一种求解随机参数结构频率灵敏度的方法

Method for Stochastic Structural Frequency Sensitivity Analysis

提出了一种随机参数结构频率灵敏度的计算方法。在结构总刚度和质量矩阵中,针对结构中每个单元的随机性不同,且各随机参数间的相关系数也不同的情况,根据各元素所含随机参数的不同以及相同随机参数幂次的大小,将刚度和质量矩阵分别展开为若干矩阵之和的形式;利用求解结构固有频率的瑞利商公式,推导得到结构固有频率关于结构中各个随机参数的函数表达式;进而求得结构各阶固有频率对各随机参数的灵敏度。通过算例验证了该方法的可行性和有效性。

A new method for calculating frequency sensitivity of stochastic structure is presented.To structural stiff matrix and mass matrix,based on the differences of randomicity of each element and the differences of ecorrelation coefficient of each stochastic parameter,according to the dissimilarity of structural parameters included in every matrix element and the power of structural parameters.The stiff matrix and mass matrix can be outspreaded to the sum of some matrixes.Then the stiff matrix and mass matrix after outspread are taken into Rayleigh formula,which is used for computing structural frequency.The expression of the sensitivity of stochastic structural from rank frequency to physical parameter and geometrical parameter of different element are educed from the expression of stochastic structural frequency.Finally,two examples are provided to illustrate the validity and feasibility of the present method.