This paper introduces a wave propagation-based damage index (DI) which relies on the estimation of phase gradients of propagating waves for accurate damage localization and on the prediction of mode conversion coefficients for damage quantification. The undamaged, or unperturbed, reference response is derived directly from the damaged component, through the application of filtering procedures in the wavenumber/frequency domain. These procedures separate incident waves from reflections caused by structural discontinuities encountered along the wave path. The DI formulation is illustrated through a numerical model of a beam with a small notch, modeled as a localized thickness reduction. The beam’s wave propagation response is simulated through the combined application of perturbation techniques and the Spectral Finite Element Method (SFEM). The resulting numerical tool allows efficient computation of the wave propagation response and the analysis of the effects of localized damages of various extent and location. The dynamic behavior of damaged beams is described through a general higher order model which couples bending and axial behavior, thus allowing the prediction of mode conversion phenomena. Numerical examples are presented to illustrate the model capabilities.

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