A direct method for updating piezoelectric smart structural models based on measured modal data

Yinlan Chen; Lina Liu; Yinlan Chen; Lina Liu

doi:10.3934/math.20231288

AIMS Mathematics

2023, Volume 8, Issue 10: 25262-25274. doi: 10.3934/math.20231288

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Research article

A direct method for updating piezoelectric smart structural models based on measured modal data

Yinlan Chen ^{1
,
,},
Lina Liu ²

1.
School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China
2.
Shunde Experimental Middle School, Foshan, 528000, China

Received: 07 July 2023 Revised: 17 August 2023 Accepted: 23 August 2023 Published: 30 August 2023
MSC : 15A24, 65F18

A direct method for simultaneously updating mass and stiffness matrices of the undamped piezoelectric smart structural models based on incomplete modal measured data is presented. By applying the generalized singular value decomposition and some matrix derivatives, the optimal approximate mass and stiffness matrices which satisfy the required eigenvalue equation and the orthogonality relation are found under the Frobenius norm sense. The method is computationally efficient as neither iteration nor eigenanalysis is required. Numerical results are included to illustrate the effectiveness of the proposed method.
- piezoelectric smart structure,
- generalized singular value decomposition,
- model updating
Citation: Yinlan Chen, Lina Liu. A direct method for updating piezoelectric smart structural models based on measured modal data[J]. AIMS Mathematics, 2023, 8(10): 25262-25274. doi: 10.3934/math.20231288

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Abstract

A direct method for simultaneously updating mass and stiffness matrices of the undamped piezoelectric smart structural models based on incomplete modal measured data is presented. By applying the generalized singular value decomposition and some matrix derivatives, the optimal approximate mass and stiffness matrices which satisfy the required eigenvalue equation and the orthogonality relation are found under the Frobenius norm sense. The method is computationally efficient as neither iteration nor eigenanalysis is required. Numerical results are included to illustrate the effectiveness of the proposed method.

References

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