泛灰数学的不确定链式结构系统固有频率分析

Universal Grey Analysis for Natural Frequencies of Uncertain Chain Structures System

针对不确定因素对系统动力特性的影响,在应用泛灰数学的基础上,对不确定链式结构系统固有频率的求解方法进行了研究。首先,通过对泛灰数四则运算结果的分析,指出了利用泛灰数进行区间分析存在的缺陷,提出了一种改进的泛灰数除法运算规则,进而将链式结构系统中的不确定性参数用泛灰数表示;其次,基于矩阵传递法,导出了系统固有频率的非线性泛灰方程,并针对该方程的求解,在运用泛灰数运算规则的基础上,提出了一种区间搜索进退算法;最后,通过算例说明了笔者算法的可行性和求解方法的有效性。

In order to investigate the influence of stochastic factors on dynamic characteristics,a universal grey number-based approach was used to carry out the solution to natural frequencies of uncertain chain structures.Based on the analysis of four arithmetic operations of the universal grey numbers,this paper presents an improved division operation for the universal grey number and discusses some drawbacks of this method for interval analysis.Based on the transfer matrix method,a nonlinear universal grey numberbased equation of natural frequencies was obtained using universal grey mathematics.Subsequently,a forward and backward searching algorithm was presented to solve the equation.The feasibility and effectiveness of the computation expressions derived in this paper were confirmed through special cases.