Improved subspace iteration method for the modal sensitivity analysis of structural vibration

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Journal of Vibration and Shock ›› 2025, Vol. 44 ›› Issue (10) : 161-169.

VIBRATION THEORY AND INTERDISCIPLINARY RESEARCH

Improved subspace iteration method for the modal sensitivity analysis of structural vibration

CAO Hongfei1,2,PENG Xi*1,2,YANG Qiuwei1,2

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Abstract

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.

Key words

Vibration mode / Sensitivity analysis / Subspace iteration method / Approximate flexibility / Computational efficiency

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CAO Hongfei1, 2, PENG Xi1, 2, YANG Qiuwei1, 2. Improved subspace iteration method for the modal sensitivity analysis of structural vibration[J]. Journal of Vibration and Shock, 2025, 44(10): 161-169

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