ASSESSMENT OF STRUCTURAL DAMAGE FROM NATURAL FREQUENCY MEASUREMENTS

A method is developed for the estimation of structural damage using measured changes in the natural frequencies. The relationship of the variation in the eigenvalues to the localized reductions in the stiffness of the undamaged structure is a set of underdetermined simultaneous equations derived from the first-order perturbation of the eigenvalue problem. An optimality criterion is introduced to solve these equations by minimizing the difference between the eigenvalue problems for the undamaged and damaged structures. The overall formulation leads to a quadratic optimization problem with linear equality and inequality constraints. Numerical tests are performed on a beam and a frame. By using exact or noise-polluted natural frequency data, reduction in the stiffness of up to 40% at single or multiple sites is detected.