Reduced basis eigenvalue solutions for damaged structures

A structural analysis must be performed repeatedly in damage analysis to predict worst-case scenarios for evaluating all possible damage cases. This study aims to approximate the dynamic reanalysis of damaged structures by using a reduced basis approach with a binomial series approximation. Considering each mode shape as a static case and using the original structure's corresponding eigenvector as the basis vector leads to approximations for a damaged structure's new eigenvalue and eigenvectors. The damage considered is the loss of moment resistance at connections in plane frames. The examples show accurate solutions based on two equations for structures with up to 36 degrees of freedom.