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Natural frequency and mode shape analysis of structures with uncertainty

机译:不确定结构的固有频率和振型分析

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摘要

Two methods called random factor method (RFM) and interval factor method (IFM) for the natural frequency and mode shape analysis of truss structures with uncertain parameters are presented in this paper. Using the RFM, the structural physical parameters and geometry can be considered as random variables. The structural stiffness and mass matrices can then, respectively, be described by the product of two parts corresponding to the random factors and the deterministic matrix. The structural natural frequencies, mode shapes and random response can be expressed as the function of the random factors. By means of the random variable's algebra synthesis method, the computational expressions for the mean value and standard deviation of natural frequencies and mode shapes are derived from the Rayleigh quotient. Using the IFM, the structural parameters can be considered as interval variables and the computational expressions for the lower and upper bounds of the natural frequency and mode shape are derived by means of the interval operations. The effect of uncertainty of individual structural parameters on structural dynamic characteristics, and the comparison of structural natural frequency and mode shape using the RFM and IFM are demonstrated by truss structures.
机译:提出了参数不确定的桁架结构固有频率和振型分析的两种方法,分别为随机因子法(RFM)和间隔因子法(IFM)。使用RFM,可以将结构物理参数和几何形状视为随机变量。然后可以通过对应于随机因素和确定性矩阵的两个部分的乘积分别描述结构刚度和质量矩阵。结构固有频率,振型和随机响应可以表示为随机因素的函数。通过随机变量的代数合成方法,从瑞利商中导出了固有频率和振型的平均值和标准偏差的计算表达式。使用IFM,可以将结构参数视为间隔变量,并通过间隔运算得出固有频率和模式形状的上下限的计算表达式。桁架结构证明了单个结构参数的不确定性对结构动力特性的影响,以及使用RFM和IFM比较结构固有频率和振型的影响。

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