指数函数剪切模量土层的地震随机反应
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摘要
基于改进的一维剪切梁模型[1],对剪切模量为其深度的某一指数函数的成层非均质土层,推导了确定自振频率、振型函数、参与系数及稳态动力响应的封闭型解析表达式。首次证明了这种土层振型函数的正交性,利用随机振动理论,并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,研究了该土层对地震的随机动力响应问题。计算表明:(1)在基岩输入地震加速度的功率谱为白噪声谱的情况下,土层的最大期望反应,均有别于过滤白噪声谱时的相应值。(2)平稳输入与输出过高地估计了土层的随机响应。
Based on a generalized non-homogeneous shear-beam model[1], for stratified foundations with exponential function shear modulus, closed-form analytical expressions are derived for determining natural frequencies, modal displacements, participation factors and steadystate response function. The orthogonality of the modal displacements is proved for the first time. And then, dynamic response of the stratified foundations to earthquake is studied by the theory of random vibration.Two cases of power spectral intensity function for the earthquake acceleration imput at the base rock are considered: the white noise spectrum and filter white noise spectrum. The numerical calculation results show that 1) 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 response of the soil layer is different from that for the case of the filter white noise spectrum; 2) both the earthquake acceleration input the base rock and the response of the soil layer are stationary random process, which overestimates the random response of the soil layer.
Based on a generalized non-homogeneous shear-beam model[1], for stratified foundations with exponential function shear modulus, closed-form analytical expressions are derived for determining natural frequencies, modal displacements, participation factors and steadystate response function. The orthogonality of the modal displacements is proved for the first time. And then, dynamic response of the stratified foundations to earthquake is studied by the theory of random vibration.Two cases of power spectral intensity function for the earthquake acceleration imput at the base rock are considered: the white noise spectrum and filter white noise spectrum. The numerical calculation results show that 1) 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 response of the soil layer is different from that for the case of the filter white noise spectrum; 2) both the earthquake acceleration input the base rock and the response of the soil layer are stationary random process, which overestimates the random response of the soil layer.
引文
[1]高玉峰,金建新,谢康和等.成层地基一维土层地震反应解析解[J].岩土工程学报,1999,21(4):489-500.
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[3]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):27-38.
[4]R.W.克拉夫,J.彭津[美]著.王光远,王焕定,董明耀等译.结构动力学[M].北京:科学出版社,1981,103-105.
[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.
[2]黄义,门玉明.结构-地基相互作用系统可靠性分析[M].西安:陕西省科学技术出版社,2000,124-130.
[3]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):27-38.
[4]R.W.克拉夫,J.彭津[美]著.王光远,王焕定,董明耀等译.结构动力学[M].北京:科学出版社,1981,103-105.
[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.
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