A new direct method for updating structural models based on measured modal data

A direct method is proposed for updating the mass and stiffness matrices of a structural model such that it can accurately reproduce the frequencies measured for the structure. To start, we assume that only the first eigen mode was measured for the structure. The updated matrices are derived by utilizing the orthogonality conditions for the eigenvectors, and by replacing the eigenvector of concern with the modal matrix, to resolve the problem of insufficient number of equations. Such a procedure is then generalized to deal with the case where the first few eigenmodes are measured for the structure. For all the examples studied, it was demonstrated that the natural frequencies predicted by the present updated model agree well with the measured ones. The updated model is physically meaningful as the bandwith of the system matrices is preserved. The merit of the present method is its simplicity, efficiency, and accuracy in computation. It can be easily applied to structures that contain a large number of degrees of freedom.