Symmetric band structure preserving finite element model updating with no spillover

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.