A fast analysis algorithm for structural vibration modal sensitivity

Xi Peng

doi:10.1016/j.istruc.2024.106623

A fast analysis algorithm for structural vibration modal sensitivity

2024-06-01

1

PRE

AI

DOI：10.1016/j.istruc.2024.106623

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Vibration modal sensitivity analysis has a wide range of applications in structural optimization design, model correction, fault detection, and reliability analysis. The existing methods for calculating modal sensitivity mainly include modal superposition method, Nelson's method, and some improved algorithms derived from them. However, the existing algorithms have the drawback of low computational efficiency when applied to modal sensitivity analysis of the large-scale structures. In view of this, the objective of this work is to develop a fast modal sensitivity analysis method that can more efficiently calculate the modal sensitivity of the large structures with thousands of degrees of freedom. This new sensitivity analysis technique integrates Sherman-MorrisonWoodbury formula, subspace iteration and forward-difference to achieve the goal of fast calculation. The innovations of the proposed method mainly include the following aspects. Firstly, the Sherman-MorrisonWoodbury formula is used to quickly calculate the perturbed flexibility matrix due to the minor modification in the structure. Then, the perturbed flexibility matrix is introduced into the subspace iteration method to calculate the perturbed modal parameters. Finally, the forward-difference algorithm is used to calculate the modal sensitivity. Two numerical examples are used to verify the superiority of the proposed modal sensitivity algorithm. Taking the 1952-bar structure as an example, the calculation time of the proposed algorithm is only 8.3 % and 18.2 % of that of the existing approximate modal superposition method and the improved Nelson's method, respectively. In terms of calculation accuracy, the results obtained by the proposed method are exactly the same as the exact solution when the perturbation scale is set to 10-5. It is found that the proposed method significantly reduces computation time compared to the existing methods on the premise that the calculation accuracy is basically unchanged.

Keyword:

Vibration mode

Sensitivity

Eigenvalue

Eigenvector

Subspace iteration

A fast analysis algorithm for structural vibration modal sensitivity

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