结构平稳随机地震反应时域分析:方法
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摘要
给出了三种常用的随机地震地面运动过程模型,即理想白噪声模型、金井清模型、改进金井清模型的相关函数表达式。引入状态向量,在状态空间中建立地震地面运动激励下的结构振动方程,并求解出结构的复模态特性和复模态反应。利用复模态叠加法推导出线性时不变多自由度体系在这三种随机地震动激励下的平稳协方差反应的解析式,可在时域内直接计算结构随机反应的统计特征。该方法物理概念清晰,结论简便明确,可作为实际工程结构平稳随机地震反应的实用分析方法。
Three typical stationary stochastic process models of seismic ground motions, the Gaussian white noise process, the filtered Gaussian white noise process with the Kanai-Tajimi power spectrum and the twice filtered Gaussian white noise process with the modified Kanai-Tajimi power spectrum, are discussed and the autocorrelation functions of the three models are provided in this paper. The equations of motion of the structures are represented by the state equations in state space subjected to the earthquake ground motion, and the complex vibration characteristics and responses are analyzed. The method of complex mode superposition is used to deduce the covariance response matrix of linear time-invariant structures under excitations of the three ground acceleration models. The statistic characteristics of the structural displacement and velocity responses may be obtained directly from the covariance response matrix without any efforts of integral calculation. This method is distinct in physical conception. All the analyses are carried out in time domain and the results are simple and clear, so it can be used to analyze the stationary responses of the structures in practice.
Three typical stationary stochastic process models of seismic ground motions, the Gaussian white noise process, the filtered Gaussian white noise process with the Kanai-Tajimi power spectrum and the twice filtered Gaussian white noise process with the modified Kanai-Tajimi power spectrum, are discussed and the autocorrelation functions of the three models are provided in this paper. The equations of motion of the structures are represented by the state equations in state space subjected to the earthquake ground motion, and the complex vibration characteristics and responses are analyzed. The method of complex mode superposition is used to deduce the covariance response matrix of linear time-invariant structures under excitations of the three ground acceleration models. The statistic characteristics of the structural displacement and velocity responses may be obtained directly from the covariance response matrix without any efforts of integral calculation. This method is distinct in physical conception. All the analyses are carried out in time domain and the results are simple and clear, so it can be used to analyze the stationary responses of the structures in practice.
引文
[1]Housner G W.Characteristics of strong motion of earthquakes[J].BSSA,1947,37(1):19~31.
[2]Kanai K.Sem i-emp irical formu la for the seism ic characteristics of the ground motion[J].Bu lletin of The Earthquake Research Institute,Un i-versity of Tokyo,1957,35(2):308~325.
[3]Tajim iH.A statisticalm ethod of determ in ing the maximum response of a bu ild ing structure during an earthquake[A].2nd WCEE[C].Tokyo,1960.
[4]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21~26.
[5]洪峰.基底隔震结构的随机地震反应分析和概率设计[D].哈尔滨:国家地震局工程力学研究所,1995.
[6]Igusa T,D er K iuregh ian A and Sackman J L.Modal decomposition m ethod for stationary response of nonclassically damped structures[J].EE-SD,1984,12:121~136.
[7]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991,11(3):45~54.
[8]周锡元.一般有阻尼线性体系地震反应的振型分解方法[A].中国地震工程研究进展[C].北京:地震出版社,1992.120~125.
[9]秦佳会,胡聿贤.非经典阻尼体系复振型随机反应分析[J].地震工程与工程振动,1990,10(4):5~19.
[10]方同.工程随机振动[M].北京:国防工业出版社,1995.
[2]Kanai K.Sem i-emp irical formu la for the seism ic characteristics of the ground motion[J].Bu lletin of The Earthquake Research Institute,Un i-versity of Tokyo,1957,35(2):308~325.
[3]Tajim iH.A statisticalm ethod of determ in ing the maximum response of a bu ild ing structure during an earthquake[A].2nd WCEE[C].Tokyo,1960.
[4]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21~26.
[5]洪峰.基底隔震结构的随机地震反应分析和概率设计[D].哈尔滨:国家地震局工程力学研究所,1995.
[6]Igusa T,D er K iuregh ian A and Sackman J L.Modal decomposition m ethod for stationary response of nonclassically damped structures[J].EE-SD,1984,12:121~136.
[7]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991,11(3):45~54.
[8]周锡元.一般有阻尼线性体系地震反应的振型分解方法[A].中国地震工程研究进展[C].北京:地震出版社,1992.120~125.
[9]秦佳会,胡聿贤.非经典阻尼体系复振型随机反应分析[J].地震工程与工程振动,1990,10(4):5~19.
[10]方同.工程随机振动[M].北京:国防工业出版社,1995.
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