基于统计线性化的非线性随机振动虚拟激励法研究及应用
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摘要
传统的虚拟激励法成功地解决了结构线性随机地震响应计算效率低的问题,却无法将非线性因素考虑在内。以统计线性化理论为基础,提出了一种可以考虑结构非线性的改进的绝对位移直接求解的虚拟激励法,采用不同的抗震分析方法,对一座单塔双索面预应力混凝土斜拉桥进行位移、速度、加速度功率谱密度以及位移、轴力响应值的计算,并进行对比分析,结果表明所提出改进的虚拟激励法不仅可以考虑结构的非线性,而且精确、高效,可以广泛地应用于桥梁工程的抗震分析中。
The traditional pseudo excitation method successfully solved the problem in low efficiency in calculation of linear structure's seismic random response,but it cannot take nonlinearity into account.Based on statistical linearization technique,a kind of improved pseudo excitation method was put forward,which can consider structure's nonlinearity and directly solve the absolute displacement.A prestressed concrete cable-stayed bridge with a single tower and double cables was taken as an example.The power spectral density of displacement,velocity and acceleration,and the responses of displacement and axial force were calculated using different seismic analysis methods.Through the comparative analysis,the results show that the improved pseudo excitation method can not only consider the structure's nonlinearity,but also has high accuracy and efficiency.It can be widely used in bridge's seismic analysis.
The traditional pseudo excitation method successfully solved the problem in low efficiency in calculation of linear structure's seismic random response,but it cannot take nonlinearity into account.Based on statistical linearization technique,a kind of improved pseudo excitation method was put forward,which can consider structure's nonlinearity and directly solve the absolute displacement.A prestressed concrete cable-stayed bridge with a single tower and double cables was taken as an example.The power spectral density of displacement,velocity and acceleration,and the responses of displacement and axial force were calculated using different seismic analysis methods.Through the comparative analysis,the results show that the improved pseudo excitation method can not only consider the structure's nonlinearity,but also has high accuracy and efficiency.It can be widely used in bridge's seismic analysis.
引文
[1]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004.
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[3]Abdullateef M A,Ashraf A.An efficient multi-point support-motion random vibration analysis technique[J].Computers&Structures,2002,80(8):1689-1697.
[4]Lin J H,Zhang Y H,Li Q S,et al.Seismic spatial effects for long-span bridges,using the pseudo excitation method[J].Engineering Structures,2004,26(9):1207-1216.
[5]Leper P,Ide I M,Paultre P.Multiple-support seismic analy-sis of large structures[J].Computers&Structures,1990,36(6):1153-1158.
[6]张笈玮.考虑地震空间效应的大跨度空间结构抗震分析与设计方法[D].天津:天津大学,2008.
[7]江洋.大跨建筑结构多点输入地震响应计算与抗震设计方法研究[D].北京:清华大学,2010.
[8]汪梦甫.非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法[J].计算力学学报,2008,25(1):94-99.WANG Meng-pu.Pseudo-excitation method for stationary random responses of non-proportionally damped MDOF sys-tems[J].Chinese Journal of Computational Mechanics,2008,25(1):94-99.
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[11]潘家强,多自由度非线性振动系统的统计线性化简化方程[J].浙江大学学报,1983,1(3):90-99.PAN Jia-qiang,Simplified statistical linearization equations of discrete nonlinear systems[J].Journal of Zhejiang Universi-ty,1983,1(3):90-99.
[12]Iwan W D,Yang I M.Application of statistical linearization technique to nonlinear multidegree-of-freedom systems[J].Transaction of the ASME-Journal of Applied Mechanics,1972,39(2):545-550.
[13]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185-190.LI Yong-hua,LI Si-ming.Pseudo excitation method based on solving absolute displacement[J].Journal of Vibration and Shock,2009,28(10):185-190.
[14]GB50011-2001.建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.GB50011-2001.Code for Seismic Design of Buildings[S].Beijing:China Architecture&Building Press,2001.
