土层地震反应显式计算中阻尼矩阵系数的选取
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摘要
针对LS-DYNA程序关于土层地震反应显式计算中形成阻尼矩阵的方法开展讨论.首先,讨论了采用质量比例阻尼矩阵假定对各阶振型阻尼比带来的影响;然后分别应用时域和频域分析方法对三种不同类型土层的地震反应进行计算,通过比较时域和频域的计算结果,探讨了采用质量比例阻尼矩阵假定对计算结果的影响;最后,对质量比例阻尼系数的确定提出了建议:当仅计算土层地震位移反应或当土层基频高于下卧基岩输入地震波的主要激励频率条件下计算土层地震加速度反应时,以目前由土层基频计算质量比例阻尼系数的方法是可行的;但当土层基频接近于,特别是远低于输入地震波的主要激励频率时,应用土层基频和输入地震波反应谱峰值频率的算术平均值替代土层基频计算质量比例阻尼系数,可有效提高土层地震加速度计算精度.
A study was made of the method for forming damping matrix in explicit algorithm of LS-DYNA in the analysis of seismic response of soil layer.First,based on the assumption of mass-proportional damping matrix,the influence on the damping ratio of each mode was discussed.Then the analysis methods of time domain and frequency domain were applied to the seismic response calculation of three different types of soil layer.Through the comparison of calculation results between time domain and frequency domain,the effects on calculation results by using mass-proportional damping matrix were explored.Finally,the determination of damping coefficients of the mass-proportional was proposed.Only when the seismic displacement reaction of soil layer is calculated or when the fundamental frequency of soil layer is higher than the input seismic wave excitation frequency of the under lying bedrock to calculate the soil seismic acceleration response,it is feasible to apply the fundamental frequency of soil layer to determine the mass-proportional damping coefficient.When the fundamental frequency is close to and especially much lower than the excitation frequency of input seismic wave,substituting the arithmetic mean of soil layer fundamental frequency and response spectrum peak frequency of input seismic wave for the soil layer fundamental frequency is recommended to calculate the mass-proportional damping coefficient.This method can effectively improve the calculation accuracy.
A study was made of the method for forming damping matrix in explicit algorithm of LS-DYNA in the analysis of seismic response of soil layer.First,based on the assumption of mass-proportional damping matrix,the influence on the damping ratio of each mode was discussed.Then the analysis methods of time domain and frequency domain were applied to the seismic response calculation of three different types of soil layer.Through the comparison of calculation results between time domain and frequency domain,the effects on calculation results by using mass-proportional damping matrix were explored.Finally,the determination of damping coefficients of the mass-proportional was proposed.Only when the seismic displacement reaction of soil layer is calculated or when the fundamental frequency of soil layer is higher than the input seismic wave excitation frequency of the under lying bedrock to calculate the soil seismic acceleration response,it is feasible to apply the fundamental frequency of soil layer to determine the mass-proportional damping coefficient.When the fundamental frequency is close to and especially much lower than the excitation frequency of input seismic wave,substituting the arithmetic mean of soil layer fundamental frequency and response spectrum peak frequency of input seismic wave for the soil layer fundamental frequency is recommended to calculate the mass-proportional damping coefficient.This method can effectively improve the calculation accuracy.
引文
[1]廖振鹏.近场波动问题的有限元解法[J].地震工程与工程振动,1984,4(2):1.LIAO Zhenpeng.A finite element method for near-field wavemotion in heterogeneous materials[J].Earthquake Engineeringand Engineering Vibration,1984,4(2):1.
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[4]张汝清,殷学纲,董明.计算结构动力学[M].重庆:重庆大学出版社,1987.ZHANG Ruqing,YIN Xuegang,DONG Ming.Computationalstructural dynamics[M].Chongqing:Chongqing UniversityPress,1987.
[5]李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].地震工程与工程振动,1992,12(4):75.LI Xiaojun,LIAO Zhenpeng,DU Xiuli.An explicit finitedifference method for viscoelastic dynamic problem[J].Earthquake Engineering and Engineering Vibration,1992,12(4):75.
[6]杨柏坡,陈庆彬,王琦萍.地震波动研究中的显式有限元法[C]//第三届全国地震工程会议论文集.大连:大连理工大学出版社,1990:211-216.YANG Baipo,CHEN Qingbin,WANG Qiping.An explicit finiteelement method of the seismic wave study[C]//Proceedings ofthe Third National Conference on Earthquake Engineering.Dalian:Dalian University of Technology Press,1990:211-216.
[7]尚晓江,苏建宇,王化峰.ANSYS/LS-DYNA动力分析方法与工程实例[M].北京:中国水利水电出版社,2008.SHANG Xiaojiang,SU Jianyu,WANG Huafeng.ANSYS/LS-DYNA dynamic analysis method and projects[M].Beijing:ChinaWater&Power Press,2008.
[8]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:自然科学版,2004,32(3):281.LOU Menglin,PAN Danguang.Hysteretic damping applicationin time domain analysis of soil layer[J].Journal of TongjiUniversity:Natural Science,2004,32(3):281.
[9]Clough R W,Penzien J.Dynamics of structures[M].NewYork:Mc-Graw Hill Inc,1993.
[2]Martin P P,Seed H B.One-dimensional dynamic groundresponse analyses[J].Journal of Geotechnical EngineeringDivision,ASCE,1982,108(7):935.
[3]李小军,廖振鹏,关慧敏.粘弹性场地地形对地震动影响分析的显式有限元-有限差分方法[J].地震学报,1995,17(3):362.LI Xiaojun,LIAO Zhenpeng,GUAN Huimin.An explicit finiteelement-finite difference method for analyzing the effect ofvisco-elastic Local topograph on the earthquake motion[J].ActaSeismologica Sinica,1995,17(3):362.
[4]张汝清,殷学纲,董明.计算结构动力学[M].重庆:重庆大学出版社,1987.ZHANG Ruqing,YIN Xuegang,DONG Ming.Computationalstructural dynamics[M].Chongqing:Chongqing UniversityPress,1987.
[5]李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].地震工程与工程振动,1992,12(4):75.LI Xiaojun,LIAO Zhenpeng,DU Xiuli.An explicit finitedifference method for viscoelastic dynamic problem[J].Earthquake Engineering and Engineering Vibration,1992,12(4):75.
[6]杨柏坡,陈庆彬,王琦萍.地震波动研究中的显式有限元法[C]//第三届全国地震工程会议论文集.大连:大连理工大学出版社,1990:211-216.YANG Baipo,CHEN Qingbin,WANG Qiping.An explicit finiteelement method of the seismic wave study[C]//Proceedings ofthe Third National Conference on Earthquake Engineering.Dalian:Dalian University of Technology Press,1990:211-216.
[7]尚晓江,苏建宇,王化峰.ANSYS/LS-DYNA动力分析方法与工程实例[M].北京:中国水利水电出版社,2008.SHANG Xiaojiang,SU Jianyu,WANG Huafeng.ANSYS/LS-DYNA dynamic analysis method and projects[M].Beijing:ChinaWater&Power Press,2008.
[8]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:自然科学版,2004,32(3):281.LOU Menglin,PAN Danguang.Hysteretic damping applicationin time domain analysis of soil layer[J].Journal of TongjiUniversity:Natural Science,2004,32(3):281.
[9]Clough R W,Penzien J.Dynamics of structures[M].NewYork:Mc-Graw Hill Inc,1993.
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