模糊随机桁架结构的动力特性双因子分析法
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摘要
针对模糊随机桁架结构的动力特性分析,提出了一种新的模糊随机有限元方法.当结构的物理参数和几何尺寸同时具有模糊随机性时,利用模糊因子法和随机因子法建立了结构刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构动力特性模糊随机变量的计算表达式;之后利用随机变量的矩法和代数综合法,推导出结构特征值的数字特征的计算式.通过算例分析了模糊随机桁架结构参数的模糊随机性对其动力特性的影响.该方法的优点是能准确反映结构某一参数的模糊随机性对结构特征值及其数字特征的影响.
A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented.Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously,the structural stiffness and mass matrices were constructed based on the fuzzy factor method and random factor method;from the Rayleigh's quotient of structural vibration,the structural fuzzy random dynamic characteristic was obtained by means of the interval arithmetic;the fuzzy numeric characteristics of dynamic characteristic were then derived by using the random variable's moment function method and algebra synthesis method.Two examples were used to illustrate the validity and rationality of the method given.The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameter on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.
A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented.Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously,the structural stiffness and mass matrices were constructed based on the fuzzy factor method and random factor method;from the Rayleigh's quotient of structural vibration,the structural fuzzy random dynamic characteristic was obtained by means of the interval arithmetic;the fuzzy numeric characteristics of dynamic characteristic were then derived by using the random variable's moment function method and algebra synthesis method.Two examples were used to illustrate the validity and rationality of the method given.The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameter on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.
引文
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[2]郭书祥,吕震宙.结构的失效可能度及模糊概率计算方法[J].应用数学和力学,2003,24(3):300—304.
[3]王光远.论不确定性结构力学的进展[J].力学进展,2002,32(2):205—211.
[4]郭书祥,吕震宙.基于可能性理论的结构模糊可靠性方法[J].计算力学学报,2002,19(1):189—193.
[5]Rao S S,Cao L.Fuzzy boundary element method for the analysis of imprecisely defined_system[J].AIAA J,2001,39(9):1788—1797.
[6]吕震宙,岳珠峰,冯蕴雯.韧脆转变的一种细观随机模糊统计分析[J].应用数学和力学,2003,24(10):1027—1034.
[7]王光远,欧进萍.在地震作用下结构的模糊随机振动[J].力学学报,1988,20(2):173—180.
[8]吕恩琳,钟佑明.模糊密度随机变量的数学描述[J].应用数学和力学,2000,21(8):861—869.
[9]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.
[10]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.
[11]CHEN Jian_jun,CHE Jian_wen,SUN Huai_an,et al.Probabilistic Dynamic analysis of truss structures[J].Structural Engineering and Mechanics,2002,13(2):231—239.
[12]GAO Wei,CHEN Jian_jun.Optimal placement of active bars in active vibration control for piezoelec-tric intelligent truss structures with random parameters[J].Computers&Structures,2003,81(1):53—60.
[13]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):378—384.
[14]Alefeld G,Claudio D.The basic properties of interval arithmetic,its software realizations and someapplications[J].Computers&Structures,1998,67(1/3):3—8.
[15]Dubois D,Prade H.Fuzzy Sets and System:Theory and Applications[M].New York:AcademicPress,1980.
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