摘要
针对实际随机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,提出了一种新的随机参数结构频率特性的计算方法。在结构总刚度和质量矩阵中,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,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;利用求解随机变量函数的矩法求得结构各阶固有频率的随机特性。通过算例验证了该方法的可行性和有效性,并分析了各随机变量对结构固有频率随机性的影响。
A new method for calculating eigen frequencies of inhomogeneous stochastic structure is put forward. In view of dissimilarity of structural parameters included in elements of stiffness and mass matrixes and in consideration of difference in power numbers of structural parameters, the two matrixes are outspreal respectively in the form of summation of some submatrixes. Rayleigh formula is used to obtain the eigen frequencies expressed as the functions of structural random parameters. According to the moment method for computing numerical characteristics of functions containing random variables, the mean values and the variances of stochastic structural frequencies can be calculated. Two examples are given to validate the feasibility of the method discussed. And the influences of the randomness of different structural physical and geometrical parameters on the structural frequencies are analyzed.
出处
《振动与冲击》
EI
CSCD
北大核心
2007年第12期55-59,共5页
Journal of Vibration and Shock
基金
国家863项目(2006AA04Z402)
陕西省自然科学基金项目(2005A09)资助
关键词
随机结构
频率特性
矩阵分解
数字特征
stochastic structure
frequency characteristic
matrix outspread
numerical characteristic
