A method is developed for the estimation of structural damage using measured changes in the natural frequencies. The natural frequencies are sensitive to variations in the stiffness of the system and can be used to detect such variations. A finite element model that correctly describes the system before damage is used as the basis of the analysis. Localized stiffness degradation in the structure is identified from the stiffness reduction in the analytical model necessary to reproduce the data measured after the damage.; The changes in the stiffness matrix are expressed in terms of the changes of the independent structural elements. Such formulation guarantees the structural connectivity and the symmetry in the stiffness matrix of the damaged structure. A first-order perturbation method is used to arrive at the sensitivities of the natural frequencies to the localized changes in the stiffness of the undamaged structure. The sensitivities of the structure thus yield an underdetermined set of simultaneous linear equations to be solved for the unknown element stiffness reductions. A unique solution is obtained using an optimization process. The derived equations are used as the linear constraints in a quadratic programming problem which minimizes any of three criteria: (1) the norm of the changes in the element stiffnesses, (2) the norm of the change in the global stiffness matrix, or (3) a residual error in the vibration eigenvalue problem. The first and second criteria force the modification in the stiffness to be small. The third criterion reflects the insensitivity of the eigenvectors to localized damage.; Numerical tests on simple structures show favorable results. By using exact or noise polluted natural frequency data, reduction in the stiffness of more than 90% at single or multiple sites can be detected.; Measurements of the changes in the natural frequencies of an aluminum cantilever beam are available in the literature. The data were used to validate the damage identification method. A 93% decrease in the stiffness and the location of the damage were identified accurately.
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