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Abstract

This paper introduces a wave propagation-based damage index which relies on the evaluation of the strain energy distribution associated with propagating waves. The presence of localized damages typically distorts the wavefield by causing reflections and diffractions. The evaluation of such distortions, in reference to the wavefield corresponding to the undamaged structure, can be used as an indicator which potentially locates, quantifies and classifies the damage.The damage index formulation is first 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. The perturbation approach and a first order model for the beam capture the coupling between bending and axial behavior caused by the damage, and allow the prediction of mode conversion phenomena. The perturbation solution allows direct comparison between undamaged and damaged strain energy contributions, which are directly associated with perturbation solutions of different orders. The resulting damage index locates the damage along the beam length and estimates its severity.Experimentally, the damage index is implemented by considering full wavefield measurements obtained through a scanning laser vibrometer. The undamaged reference response is derived directly from measurements on the damaged component, through the application of a filtering procedure operating in the wavenumber/frequency domain.

Saint-Venant’s Principle in Dynamics of Structures

“…Yilmaz [122] derived similar energy decay estimates for a system of coupled parabolic-hyperbolic equations with clamed surfaces under nonlinear conditions. Chirita and Ciarleta [123] gave spatial decay estimate for an anisotropic homogeneous and compressible cylinder. The lateral surface and far end of the cylinder are constrained by zero displacement condition.…”

“…The papers by Scalia [129] and Chirita and Ciarletta [123] mentioned above, in a different context, analyzed anisotropic materials and therefore belong as well to this group of studies.…”