与指定地震记录相关的非平稳地震动场的模拟
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摘要
地震动的非平稳特性主要是由其相位差谱决定的,相位差谱与相位导数之间存在线性倍数关系。根据相位导数的计算公式,从能量的角度解释了相位导数的均值决定了时程峰值的大致发生时刻,相位导数的方差决定了强震段的持续时间。改进了均匀调制非平稳过程的相位导数概率密度函数计算公式中强度谱矩的计算方法,使之能够适用于一般非平稳时程。在模拟与指定地震记录相关的非平稳地震动场方法中,计算指定地震记录相位导数的概率密度函数,并按照该函数生成各点的相位导数,得到各点的随机相位谱;然后采用基于功率谱表示的地震动场合成方法,利用快速傅里叶变换技术生成地震动时程。
The non-stationary characteristics of an earthquake ground motion are dependent on its phase difference spectrum being proportional to phase derivatives.From the view point of energy of an acceleration time history,the time of PGA is related to the mean value of phase derivatives while the duration of strong ground motion is related to the variance of phase derivatives.The intensity spectral moment formula of a uniformly modulated non-stationaly random process was modified here in order that the modified formula was applicable to the general non-stationary process.In the process of simulating a non-stationary earthquake ground motion field correlated to a specified earthquake record,the probability density function of the phase derivatives for the specified earthquake record was calculated;then both the phase derivatives and the random phase spectra of the synthesized ground motion points were generated.The time histories of the simulated ground motion field based on a power spectrum expression were generated with fast Fourier transformation.
The non-stationary characteristics of an earthquake ground motion are dependent on its phase difference spectrum being proportional to phase derivatives.From the view point of energy of an acceleration time history,the time of PGA is related to the mean value of phase derivatives while the duration of strong ground motion is related to the variance of phase derivatives.The intensity spectral moment formula of a uniformly modulated non-stationaly random process was modified here in order that the modified formula was applicable to the general non-stationary process.In the process of simulating a non-stationary earthquake ground motion field correlated to a specified earthquake record,the probability density function of the phase derivatives for the specified earthquake record was calculated;then both the phase derivatives and the random phase spectra of the synthesized ground motion points were generated.The time histories of the simulated ground motion field based on a power spectrum expression were generated with fast Fourier transformation.
引文
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[10]田玉基,杨庆山.基于相位差谱的空间相关非平稳地震动场的模拟[J].计算力学学报,2010,27(5):828-833. TIAN Yu-ji,YANG Qing-shan.Phase-difference-based simulation of spatial correlated and non-stationary seismic ground motions[J].Chinese Journal of Computational Mechanics,2010,27(5):828 -833.
[11]田玉基,杨庆山.多阻尼比设计反应谱的非平稳地震动场拟合[J].振动与冲击,2010,29(1):43-47. TIAN Yu-ji,YANG Qing-shan.MULTI-damping-ratio design spectra fitting with correlated and non-stationary seismic fields [J].Journal of Vibration and Shock,2010,29(1):43 -47.
[12]Harichandran R S.Vanmarke E H.Stochastic variation of earthquake ground motion in space and time[J].Journal of Engineering Mechanics,ASCE,1986,112(2):154-174.
[2]秦权,孙晓燕,贺瑞,等,苏通桥对非一致地震地面运动的反应和人工波质量的讨论[J].工程力学,2006, 23(9):71-83. QIN Quan,SUN Xiao-yan,HE Rui,et al.Responses of sutong cable-stayed bridge to asynchronous earthquake ground motions and quality of synthetic time histories[J]. Engineering Mechanics,2006,23(9):71 -83.
[3]杨庆山,刘文华,田玉基.国家体育场在多点激励作用下的地震反应分析[J].土木工程学报,2008,41(2):35 -41. YANG Qing-shan,LIU Wen-hua,TIAN Yu-ji.Response analysis of National Stadium under spacially variaable earthquake ground motions[J].China Civil Engineering Journal,2008,41(2):35-41.
[4]Shinozuka M,Deodatis G.Simulation of multi-dimensional Gaussian stochastic fields by spectral representation[J]. Applied Mechanics Reviews,ASME,1996,49(1):29 -53.
[5]Deodatis G.Non-stationary stochastic vector processes; seismic ground motion applications[J].Probabilistic Engineering Mechanics,1996,11(3):149-168.
[6]Suarez L E,Montejo L A.Generation of artificial earthquakes via the wavelet transform[J].International Journal of Solids and Structures,2005,42(21 -22):5905 -5919.
[7]Ohsaki Y.On the significance of phase content in earthquake ground motions[J].Earthquake Engineering and Structural Dynamics,1979,7(5):427 -439.
[8]Boore D M.Phase derivatives and simulation of strong ground motions[J].Bulletin of the Seismological Society of America,2003,93(3):1132-1143.
[9]Nigam N C.Phase properties of a class of random processes [J].Earthquake Engineering and Structural Dynamics, 1982,10(5);711 -717.
[10]田玉基,杨庆山.基于相位差谱的空间相关非平稳地震动场的模拟[J].计算力学学报,2010,27(5):828-833. TIAN Yu-ji,YANG Qing-shan.Phase-difference-based simulation of spatial correlated and non-stationary seismic ground motions[J].Chinese Journal of Computational Mechanics,2010,27(5):828 -833.
[11]田玉基,杨庆山.多阻尼比设计反应谱的非平稳地震动场拟合[J].振动与冲击,2010,29(1):43-47. TIAN Yu-ji,YANG Qing-shan.MULTI-damping-ratio design spectra fitting with correlated and non-stationary seismic fields [J].Journal of Vibration and Shock,2010,29(1):43 -47.
[12]Harichandran R S.Vanmarke E H.Stochastic variation of earthquake ground motion in space and time[J].Journal of Engineering Mechanics,ASCE,1986,112(2):154-174.
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