Tracking the variation of complex mode shapes for damage quantification and localization in structural systems

Real structures' mode shapes estimated by modal analysis techniques have a common feature: in most cases they are complex, and this complexity can derive from nonproportional damping, nonlinearities, mass loading effects, high modal density and localized damage, among others. Starting from the contributions available in the literature, the present paper investigates, from a numerical and experimental point of view, the correlation existing between localized damage and variation of global modal complexity indices conventionally employed to quantify the nonproportionality of damping in structural systems. Finally, driven by the inferences made through numerical and experimental test cases by tracking the variation of complex modes over multiple and progressive damage scenarios, a new index for damage localization and quantification is formulated and validated against real data.