Updating large models for mechanical systems using incomplete modal measurement

Abstract

The problem of model updating for mechanical or structural systems is addressed by using incomplete modal measurement. The proposed method requires only the modal frequencies and mode shapes at some selected degrees of freedom for a few modes. The method updates the mass and stiffness matrix without imposing any parameterization and it utilizes the information from both the nominal finite-element model and the modal data. The method is computationally efficient as neither iteration nor numerical optimization is required. It does not require computation of the complete set of eigenvalues and eigenvectors of the nominal model. Instead, only the ones corresponding to the observed modes are needed. The method first updates the modal frequencies. Then, an efficient algorithm is presented to construct a transformation matrix. This matrix is used to correct the nominal eigenvectors so that the updated model is compatible with the measurement of the eigenvectors. A twelve-degree-of-freedom truss is used to provide insights of the proposed method. Finally, a 1600-degree-of-freedom spring-mass system is considered to illustrate the efficiency of the proposed method for large structure.