Investigating the relation between complex mode shapes and local damage for structural assessment

Modal parameters define the inherent characteristics of real-world structures, being therefore employed as reference information for various purposes, including the assessment of structural damage, the evaluation of operational and environmental effects, and the calibration of realistic numerical models. Among frequencies, damping ratios and mode shapes, the latter have been proved far more effective in localizing structural damage given their spatial dependency on the nodal coordinates of vibrating systems. Most of modal analysis applications resort to the real part of these quantities for vibration-based damage identification of structural systems, assuming them as classically damped. However, the classical viscous damping assumption is often idealistic for real-world structures as the damping matrix cannot be considered as proportional to mass and stiffness matrices. It follows that the mode shapes of real systems are complex in nature, and their complexity level can vary with damage. Based on the above considerations, this work intends to shed light on the relationship between structural damage and modal complexity. Numerical investigations are carried out to track the variation of complex mode shapes in a multi-span bridge subjected to progressive damage scenarios and to infer about the generalization of a new index that relies on the variation of the imaginary content of complex eigenmodes to detect, locate and assess the structural damage.