Model Updating by Adding Known Masses

Document Type



Engineering (HMC), Mathematics (HMC)

Publication Date



New approaches are developed that use measured data to adjust the analytical mass and stiffness matrices of a system so that the agreement between the analytical modes of vibration and the modal survey is improved. By adding known masses to the structure of interest, measuring the modes of vibration of this mass-modified system, and finally using this set of new data in conjunction with the initial modal survey, the analytical mass matrix of the structure can be corrected, after which the analytical stiffness matrix can be readily updated. By manipulating the correction matrices into vector forms, the connectivity information can be enforced, thereby preserving the physical configuration of the system and reducing the sizes of the least-squares problems that need to be solved. Solution techniques for updating the system matrices are introduced, and the numerical issues associated with solving overdetermined and underdetermined least squares problems are investigated. The effects of round-off errors are also studied, and heuristic criteria are given for determining the minimum number of modes that need to be measured in order to ensure sufficiently accurate updated mass and stiffness matrices. Numerical experiments are presented to validate the proposed model-updating techniques, to illustrate the effects of the number of measured modes on the quality of the updated model, to show how the magnitudes and locations of the added masses influence the updated matrices, and to highlight the numerical issues discussed in this paper.

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© 2001 John Wiley & Sons