基于传递矩阵法的不确定链式结构固有频率区间分析

INTERVAL ANALYSIS FOR NATURAL FREQUENCIES OF AN UNCERTAIN STRUCTURE BASED ON TRANSFER MATRIX METHOD

基于传递矩阵法,将链式结构中的不确定性参数用区间数来表示,导出关于系统固有频率的非线性区间方程,并针对该方程的求解,提出了一种区间逐步离散算法。此方法通过不确定性参数取区间离散值,将区间方程转化为相应的确定性方程,再搜索方程解中的最大最小值来确定系统各阶固有频率的边界。文中给出两个具有不确定性参数的链式结构算例,计算结果表明该算法是可行和有效的。

Based on transfer matrix method,a generalized interval equation of natural frequencies of a chain type structure is obtained by using interval numbers to represent its uncertain structural parameters.An intervaldiscretizing step by step method is presented to solve the obtained nonlinear interval equation.Using this method,each uncertain parameter is given one value for an interval divided,so that the solution of an interval equation is changed to the certain normal one.And then the bounds of each natural frequency of the system are determined by searching for the maximum and minimum of the solutions.Two examples of chain structures with uncertain parameters are given and the calculated results show that this method is correct and efficient for natural frequency analysis.