基于时-频包线函数的多点地震动合成
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摘要
地震动频率非平稳特性对结构响应有重要影响。本文通过引入随频率变化的包线函数,近似模拟地震动频率的非平稳特性,建立了能够考虑地震动频率非平稳特性的空间相关多点地震动的合成方法。实例分析表明,本文给出的拟合方法能够较好地反映地震动频率的非平稳特性,强调地震动时程在下降段的低频成分。由于在本文给出的模拟方法中,可以采用不同的时-频分析工具构建随频率变化的强度包线函数,所以非常适合于工程应用。
There is important effect of non-stationarity of frequency in earthquake ground motion on structural responses. Therefore,the non-stationarity of earthquake ground motion is simulated by introducing the frequency-dependent amplitude envelope function. Based on this,a simulation method for spatial correlated multi-supported ground motion is developed,which can consider the non-statioarity of frequency in ground motion. An example is used to analyze the effect of amplitude envelope function,and the results show that simulation method derived in this paper can consider the non-stationarity of frequency,and emphasizes the effect of low-frequency component in later seismic actions. In addition,because frequency-dependent amplitude envelope function can be established by many time-frequency analysis tools,the simulation formula developed in this paper is suitable for application in engineering.
There is important effect of non-stationarity of frequency in earthquake ground motion on structural responses. Therefore,the non-stationarity of earthquake ground motion is simulated by introducing the frequency-dependent amplitude envelope function. Based on this,a simulation method for spatial correlated multi-supported ground motion is developed,which can consider the non-statioarity of frequency in ground motion. An example is used to analyze the effect of amplitude envelope function,and the results show that simulation method derived in this paper can consider the non-stationarity of frequency,and emphasizes the effect of low-frequency component in later seismic actions. In addition,because frequency-dependent amplitude envelope function can be established by many time-frequency analysis tools,the simulation formula developed in this paper is suitable for application in engineering.
引文
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[2]Der Kiureghian A.A coherency model for spatially varying ground motions[J].Earthquake Engineering&Structural Dynamic,1996,25:99-111.
[3]Shinozuka M and Deodatis G.Stochastic process models for earthquake ground motion[J].Probabilistic Engineering Mechanics,1988 3(3):114-123.
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[5]屈铁军,王前信.空间相关的多点地震动合成-1基本公式[J].地震工程与工程振动,1998,18(1):8-15.QU Tiejun,WANG Qianxin.Simulation of spatial correlative time histories of multi-point ground motion,Part 1:fundamental formulas[J].Journal Earthquake Engineering and Engineering Vibration.1998,18(1):8-15.(in Chinese)
[6]Shama A A..Simplified procedure for simulating spatially correlated earthquake ground motions[J].Engineering Structures,2007,29(2):248-258.
[7]吴勇信,高玉峰.基于功率谱矩阵开方分解的空间相关多点地震动合成方法[J].工程力学,2012,29(4):29-35.WU Yongxin,GAO Yufeng.Simulation of spatial correlative ground motions based on the square root operation of power spectrum matrix[J].Engineering Mechanics,2012,29(4):29-35.(in Chinese)
[8]Shrikhande M and Gupta V K.Synthesizing ensembles of spatially correlated accelerograms[J].Journal of Engineering Mechanics.ASCE,1998,124(11):1185-1192.
[9]董汝博,周晶,冯新.非平稳空间相关多点地震动合成方法研究[J].地震工程与工程振动,2007,27(3):10-14.DONG Rubo,ZHOU Jing,FENG Xin.Simulation of non-stationary spatial correlative time histories of multi-point ground motion[J].Journal Earthquake Engineering and Engineering Vibration,2007,27(3):10-14.(in Chinese)
[10]Nigam N C.Introduction to Random Vibrations[M].MIT Press:Cambridge,Mass,1983.
[11]Newland D E Wavelet analysis of vibration,Part 2:Wavelet maps[J].Journal of Vibration and Aeoustics,1994,116:417-425.
[12]许谋奎,张猛,张增军.多点地震动合成简化方法研究[J].地震工程与工程振动,2009,29(1):58-62.XU Moukui,ZHANG Meng,ZHANG Zengjun.Study on simplified method of simulation for multi-point ground motion[J].Journal Earthquake Engineering and Engineering Vibration,2009,29(1):58-62.(in Chinese)
[13]阿布都瓦里斯.基于台阵观测资料的地震动空间变化特性研究[D].北京:中国地震局地球物理研究所,2013.Abduwaris.Study on spatial variation of ground motions based on array records[D].Beijing:Institute of Geophysics,China Earthquake Administration,2013.(in Chinese)
[2]Der Kiureghian A.A coherency model for spatially varying ground motions[J].Earthquake Engineering&Structural Dynamic,1996,25:99-111.
[3]Shinozuka M and Deodatis G.Stochastic process models for earthquake ground motion[J].Probabilistic Engineering Mechanics,1988 3(3):114-123.
[4]Hao H,Oliveira C S and Penzien J.Multiple-station ground motion processing and simulation based on SMART-1 array data[J].Nuclear Engineering and Design,1989,111(3):293-310.
[5]屈铁军,王前信.空间相关的多点地震动合成-1基本公式[J].地震工程与工程振动,1998,18(1):8-15.QU Tiejun,WANG Qianxin.Simulation of spatial correlative time histories of multi-point ground motion,Part 1:fundamental formulas[J].Journal Earthquake Engineering and Engineering Vibration.1998,18(1):8-15.(in Chinese)
[6]Shama A A..Simplified procedure for simulating spatially correlated earthquake ground motions[J].Engineering Structures,2007,29(2):248-258.
[7]吴勇信,高玉峰.基于功率谱矩阵开方分解的空间相关多点地震动合成方法[J].工程力学,2012,29(4):29-35.WU Yongxin,GAO Yufeng.Simulation of spatial correlative ground motions based on the square root operation of power spectrum matrix[J].Engineering Mechanics,2012,29(4):29-35.(in Chinese)
[8]Shrikhande M and Gupta V K.Synthesizing ensembles of spatially correlated accelerograms[J].Journal of Engineering Mechanics.ASCE,1998,124(11):1185-1192.
[9]董汝博,周晶,冯新.非平稳空间相关多点地震动合成方法研究[J].地震工程与工程振动,2007,27(3):10-14.DONG Rubo,ZHOU Jing,FENG Xin.Simulation of non-stationary spatial correlative time histories of multi-point ground motion[J].Journal Earthquake Engineering and Engineering Vibration,2007,27(3):10-14.(in Chinese)
[10]Nigam N C.Introduction to Random Vibrations[M].MIT Press:Cambridge,Mass,1983.
[11]Newland D E Wavelet analysis of vibration,Part 2:Wavelet maps[J].Journal of Vibration and Aeoustics,1994,116:417-425.
[12]许谋奎,张猛,张增军.多点地震动合成简化方法研究[J].地震工程与工程振动,2009,29(1):58-62.XU Moukui,ZHANG Meng,ZHANG Zengjun.Study on simplified method of simulation for multi-point ground motion[J].Journal Earthquake Engineering and Engineering Vibration,2009,29(1):58-62.(in Chinese)
[13]阿布都瓦里斯.基于台阵观测资料的地震动空间变化特性研究[D].北京:中国地震局地球物理研究所,2013.Abduwaris.Study on spatial variation of ground motions based on array records[D].Beijing:Institute of Geophysics,China Earthquake Administration,2013.(in Chinese)
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