Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped and damped structures assuming damage results in a localized change in a subset (not full set) of the property matrices (mass, stiffness and damping matrices). The algorithms make use of a finite element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite element model. In this work, the concept of the Minimum Rank Perturbation Theory (MRPT) is adopted to simultaneously determine the damage extent of all property matrices of undamped and proportionally damped structures. Note that the property matrices are the mass, stiffness and damping matrices. Illustrative examples are presented to show the performance of the proposed theory. [S0739-3717(00)01904-8]

Issue Section:
Technical Papers
Keywords:
damping, eigenvalues and eigenfunctions, perturbation theory, vibrations, nondestructive testing, finite element analysis
Topics:
Damage, Damping, Stiffness, Eigenvalues, Finite element model, Algorithms, Perturbation theory
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