区间参数结构动力特征值分析的仿射算法

Dynamic eigenvalues analysis of interval parameters structures with affine arithmetic

将不确定结构系统中的区间参数用仿射型来表示,对获得的广义区间特征值方程的求解方法进行了研究,提出了一种改进的仿射算法。此方法考虑到广义特征值方程中各区间元素的相关性,通过独立的区间参数在子区间上转为仿射型,将特征值方程的求解转化为相应的确定性问题,再利用常规的仿射算法,搜索方程解中的最大最小值来确定各阶特征值边界。先用数学算例对所提改进的仿射算法的有效性进行了验证,随后将其应用于工程算例的特征值区间分析中,并与其它算法进行了比较。结果表明该算法是合理可行的,有较高的准确性。

By describing the interval parameters of an uncertain structure with affine forms, a generalized eigenvalue interval equation was researched, and an improved atone arithmetic for dynamic eigenvalues analysis of interval parameter structures was presented. The atone arithmetic considers the correlations between the interval elements in the generalized eigenvalue equation, transforms independent uncertain parameters into affine forms, and transforms the solution of an eigenvalue equation into the corresponding certain one. With the general affine arithmetic, the eigenvalue bounds of each order are determined by searching for the maximum and minimum in the solutions. Some mathematical examples and the further engineering applications confirm the feasibility, validity and higher accuracy of this approach.