指数函数模量成层土上剪切梁的随机地震反应
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摘要
按照剪切梁理论,给出了指数函数剪切模量成层土上剪切梁的自振频率方程及任意阶振型函数的解析表达式,应用振型叠加原理计算了这种梁的地震反应,然后利用随机振动理论,基于基岩输入地震加速度的功率谱密度函数、白噪声谱和过滤白噪声谱,研究了该梁对地震的随机动力响应问题。计算结果表明:在基岩输入地震加速度的功率谱为白噪声谱的情况下,土层和梁的最大期望反应均有别于过滤白噪声谱时的相应值;平稳输入与输出时,地基和梁的最大期望反应总是不小于非平稳过程时的相应值。
The formulas for computing natural frequencies and modes of shear beam on the stratified foundation with exponential function shear modulus are derived according to shear beam theory.The seismic response of this kind of beam is calculated by using the mode-superposition scheme.Dynamic responses of the beam and the soil layer to earthquake are studied by the theory of random vibration.Two cases of power spectral intensity function for the earthquake acceleration input at the base rock are considered: the white noise spectrum and filter white noise spectrum.The numerical calculation results show that under the case that the power spectral density of the earthquake acceleration input at the base rock is the white noise spectrum;the maximum expected responses of the soil layer and the beam are different from that for the case of the filter white noise spectrum.Both the earthquake acceleration input the base rock and the response are stationary random process,the maximum expected responses of the soil layer and the beam are bigger than the ones with no stationary process.5 figs,7 refs.
The formulas for computing natural frequencies and modes of shear beam on the stratified foundation with exponential function shear modulus are derived according to shear beam theory.The seismic response of this kind of beam is calculated by using the mode-superposition scheme.Dynamic responses of the beam and the soil layer to earthquake are studied by the theory of random vibration.Two cases of power spectral intensity function for the earthquake acceleration input at the base rock are considered: the white noise spectrum and filter white noise spectrum.The numerical calculation results show that under the case that the power spectral density of the earthquake acceleration input at the base rock is the white noise spectrum;the maximum expected responses of the soil layer and the beam are different from that for the case of the filter white noise spectrum.Both the earthquake acceleration input the base rock and the response are stationary random process,the maximum expected responses of the soil layer and the beam are bigger than the ones with no stationary process.5 figs,7 refs.
引文
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[2]Lin J H.Fast CQC algorithm of PSD matrices forrandom seismic responses[J].Computer andStructures,1992,44(3):683-687.
[3]Wolf J P.Dynamic soil-structure interaction[M].New Jersey:Prentice-Hall,1985.
[4]王春玲,黄义,张为民.指数函数剪切模量的成层土地震反应解析解[J].长安大学学报:自然科学版,2003,23(4):15-17.WANG Chun-ling,HUANG Yi,ZHANG Wei-min.General solution to earthquake response of stratifiedfoundations with exponential function shear modulus[J].Journal of Chang an University:Natural ScienceEdition,2003,23(4):15-17.
[5]栾茂田,金崇磐,林皋.非均质地基振动特性及地震反应分析[J].大连理工大学学报,1992,32(1):81-87.LUAN Mao-tian,JIN Chong-pan,LIN Gao.Vibration behavior and seismic response of verticallynon-homogeneous soil deposits[J].Journal of DalianUniversity of Technology,1992,32(1):81-87.
[6]王春玲,黄义.指数函数剪切模量土层的地震随机反应[J].岩土力学,2003,24(6):892-895.WANG Chun-ling,HUANG Yi.Seismic randomresponse of stratified foundations with exponentialfunction shear modulus[J].Rock and SoilMechanics,2003,24(6):892-895.
[7]曾心传,秦小军.土层对地震的随机反应分析[J].地震工程与工程振动,1998,18(3):27-39.ZENG Xin-chuan,QIN Xiao-jun.Analysis of randomresponse of soil layer to earthquake[J].EarthquakeEngineering and Engineering Vibration,1998,18(3):27-39.
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