钢框架基于复模态随机反应分析的抗震可靠度研究

The research of seismic reliability of a steel frame based on complex modal method for analysis of random response

首次将复模态法应用于钢框架结构的随机地震反应分析中,通过算例对钢框架结构在平稳地震激励下的抗震可靠度进行了计算分析。同时,提出了钢框架在非平稳地震激励下的反应统计量的求解方法。研究表明,钢框架结构在非平稳地震激励下的随机反应分析,可以利用扩阶的方法来进行,将求解结构非平稳随机响应转化为求解扩阶系统在均匀调制白噪声激励下的响应。采用复模态分析法可较方便地求解出结构在非平稳地震激励下弹性随机反应的协方差函数及均方差的解析表达式。

Complex modal method is introduced into analysis of stochastic seismic response of a steel frame for the first time. Through a calculating example, the seismic reliability of a steel frame structure under stationary seismic excitation is analysed. At the same time, the solution method which can obtain response statistics of the steel frame under non-stationary seismic excitation is proposed. It is shown that the stochastic response analysis of structures under non-stationary seismic excitation can be done by the method of augmenting-exponent-number. The non-sta- tionary stochastic response of the structure can be converted into the response of augmenting-exponent-number system under homogeneous modulation white noise excitation. The analytical expression of covariance function and mean square deviation of elastic stochastic response of the structure under non-stationary seismic excitation can be obtained more easily with the complex modal method.