钢框架基于复模态随机反应分析的抗震可靠度研究
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摘要
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-stationary 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.
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-stationary 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.
引文
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[5]陈健云,王建有.基于复模态的有限元模型修正算法[J].世界地震工程,2004,20(2):12-16.CHEN Jianyun,WANG Jianyou.Finite element model updating method based on complex mode[J].World Earthquake Engineering,2004,20(2):12-16.
[6]方同.工程随机振动[M].国防工业出版社,1995.FANG Tong.Random vibration of engineering[M].Beijing:National Defence Industry Press,1995.
[7]Amin M,Ang A H.Nonstationary stochastic model of earthquake ground motions[J].Earthquake Engineering and Structural Dynamics,1979,7(5):176-181.
[8]吕大刚,王光远.基于损伤性能的抗震结构最优设防水准的决策方法[J].土木工程学报,2001,34(1):44-49...LUDagang,WANG Guangyuan.Decision-making method of optimal fortification level for aseismic structures based on damage performance[J].China Civil Engineering Journal,2001,34(1):44-49.
[9]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[M].北京:地震出版社,1993.LI Guiqing,CAO Hong,LI Qiusheng,et al.The theory and its application on the structural dynamic reliability[M].Beijing:Earthquake Press,1993.
[10]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑工程学院学报,1994,27(5):1-10.OU Jinping,DUAN Yubo,LIU Huiyi.Structural random earthquake action and its statistical parameters[J].J.Harbin Archit.&Civ.Eng.Inst.,1994,27(5):1-10.
[11]欧进萍,牛荻涛,王光远.多层非线性抗震结构的模糊动力可靠性分析与设计[J].地震工程与工程振动,1990,10(4):27-37.OU Jinping,NIU Ditao,WANG Guangyuan.Analysis and design of fuzzy dynamic reliability of multi-layer nonlinear seismic structure[J].Jour-nal of Earthquake Engineering and Engineering Vibration,1990,10(4):27-37.
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