模糊随机桁架结构在模糊随机激励下的动力响应
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摘要
研究了模糊随机参数桁架结构在模糊随机荷载激励下的复合模糊随机振动动力响应的问题。同时考虑结构的物理参数、几何尺寸和外载荷幅值的模糊随机性,从Duham e l积分式出发,利用振型迭加法求出了结构动力响应模糊随机变量的表达式;再由随机函数的矩法推导出结构模糊随机动力响应的模糊数字特征。最后,通过算例考察了结构参数和作用荷载的模糊随机性对结构动力响应的影响,并用M on te C arlo数值法对算例进行模拟,验证了文中模型和分析方法是可行有效的。
The dynamic response analysis of the composite fuzzy random vibration for a truss,which possesses with fuzzy random parameters ordis under the excitation of fuzzy random loads is studied.Considering the fuzzy-randomness of structural physical parameters,geometric dimensions and the amplitude of the load simultaneously,from the Duhamel integral,structural dynamic responses are derived by the mode superposition method.Then,the fuzzy numerical characteristics of fuzzy random dynamic responses are derived by using the moment function method for random variables.Finally,the influences of fuzzy randomness of the structural parameters and the load on the dynamic response are examined through an example.The rationality and validity of the modeling and approach presented in this paper are illustrated by applying Monte Carlo method to the simulation of the example.
The dynamic response analysis of the composite fuzzy random vibration for a truss,which possesses with fuzzy random parameters ordis under the excitation of fuzzy random loads is studied.Considering the fuzzy-randomness of structural physical parameters,geometric dimensions and the amplitude of the load simultaneously,from the Duhamel integral,structural dynamic responses are derived by the mode superposition method.Then,the fuzzy numerical characteristics of fuzzy random dynamic responses are derived by using the moment function method for random variables.Finally,the influences of fuzzy randomness of the structural parameters and the load on the dynamic response are examined through an example.The rationality and validity of the modeling and approach presented in this paper are illustrated by applying Monte Carlo method to the simulation of the example.
引文
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[2]R ao S S,C ao L.Fuzzy boundary e lem en t m ethod forthe ana lys is of im prec ise ly defined-system[J].A IAAJourna l,2001,39(9):1 788—1 797.
[3]Kw akernaak H.Fuzzy random variab les,Ⅰ,Ⅱ[J].In form ation Sc ience,1978,15(17):253—278.
[4]M iyakosh iM,Sh im bo M.A strong law of largenum bers for fuzzy random variab les[J].Fuzzy Setsand System s,1984,12(2):133—142.
[5]吕恩琳,钟佑明.模糊概率随机变量[J].应用数学和力学,2003,24(4):434—440.
[6]王光远,欧进萍.结构地震模糊随机振动[J].力学学报,1988,20(2):173—180.
[7]吕恩琳.模糊随机有限元平衡方程的摄动解法[J].应用数学和力学,1997,18(7):631—638.
[8]Chen J J,Che J W,Sun H A,et a l.P robab ilisticdynam ic ana lys is of truss structures[J].S tructura lEng ineering&M echan ics,2002,13(2):231—239.
[9]马娟,陈建军,黄平,等.模糊桁架结构在模糊激励下的动力响应分析[J].力学学报,2005,37(3):381—384.
[10]A lefe ld G,C laud io D.T he bas ic properties of in terva larithm etic,its softw are rea lizations and som eapp lications[J].Com pu ters&S tructures,1998,67(1):3—8.
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