改进的区间参数结构频响函数迭代解法

A modified iteration method to solve frequency response function of structures with interval parameters

针对区间不确定性系统频响函数求解提出了一种改进的迭代方法。采用区间分析方法描述不确定性结构参数,将频响函数求解转化为区间线性方程组形式,使用定点迭代方法,构造迭代格式;为了解决迭代方法中出现的收敛性问题,结合子区间概念提出改进的迭代方法,计算结构频响函数的区间。以弹簧-质量系统为仿真算例,研究了子区间数目对计算结果的影响。最后,将方法应用于文献中的工程结构,对比研究表明:该方法适用于全频段频响函数分析、具有较高的精度和效率。

A modified iteration method for solving frequency response function of a structure with uncertain parameters was presented. Interval parameters were adopted to represent structural uncertain parameters. The equation to solve a structural frequency response function was converted to a group of interval linear equations. The iteration matrix was obtained by using the fixed point iteration theorem. Due to a convergence problem in iteration,sub-intervals were introduced and a modified iteration method was proposed to get the upper and lower bounds of the frequency response function. The accuracy of the solution was improved and the convergence problem was solved after modification. A springmass system was adopted in simulation to explore the influence of sub-interval＇s quantity. At last,a comparative study was conducted using a structure in reference. The results showed that the proposed method is suitable for a full frequency band frequency response analysis with better accuracy and computation efficiency.