Expansion of incomplete frequency response functions and prediction of unknown input forces

Abstract

The dynamic properties of structural and mechanical systems are commonly predicted using frequency response functions (FRFs), which represent the relationship between input forces and the corresponding responses in the frequency domain. Analytically calculated responses seldom coincide with actual responses because of modeling and construction errors, performance deterioration in service, etc. The inconsistency requires the correction of the FRF matrix for subsequent analysis, performance evaluation, etc. Obtaining the complete FRF matrix corresponding to all the degrees of freedom at measurement is not practical. This paper derives the mathematical form to expand the incomplete FRF matrix at measurement using the least-squares approach constrained by measured FRFs and correct the FRF matrix at the intact state. Additionally, this paper provides two analytical methods to predict unknown input dynamic excitations using the expanded FRF matrix and direct approaches. Numerical applications elucidate the validity and drawbacks of the proposed methods.