【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。更多还原

【Abstract】 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.更多还原