Stiffness Matrix Properties for Reduced Order Models of Linear Structural Systems

Abstract

This paper discusses a theoretical approach to investigate the dependency relationship between the stiffness matrix and the complex eigenvectors in the identification of structural systems for the case of insufficient instrumentation setup. The main result of the study consists of proving, in the case of classical damping, the independency of the stiffness subpartition corresponding to the measured degrees-of-freedom from the unmeasured ones. The same result is shown to be valid in the case of nonclassical damping but only for tridiagonal sparse stiffness matrix systems. A numerical procedure proves the above results and also shows the dependency relationship for the general nonclassical damping cases.