Modal curvature-based damage localization in weakly damaged continuous beams

Modal curvatures have been claimed to contain local information on damage and to be less sensitive to environmental variables than natural frequencies. However, simply using the difference between modal curvatures in the undamaged and damaged states can result into localization errors, due to the complex pattern that this quantity presents when considering broad damages or higher order modes. In this paper, we consider weakly damaged continuous beam and we exploit a perturbative solution of the beam equation of motion to obtain an analytical expression of the modal curvature variations in terms of damage distribution. The solution is then used to introduce a filtering technique of the modal curvature variation and to set up the inverse problem of damage localization based on modal curvatures only. Using numerical examples and experimental tests, we show that modal curvatures can be used for precise damage localization, once properly filtered.