Symmetric structured finite element model updating with prescribed partial eigenvalues while maintaining no spillover

Abstract

This paper focuses on the Finite Element Model Updating (FEMU) problem for undamped systems. We examine the challenge of updating symmetric structured models using only a few specified eigenvalues, ensuring that the models retain their fundamental structural characteristics and avoid any spillover effects. Notably, we have access to only a few eigenvalues of the updated model, with no prior knowledge of the corresponding eigenvectors. Our objective is to identify an updated model that incorporates the desired eigenvalues while keeping the unmeasured eigenvalues unchanged. To achieve this, we first establish an equivalent condition for the existence of solutions to the problem and characterize all the solutions provided they exist. Additionally, we reformulate the problem of minimizing the perturbations to the system matrices as a constrained optimization problem. We present several numerical examples to illustrate the effectiveness of our proposed method.