随机参数刚架结构的平稳随机位移响应动力可靠性分析
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摘要
研究物理参数具有随机性的刚架结构的平稳随机位移响应动力可靠性的计算方法。考虑结构的物理参数具有随机性,从结构随机响应的频域表达式出发,利用求解随机变量数字特征的代数综合法和矩法,导出随机参数刚架结构在平稳随机激励下的位移及速度响应均方值的数字特征,再由动力可靠性的Poisson公式导出结构动力可靠度的计算公式。通过算例就各参数的随机性对结构动力可靠度的影响进行分析,验证本文方法的可行性。
A method of calculating displacement dynamic reliability of stochastic rigid frames under stationary random excitation is discussed. Considering the randomness of the structural physical parameters and utilizing the random variable's functional moment method and the algebra synthesis method, the mean value and the variance of the mean square value of the structural displacement response under stationary random excitation are computed firstly from the expressions of structural stationary response in frequency domain. And then the expressions of the mean value and the variance of stochastic rigid frames dynamic reliability are educed from the Poisson formula of calculating dynamic reliability. Finally, the influence of the random of structural physical on the structural dynamic reliability is analyzed through the examples, validating the feasibility of this method.
A method of calculating displacement dynamic reliability of stochastic rigid frames under stationary random excitation is discussed. Considering the randomness of the structural physical parameters and utilizing the random variable's functional moment method and the algebra synthesis method, the mean value and the variance of the mean square value of the structural displacement response under stationary random excitation are computed firstly from the expressions of structural stationary response in frequency domain. And then the expressions of the mean value and the variance of stochastic rigid frames dynamic reliability are educed from the Poisson formula of calculating dynamic reliability. Finally, the influence of the random of structural physical on the structural dynamic reliability is analyzed through the examples, validating the feasibility of this method.
引文
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3Ren Y J,Elishakoff I,Shinozuka M.Finite element method for stochastic beams based on variational principles.Journal of Applied Mechanics,1997,64:664~669.
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5Crandall S H.First-crossing probabilities of thelinear oscillator.Journal of Sound and Vibration,1970,12(3):285~299.
6LI Gui Qing,CAO Hong,LI QuiSheng,et al.Structural dynamic reliabilitytheory and application.Beijing:Earthquake Press,1993(In Chinese)(李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用.北京:地震出版社,1993).
7LI QiuSheng,CAO Hong.Dynamic reliability analysis of tall building and high-rise structures with distributed parameters under the action of wind loads.Engineering Mechanics,1987,4(1):117~125(In Chinese)(李秋胜,曹宏.风荷作用下可连续化的高层建筑和高耸结构的动力可靠性分析.工程力学,1987,4(1):117~125).
8CHENJianJun,ZEN YuGeng,DAI BaoHua.A dynamic reliability analysis of multidegree-of-freedom system under stationary random response.Journal of Xidian University,1989,169(4):24~31(In Chinese)(陈建军,曾余庚,戴宝华.多自由度体系在平稳随机反应下的动力可靠性分析.西安电子科技大学学报,1989,169(4):24~31).
9Chen J J,Duan B Y,Zen YG.Study on dynamic reliability analysis of the structures with multidegree-of-freedom system.Computers&Structures,1997,62(5):877~881.
10Chen J J.Analysis of engineering structures response to random wind excitation.Computers&Structures,1994,51(6):687~693.
2LINJiaHao,YI Ping.Stationary response of structure with stochastic parameters.Chinese Journal of Computational Mechanics,2001,18(4):402~408(In Chinese)(林家浩,易平.线性随机结构的随机平稳响应.计算力学学报,2001,18(4):402~408).
3Ren Y J,Elishakoff I,Shinozuka M.Finite element method for stochastic beams based on variational principles.Journal of Applied Mechanics,1997,64:664~669.
4LI Gui Qing,CAO Hong.Review on the dynamic reliability of structures.Earthquake Engineering an Engineering Vibration,1983,3(3):42~61(In Chinese)(李桂青,曹宏.动力可靠性述评.地震工程与工程震动,1983,3(3):42~61).
5Crandall S H.First-crossing probabilities of thelinear oscillator.Journal of Sound and Vibration,1970,12(3):285~299.
6LI Gui Qing,CAO Hong,LI QuiSheng,et al.Structural dynamic reliabilitytheory and application.Beijing:Earthquake Press,1993(In Chinese)(李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用.北京:地震出版社,1993).
7LI QiuSheng,CAO Hong.Dynamic reliability analysis of tall building and high-rise structures with distributed parameters under the action of wind loads.Engineering Mechanics,1987,4(1):117~125(In Chinese)(李秋胜,曹宏.风荷作用下可连续化的高层建筑和高耸结构的动力可靠性分析.工程力学,1987,4(1):117~125).
8CHENJianJun,ZEN YuGeng,DAI BaoHua.A dynamic reliability analysis of multidegree-of-freedom system under stationary random response.Journal of Xidian University,1989,169(4):24~31(In Chinese)(陈建军,曾余庚,戴宝华.多自由度体系在平稳随机反应下的动力可靠性分析.西安电子科技大学学报,1989,169(4):24~31).
9Chen J J,Duan B Y,Zen YG.Study on dynamic reliability analysis of the structures with multidegree-of-freedom system.Computers&Structures,1997,62(5):877~881.
10Chen J J.Analysis of engineering structures response to random wind excitation.Computers&Structures,1994,51(6):687~693.
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