Structural Engineering and Mechanics

  • 제88권5호
  • /
  • Pages.493-500
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  • 2023
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

The structured multiparameter eigenvalue problems in finite element model updating problems

  • Zhijun Wang (School of Mathematical Science, Dalian University of Technology) ;
  • Bo Dong (School of Mathematical Science, Dalian University of Technology) ;
  • Yan Yu (Business School, Dalian University of Foreign Languages) ;
  • Xinzhu Zhao (School of Mathematics, Liaoning University) ;
  • Yizhou Fang (School of Mathematical Science, Dalian University of Technology)
  • 투고 : 2023.02.04
  • 심사 : 2023.11.17
  • 발행 : 2023.12.10
⟨ 이전 논문 다음 논문 ⟩

초록

The multiparameter eigenvalue method can be used to solve the damped finite element model updating problems. This method transforms the original problems into multiparameter eigenvalue problems. Comparing with the numerical methods based on various optimization methods, a big advantage of this method is that it can provide all possible choices of physical parameters. However, when solving the transformed singular multiparameter eigenvalue problem, the proposed method based on the generalised inverse of a singular matrix has some computational challenges and may fail. In this paper, more details on the transformation from the dynamic model updating problem to the multiparameter eigenvalue problem are presented and the structure of the transformed problem is also exposed. Based on this structure, the rigorous mathematical deduction gives the upper bound of the number of possible choices of the physical parameters, which confirms the singularity of the transformed multiparameter eigenvalue problem. More importantly, we present a row and column compression method to overcome the defect of the proposed numerical method based on the generalised inverse of a singular matrix. Also, two numerical experiments are presented to validate the feasibility and effectiveness of our method.

키워드

과제정보

This work was supported by the National Natural Science Foundation of China under Grant 12371376, 11801382 and Liaoning Provincial Natural Science Foundation of China under Grant 2020-MS-278 and Scientific Research Fund of Liaoning Provincial Education Department under Grant 2020JYT04.

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