改进的 Neumann-LU混合法在失谐整体叶盘随机分析中的应用 *

Applicationof Improved HybridNeumann-LU Approachon Stochastic Analysisof Mistuned Blisk

关键词:  失谐整体叶盘  随机分析  分解法  Numann展开式法  Neumann-LU混合法

Key words:  Mistuned blisk  Stochastic analysis  Factorization method  Neumann expansion method  Hybrid Neumann-LU approach

摘要:

为了降低失谐整体叶盘的随机分析矩阵求逆的计算成本，提出一种基于 Neumann级数和 LU分解的改进 Neumann-LU混合法。一方面，在非共振频率附近的大区域采用 Neumann级数频域展开式以提高计算效率；另一方面，在共振频率附近小区域采用 LU分解法以提高计算计算精度；根据 Neu. mann级数展开项数来选定自适应阀值，实现两种矩阵求逆方法的自动转换而不用消耗额外的计算资源。选取具有失谐特征的整体叶盘为研究对象，分别运用改进的 Neumann-LU混合法和单一 LU分解法求解叶片在阶次激励下的频域响应，并从计算效率和计算精度方面进行比较。研究结果表明，在保证计算精度误差不大于 0.1%的前提下，改进的 Neumann-LU混合法可以提高失谐整体叶盘随机分析大约 55%的计算效率。

Abstract:

For decreasing computational cost of matrix inversion in the stochastic analysis of mistuned blisk，an improved hybrid Neumann-LU approach was proposed based on Neumann expansion coupled with LU factorization. On the one hand，the Neumann expansion in the frequency domain was used to enhance computa.tional efficiency outside the region of resonant frequencies; on the other hand，the LU factorization in the neigh.borhood of the resonant frequencies was utilized for improving computational accuracy; in which，the number of the expansion terms was regarded as an adaptive indicator to select the matrix inversion technique to be used with.out introducing any additional computational cost. Finally，according to different mistuning patterns via stiffness