基于模态重分析的GFEM模型突风响应计算

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (13) : 333-340.

论文

肖宇1，刘景光1，邬旭辉1，常亮2

作者信息 +

Calculation of gust response of GFEM model based on modal reanalysis

XIAO Yu1, LIU Jingguang1, WU Xuhui1, CHANG Liang2

Author information +

文章历史 +

摘要

基于模态重分析技术，提出一种适合全局有限元模型（GFEM）的突风动响应高效计算方法。针对模型局部结构重量或刚度的细微变化，进行增量建模，充分利用现有构型结果，避免了传统分析中重复计算的步骤。对于质量阵的变化，以已有构型模态向量为初始向量，通过迭代分析进行特征值求解，针对刚度阵的微小变化，特别引入Sherman-Morrison-Woodbury公式，实现刚度逆矩阵的增量分析，从而克服了大规模GFEM模型的特征值求解效率低的问题，最终建立了一套适合于工程应用的GFEM突风高效动响应分析方法。采用GTA模型进行了突风分析算法的验证，在此基础上，基于某模型机翼，对模态重分析算法在突风动响应分析中的应用进行了研究。结果表明，通过LU分解可避免保存稠密形式的刚度逆矩阵，通过合理的松弛因子和收敛阈值，可有效提升计算效率。

Abstract

Based on the modal reanalysis technology, an efficient calculation method for gust dynamic response suitable for Global Finite Element Models (GFEM) was proposed. Incremental modeling was carried out to address local minor changes in the mass or stiffness of the model structure, fully utilizing existing configuration results and avoiding the repetitive calculation steps in the traditional analysis. For the changes of the mass matrix, the existing configuration modal vectors were taken as the initialization vectors, and the eigenvalues were solved iteratively. For the minor changes of the stiffness matrix, the Sherman-Morrison-Woodbury formula was introduced to implement the incremental analysis of the stiffness inverse matrix, and the problem of low efficiency in eigenvalue solution of large-scale GFEM models can be avoided, and finally a set of efficient GFEM gust dynamic response methods suitable for engineering applications was established. The gust analysis algorithm was validated with the GTA model, then, the application of the modal reanalysis algorithm on the gust response analysis was studied based on a certain model wing. The results show that saving the dense form of the stiffness inverse matrix can be avoided by the LU decomposition, and the calculation efficiency can be effectively improved by adopting a reasonable relaxation factor and convergence threshold.

导出引用

肖宇1，刘景光1，邬旭辉1，常亮2. 基于模态重分析的GFEM模型突风响应计算[J]. 振动与冲击, 2024, 43(13): 333-340

XIAO Yu1, LIU Jingguang1, WU Xuhui1, CHANG Liang2. Calculation of gust response of GFEM model based on modal reanalysis[J]. Journal of Vibration and Shock, 2024, 43(13): 333-340

参考文献

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