu Guohuan, Li Hongnan, Guo Wei. Existing problem of displacement input model for calculating structural responses under earthquake ground motion and its an actual effective solution method called AMCE[J]. Chinese Journal of Computational Mechanics, 2009, 26(6): 862-869. (in Chinese)
[6] 柳国环, 李宏男, 国巍等求解结构地震响应位移输入模型中存在问题的一种新解决办法[J]. 工程力学, 2010, 27(9): 55-62.
Liu Guohuan, Li Hongnan, Guo Wei, et al. A new method for solving problem of current displacement input model for calculating structural seismic responses [J]. Engineering Mechanics, 2010, 27(9): 55-62. (in Chinese)
[7] 罗超, 楼梦麟, 桂国庆. 大跨度结构多点地震反应计算方法的比较[J]. 同济大学学报(自然科学版), 2015, 43(1): 8-15.
Luo Chao, Lou Menglin, Gui Guoqing. Comparison for cal-culation methods of longspan structure under multi-support seismic excitation[J]. Journal of Tongji University (Natural Science), 2015, 43(1): 8-15. (in Chinese)
[8] 柳国环, 练继建, 赵悦. 非经典阻尼的位移输入模型和多点反应谱注记[J]. 哈尔滨工业大学学报, 2014, 46(6): 79-85.
Liu Guohuan, Lian Jijian, Zhao Yue. Notes on displacement input model and multi-supported response spectrum of non-classical damping[J] Journal of Harbin Institute of Technol-ogy, 2014, 46(6): 79-85. (in Chinese)
[9] 李永华, 卓平山, 胡远辉. 多点激励下绝对位移直接求解法算法的误差频域分析[J]. 振动与冲击, 2012, 31(12): 112-119.
Li Yonghua, Zhuo Pingshan, Hu Yuanhui. Error analysis of seismic response obtained by directly solving absolute dis-placement in frequency domain under multi-support earth-quake excitations[J]. Journal of Vibration and Shock, 2012, 31(12): 112-119. (in Chinese)
[10] 惠迎新, 王克海, 何文杰. 跨断层桥梁非一致激励输入模型适用性研究[J]. 建筑科学与工程学报, 2016, 33(5): 100-107.
Hui Yingxin, Wang Kehai, He Wenjie. Applicability research on multi-support excitation input model of bridges crossing fault[J]. Journal of Architecture and Civil Engineering, 2016, 33(5): 100-107.
[11] 国巍, 余志武, 柳国环, 等. 大跨隔震结构多点地震计算模型的几点注记[J]. 哈尔滨工业大学学报, 2013, 45(10): 86-92+99.
Guo Wei, Yu Zhiwu, Liu Guohuan, et al. Notes about calcu-lation models for seismic analysis of long-span isolated structure under multi-point earthquake excitations [J]. Journal of Harbin Institute of Technology, 2013, 45(10): 86-92+99. (in Chinese)
[12] Kircher, CA, Haselton, CB, and Deierlein, GG. Overview of Ground Motions, ATC-63 Project [C]//COSMOS Annual Meeting, November 17, 2006, Berkeley, CA.
[13] Kim Y W, Jhung M J. A Study on large mass method for dynamic problem of multiple degree-of-freedom system ex-cited by ground acceleration time history [J]. Journal of Me-chanical Science and Technology, 2014, 28(1): 25-41.
[14] 闫晓宇, 李忠献, 韩强, 等. 多点激励下大跨度连续刚构桥地震响应振动台阵试验研究[J]. 土木工程学报, 2013, 46(7): 81-89.
Yan Xiaoyu, Li Zhongxian, Han Qiang, et, al. Shaking tables test study on seismic responses of a long-span rigid-framed bridge under multi-support excitation [J]. China Journal Civil Engineering, 2013, 46(7): 81-89. (in Chinese)
[15] 张超, 巫生平. 非一致激励对三塔自锚式悬索桥地震响应的影响[J]. 振动与冲击, 2015，34(2):197-203.
ZHANG Chao, WU Shengping. Effects of non-uniformexcitation on seismic responses of a three-tower self-anchored suspension bridge[J]. Journal of Vibration and Shock, 2015, 34(2) : 197-203. (in Chinese)