关于土层地震反应分析中阻尼矩阵建模方式的讨论
|
摘要
阻尼矩阵的选择对土层时域内地震反应计算的准确性有重要意义。本文构造了质量比例阻尼、刚度比例阻尼、Rayleigh阻尼、Caughey阻尼和Clough阻尼矩阵,研究各阻尼对土层地震反应分析精度的影响。以苏通大桥5号桥塔基础处的工程场地为例,分别以人工合成基岩波,Northridge波、Parkfield波和汶川波为输入,得到不同阻尼模型下土层的地震反应,结果表明Clough阻尼在计算精度和误差稳定性上要优于其他阻尼模型,针对Clough阻尼的不足之处提出了改进方法,算例表明改进后的Clough阻尼能在保证计算精度的前提下减少计算机的存储量和计算量。
Damping matrix is very important to accuracy of seismic ground response analysis in time domain. The damping matrices corresponding to mass-proportional damping,stiffness-proportional damping,Rayleigh damping,Caughey damping and Clough damping were constructed to study their influence on the accuracy of the seismic response analysis of the soil layer. Taking soil layerat No. 5 tower of Sutong bridge as an example,the seismic responses of the soil layer with different damping models were computed by using artificial bedrock waves,Northridge waves,Parkfield waves and Wenchuan waves as inputs. The results show that Clough damping can reduce error of seismic response analysis and improve error stability,and is superior to other damping models in computational accuracy and error stability. An improved method was proposed for the deficiency of Clough damping. The improved Clough damping can reduce the storage and computational quantity of the computer on the premise of ensuring the computational accuracy.
Damping matrix is very important to accuracy of seismic ground response analysis in time domain. The damping matrices corresponding to mass-proportional damping,stiffness-proportional damping,Rayleigh damping,Caughey damping and Clough damping were constructed to study their influence on the accuracy of the seismic response analysis of the soil layer. Taking soil layerat No. 5 tower of Sutong bridge as an example,the seismic responses of the soil layer with different damping models were computed by using artificial bedrock waves,Northridge waves,Parkfield waves and Wenchuan waves as inputs. The results show that Clough damping can reduce error of seismic response analysis and improve error stability,and is superior to other damping models in computational accuracy and error stability. An improved method was proposed for the deficiency of Clough damping. The improved Clough damping can reduce the storage and computational quantity of the computer on the premise of ensuring the computational accuracy.
引文
[1]楼梦麟,潘旦光.滞后阻尼在土层时域分析中的应用[J].同济大学学报,2004,32(3):281-285.LOU Menglin,PAN Danguang. Hysteretic damping application in time domain analysis of soil layer[J]. Journal of Tongji University,2004,32(3):281-285.(in Chinese)
[2]楼梦麟,殷琳.高土坝地震反应分析的阻尼讨论[J].水力发电学报,2009,28(5):103-107.LOU Menglin,YIN Lin. Discussion on damping models for seismic response analysis of high earth dams[J]. Journal of Hydroelectric Engineering,2009,28(5):103-107.(in Chinese)
[3]楼梦麟,邵新刚.土层地震反应显式计算中阻尼矩阵系数的选取[J].同济大学学报(自然科学版),2013,41(8):1126-1132.LOU Menglin,SHAO Xingang. Damping matrix coefficient selection in explicit calculation of soil layer seismic response[J]. Journal of Tongji University(National Science),2013,41(8):1126-1132.(in Chinese)
