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Structural Engineering and Mechanics
  Volume 88, Number 5, December10 2023 , pages 493-500
DOI: https://doi.org/10.12989/sem.2023.88.5.493
 


The structured multiparameter eigenvalue problems in finite element model updating problems
Zhijun Wang, Bo Dong, Yan Yu, Xinzhu Zhao and Yizhou Fang

 
Abstract
    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.
 
Key Words
    dynamic analysis; finite element model updating; generalised inverse; row and column compression method; singular multiparameter eigenvalue problem
 
Address
Zhijun Wang: School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, China
Bo Dong: School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, China
Yan Yu: Business School, Dalian University of Foreign Languages, Dalian 116044, China
Xinzhu Zhao: School of Mathematics, Liaoning University, Shenyang, China
Yizhou Fang: School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, China
 

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