改进的 Neumann-LU混合法在失谐整体叶盘随机分析中的应用 *

推进技术 ›› 2018, Vol. 39 ›› Issue (7): 1626-1632.

改进的 Neumann-LU混合法在失谐整体叶盘随机分析中的应用 *

高峰,孙伟

东北大学机械工程与自动化学院，辽宁沈阳 110819,东北大学机械工程与自动化学院，辽宁沈阳 110819

发布日期:2021-08-15
作者简介:高峰，男，博士生，研究领域为机械系统动力学及硬涂层减振。 E-mail: peakgaoneu@163.com 通讯作者:孙伟，男，博士，教授，研究领域为机械系统动力学及振动控制。
基金资助:
国家自然科学基金( 51375079)；中央高校基本科研业务费项目( N150304008)。

Applicationof Improved HybridNeumann-LU Approachon Stochastic Analysisof Mistuned Blisk

School of Mechanical Engineering & Automation，Northeastern University，Shenyang 110819，China and School of Mechanical Engineering & Automation，Northeastern University，Shenyang 110819，China

Published:2021-08-15

摘要/Abstract

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。

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

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

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

高峰,孙伟. 改进的 Neumann-LU混合法在失谐整体叶盘随机分析中的应用 *[J]. 推进技术, 2018, 39(7): 1626-1632.

GAO Feng,SUN Wei. Applicationof Improved HybridNeumann-LU Approachon Stochastic Analysisof Mistuned Blisk[J]. Journal of Propulsion Technology, 2018, 39(7): 1626-1632.

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