振动模态（特征值和特征向量）的灵敏度分析在结构振动控制、优化设计和损伤识别中被广泛应用。目前主流的模态灵敏度分析方法是模态叠加法、Nelson方法以及它们的改进算法。但这些算法应用于大规模工程结构的模态灵敏度分析时，普遍存在着计算效率不高的缺陷。为了节省计算成本，本文提出一种结构振动模态灵敏度分析的改进子空间迭代方法。首先通过差分运算，把模态灵敏度的计算问题转化为结构发生微小修改后的模态特征对计算问题；然后，提出一种近似柔度计算公式，用于快速估算结构修改后刚度矩阵的逆矩阵，并将其应用于子空间迭代法的过程中，以迅速获得结构微小修改后的模态特征对，据此便可快速计算出相应的模态灵敏度。以两个结构模型为例验证了所提方法，结果表明，所提方法的计算精度与现有的模态灵敏度算法基本相同，但计算时间大幅度减少了，显示出了这种新方法的计算效率显著优于现有方法，更加适合于分析大型结构的振动模态灵敏度。

Sensitivity analysis of structural vibration modes (eigenvalues and eigenvectors) is widely used in structural vibration control, optimal design and damage identification. At present, the main modal sensitivity algorithms are modal superposition method, Nelson’s method and their improved algorithms. When these algorithms are applied to modal sensitivity analysis of large-scale engineering structures, there is generally a defect of low computational efficiency. In order to save the calculation cost, this paper proposes an improved subspace iteration method of modal sensitivity based on approximate flexibility. Firstly, the calculation problem of modal sensitivity is transformed into the calculation problem of modal eigen-pairs after minor modification of the structure by difference operation. Then, an approximate flexibility calculation formula is proposed to quickly estimate the inverse of the modified stiffness matrix of the structure, which is applied to the subspace iteration process to quickly obtain the modal eigen-pairs after minor modification, and accordingly the corresponding modal sensitivity can be quickly calculated. Two structural models are taken as examples to verify the proposed method. The results show that the calculation accuracy of the proposed method is basically consistent with the existing modal sensitivity algorithm, but the calculation time is greatly reduced. The proposed method is more suitable for vibration modal sensitivity analysis of large-scale engineering structures than the existing methods.