[4]楼梦麟,邵新刚.深覆盖土层Rayleigh阻尼矩阵建模问题的讨论[J].岩土工程学报,2013,35(7):1272-1279.LOU Menglin,SHAO Xingang. Discussion on modeling issues of Rayleigh damping matrix in soil layers with deep deposit[J]. Chinese Journal of Geotechnical Engineering,2013,35(7):1272-1279.(in Chinese)
[5]刘红石.相对误差与Rayleigh阻尼比例系数的确定[J].湖南工程学院学报,2001,11(3-4):36-38.LIU Hongshi. Relative error and determination of Rayleigh damping scale coefficient[J]. Journal of Hunan Institute of Engineering,2001,11(3-4):36-38.(in Chinese)
[6] Yang D B,Zhang Y G,Wu J Z. Computation of Rayleigh damping coefficients in seismic time-history analysis of spatial structures[J]. Journal of the International Association for Shell and Structures,2010,51(2):125-135
[7]潘旦光.地震反应分析中Rayleigh阻尼系数的优化解[J].工程力学,2013,30(11):15-20.PAN Danguang. An optimization solution for rayleigh damping coefficients in seismic response analysis[J]. Engineering Mechanics,2013,30(11):15-20.(in Chinese)
[8]王淮峰,楼梦麟,张如林.加权最小二乘法求解Rayleigh阻尼系数的讨论[J].计算力学学报,2017,34(5):603-607WANG Huaifeng,LOU Menglin,ZHANG Rulin. Discussion on weighted least-squares method for solving Rayleigh damping Coefficients[J]. Chinese Journal of Computational Mechanics,2017,34(5):603-607(in Chinese)
[9]殷琳.地下结构振动台模型试验与数值模拟[D].上海:同济大学,2012.YIN Lin. Shaking table model test of underground structure and numerical analysis[D]. Shanghai:Tongji University,2012.(in Chinese)
[10]潘旦光.地震反应分析中Caughey阻尼系数的优化解[J].固体力学学报,2015,36(3):264-275.PAN Danguang. Optimal solution of caughey damping coefficients in seismic response analysis[J]. Chinese Journal of Solid Mechanics,2015,36(3):264-275.(in Chinese)
[11] Enrique Luco J. A note on classical damping matrices[J]. Earthquake Engineering and Structural Dynamics,2008,37(4):615-626.
[12]董军,邓洪洲,王肇民.结构动力分析阻尼模型研究[J].世界地震工程,2000,16(4):63-69.DONG Jun,DEN Hongzhou,WANG Zhaomin. Studies on the damping models for structural dynamic time history analysis[J]. World Information on Earthquake Engineering,2006,16(4):63-69.(in Chinese)
[13]董云,楼梦麟.基于结构基频确定Rayleigh阻尼系数的优化方法及其讨论[J].湖南大学学报(自然科学版),2014,41(2):8-13.DONG Yun,LOU Menglin. An optimization solution for Rayleigh damping coefficients based on the fundamental frequency of structure[J]. Journal of Hunan University(Natural Science),2014,41(2):8-13.(in Chinese)
[14]楼梦麟.结构动力分析的子结构法[M].上海:同济大学出版社,1997:21.LOU Menglin. Substructure Method of Structure Dynamic Analysis[M]. Shanghai:Press of Tongji University,1997:21.(in Chinese)
[15]楼梦麟,李顺,潘曦.地震作用下大型桥梁高桩基础的运动特性[J].力学季刊,2012,33(2):281-289.LOU Menglin,LI Shun,PAN Xi. Motion characteristics of large-scale bridge pile foundation under earthquake[J]. Chinese Quarterly of Mechanics,2012,33(22):281-289.(in Chinese)
[16]邬都,楼梦麟.水平成层土层地震反应分析的一维有限元方法[J].震灾防御技术,2008,3(1):45-52.WU Du,Lou Menglin. Seismic response analysis in horizontal layer with 1-D finite element method[J]. Technology for Earthquake Disaster Prevention,2008,3(1):45-52.(in Chinese)
[2]楼梦麟,殷琳.高土坝地震反应分析的阻尼讨论[J].水力发电学报,2009,28(5):103-107.LOU Menglin,YIN Lin. Discussion on damping models for seismic response analysis of high earth dams[J]. Journal of Hydroelectric Engineering,2009,28(5):103-107.(in Chinese)
