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

• The problem of damage identification in nonproportionally damped systems is analysed. • Two structures are modelled to track global and local complexity with increasing damage. • The pointwise change of the real and imaginary parts of the modes is examined. • The complex modal analysis is extended to a real structure experimentally damaged. • A new index based on complex eigenmode variation is proposed for damage localization. Real structures mode shapes estimated by modal analysis techniques have a common feature: in most cases they are complex, and their level of complexity can be soundly influenced by the presence and extent of physical damage, which also affects the distribution of energy dissipation mechanisms within the structures. 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. [ABSTRACT FROM AUTHOR]