Modal Scaling from Known Mass Perturbations

Abstract

When the identification of a linear system is carried out without deterministic input information the scaling constants that connect the eigensolution to the matrices of the physical system are not determined. One way to generate information to compute these constants is by testing the structure with known modifications and examining how the eigensolution changes. Closed-form uncoupled expressions have been derived from this idea by requiring that the changes in the frequencies, or the mode shapes, be small. For general modifications, however, the solution is currently sought in the less convenient framework of a nonlinear optimization. This paper presents a new formulation that can accommodate arbitrary modifications yet retains the computational advantages of a closed-form solution. Results from a statistical simulation study suggest that the new expression is not only computationally attractive, but can lead to improvements in accuracy when compared to the existing alternatives.