[3]楼梦麟,邵新刚.土层地震反应显式计算中阻尼矩阵系数的选取[J].同济大学学报(自然科学版),2013,41(8):1126-1132.LOU Menglin,SHAO Xingang. Damping matrix coefficient selection in explicit calculation of soil layer seismic response[J]. Journal of Tongji University(National Science),2013,41(8):1126-1132.(in Chinese)
[4]楼梦麟,邵新刚.深覆盖土层Rayleigh阻尼矩阵建模问题的讨论[J].岩土工程学报,2013,35(7):1272-1279.LOU Menglin,SHAO Xingang. Discussion on modeling issues of Rayleigh damping matrix in soil layers with deep deposit[J]. Chinese Journal of Geotechnical Engineering,2013,35(7):1272-1279.(in Chinese)
[5]刘红石.相对误差与Rayleigh阻尼比例系数的确定[J].湖南工程学院学报,2001,11(3-4):36-38.LIU Hongshi. Relative error and determination of Rayleigh damping scale coefficient[J]. Journal of Hunan Institute of Engineering,2001,11(3-4):36-38.(in Chinese)
[6] Yang D B,Zhang Y G,Wu J Z. Computation of Rayleigh damping coefficients in seismic time-history analysis of spatial structures[J]. Journal of the International Association for Shell and Structures,2010,51(2):125-135
[7]潘旦光.地震反应分析中Rayleigh阻尼系数的优化解[J].工程力学,2013,30(11):15-20.PAN Danguang. An optimization solution for rayleigh damping coefficients in seismic response analysis[J]. Engineering Mechanics,2013,30(11):15-20.(in Chinese)
[8]王淮峰,楼梦麟,张如林.加权最小二乘法求解Rayleigh阻尼系数的讨论[J].计算力学学报,2017,34(5):603-607WANG Huaifeng,LOU Menglin,ZHANG Rulin. Discussion on weighted least-squares method for solving Rayleigh damping Coefficients[J]. Chinese Journal of Computational Mechanics,2017,34(5):603-607(in Chinese)
[9]殷琳.地下结构振动台模型试验与数值模拟[D].上海:同济大学,2012.YIN Lin. Shaking table model test of underground structure and numerical analysis[D]. Shanghai:Tongji University,2012.(in Chinese)
[10]潘旦光.地震反应分析中Caughey阻尼系数的优化解[J].固体力学学报,2015,36(3):264-275.PAN Danguang. Optimal solution of caughey damping coefficients in seismic response analysis[J]. Chinese Journal of Solid Mechanics,2015,36(3):264-275.(in Chinese)
[11] Enrique Luco J. A note on classical damping matrices[J]. Earthquake Engineering and Structural Dynamics,2008,37(4):615-626.
[12]董军,邓洪洲,王肇民.结构动力分析阻尼模型研究[J].世界地震工程,2000,16(4):63-69.DONG Jun,DEN Hongzhou,WANG Zhaomin. Studies on the damping models for structural dynamic time history analysis[J]. World Information on Earthquake Engineering,2006,16(4):63-69.(in Chinese)
[13]董云,楼梦麟.基于结构基频确定Rayleigh阻尼系数的优化方法及其讨论[J].湖南大学学报(自然科学版),2014,41(2):8-13.DONG Yun,LOU Menglin. An optimization solution for Rayleigh damping coefficients based on the fundamental frequency of structure[J]. Journal of Hunan University(Natural Science),2014,41(2):8-13.(in Chinese)
[14]楼梦麟.结构动力分析的子结构法[M].上海:同济大学出版社,1997:21.LOU Menglin. Substructure Method of Structure Dynamic Analysis[M]. Shanghai:Press of Tongji University,1997:21.(in Chinese)
[15]楼梦麟,李顺,潘曦.地震作用下大型桥梁高桩基础的运动特性[J].力学季刊,2012,33(2):281-289.LOU Menglin,LI Shun,PAN Xi. Motion characteristics of large-scale bridge pile foundation under earthquake[J]. Chinese Quarterly of Mechanics,2012,33(22):281-289.(in Chinese)
[16]邬都,楼梦麟.水平成层土层地震反应分析的一维有限元方法[J].震灾防御技术,2008,3(1):45-52.WU Du,Lou Menglin. Seismic response analysis in horizontal layer with 1-D finite element method[J]. Technology for Earthquake Disaster Prevention,2008,3(1):45-52.(in Chinese)