[15]石永久,江洋,王元清.直接求解法在结构多点输入地震响应计算中的应用与改进[J].工程力学,2011,28(1):75-81.SHI Yong-jiu,WANG Yang,WANG Yuan-qing.Application and improvement of direct solving method in seismic response analysis of structures under multi-support excitations[J].Journal of Engineering Mechanics,2011,28(1):75-81.
[16]Kiureghian A D,Neuenhofer A.Response spectrum method for multi-support seismic excitations[J].Earthquake Engi-neering&Structural Dynamics,1992,21(8):713-740.
[2]Ernesto H Z,Vanmarcke E H.Seismic random-vibrationanalysis of multisupport-structural systems[J].Journal ofEngineering Mechanics,1994,120(5):1107-1128.
[3]Abdullateef M A,Ashraf A.An efficient multi-point support-motion random vibration analysis technique[J].Computers&Structures,2002,80(8):1689-1697.
[4]Lin J H,Zhang Y H,Li Q S,et al.Seismic spatial effects for long-span bridges,using the pseudo excitation method[J].Engineering Structures,2004,26(9):1207-1216.
[5]Leper P,Ide I M,Paultre P.Multiple-support seismic analy-sis of large structures[J].Computers&Structures,1990,36(6):1153-1158.
[6]张笈玮.考虑地震空间效应的大跨度空间结构抗震分析与设计方法[D].天津:天津大学,2008.
[7]江洋.大跨建筑结构多点输入地震响应计算与抗震设计方法研究[D].北京:清华大学,2010.
[8]汪梦甫.非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法[J].计算力学学报,2008,25(1):94-99.WANG Meng-pu.Pseudo-excitation method for stationary random responses of non-proportionally damped MDOF sys-tems[J].Chinese Journal of Computational Mechanics,2008,25(1):94-99.
[9]唐国梁,姚昌仁.统计线性化方法及其计算机数值解[J].北京工业学院学报,1986,1(1):142-152.TANG Guo-liang,YAO Chang-ren.Statistical linearization technique and its computer numerical solution[J].Journal of Beijing University of Technology,1986,1(1):142-152.
[10]林建龙,卢翰庭.统计线性化方法在大型货车垂向振动分析中的应用[J].铁道学报,1990,12(3):1-7.LIN Jian-long,LU Han-ting.Research on application of the statistical linearization technique to analyzing the vertical vi-bration response of freight cars[J].Journal of the ChinaRailway Society,1990,12(3):1-7.
[11]潘家强,多自由度非线性振动系统的统计线性化简化方程[J].浙江大学学报,1983,1(3):90-99.PAN Jia-qiang,Simplified statistical linearization equations of discrete nonlinear systems[J].Journal of Zhejiang Universi-ty,1983,1(3):90-99.
[12]Iwan W D,Yang I M.Application of statistical linearization technique to nonlinear multidegree-of-freedom systems[J].Transaction of the ASME-Journal of Applied Mechanics,1972,39(2):545-550.
[13]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185-190.LI Yong-hua,LI Si-ming.Pseudo excitation method based on solving absolute displacement[J].Journal of Vibration and Shock,2009,28(10):185-190.
[14]GB50011-2001.建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.GB50011-2001.Code for Seismic Design of Buildings[S].Beijing:China Architecture&Building Press,2001.
[15]石永久,江洋,王元清.直接求解法在结构多点输入地震响应计算中的应用与改进[J].工程力学,2011,28(1):75-81.SHI Yong-jiu,WANG Yang,WANG Yuan-qing.Application and improvement of direct solving method in seismic response analysis of structures under multi-support excitations[J].Journal of Engineering Mechanics,2011,28(1):75-81.
[16]Kiureghian A D,Neuenhofer A.Response spectrum method for multi-support seismic excitations[J].Earthquake Engi-neering&Structural Dynamics,1992,21(8):713-740.
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