Symmetric band structure preserving finite element model updating with no spillover. (1st February 2019)

• Record Type: Journal Article
• Authors: Rakshit, Suman; Khare, Swanand R.
• Is Part Of: Mechanical systems and signal processing. Volume 116(2019)
• Page Start: 415
• Page End: 431
• Publication Date: 2019-02-01
• Subjects: 15A22 -- 15A18 -- 65F18; Linear matrix pencil -- Symmetric band matrix -- Finite element model updating problem -- Vectorization of a matrix -- Kronecker product of two matrices; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2018.05.041
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: Finite element model is updated preserving the symmetric band structure of the original model and the no spillover property. A necessary and sufficient condition for the existence of solution of the symmetric band structure preserving finite element model updating with no spillover is obtained. We find explicit analytical expressions for the solution of this problem. We find the minimum norm solution of this problem. Abstract: Two most important yet difficult characteristics of the finite element model updating problem are to preserve the finite element inherited structures in the updated model and maintain no spillover of the eigenvalues and eigenvectors that do not take part in the updating process. Finite element matrices which arise due to the discretization of a distributed parameter system using finite element techniques are in general symmetric as well as band structure (diagonal, tridiagonal, pentadiagonal, etc). In this paper, symmetric band finite element model updating problem with no spillover (SFEMUN) is considered for the undamped model. A necessary and sufficient condition for the existence of the solution of the SFEMUN is derived. This equivalence enables us to characterize the class of solutions to SFEMUN. Further, an explicit expression for the minimum norm symmetric band solution of the SFEMUN is also presented. Numerical experiments on a spring mass problem illustrate that our proposed method is accurate and efficient.