Modal Density Influence on Modal Complexity Quantification in Dynamic Systems

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

“…Therefore, as mentioned in the Introduction, several indicators based on mode shapes complexity have been proposed in the literature for damage identification purposes. Among the most relevant are the Modal Phase Collinearity (MPC) [11], the Modal Imaginary Ratio (MIR) [6], the Modal Dispersity (MD) and the Modal Polygon Area (MPA) [12]. MIR, MD, MPA lead to positive values ranging between zero -in case of null or proportional damping and real-valued vectors -and one -in case of non-proportional damping and fully complex modes; conversely MPC is equal to one for real mode shapes.…”

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

“…Non-uniform energy dissipation mechanisms due to non-proportional damping distribution within the structure lead to complex vibration modes. As a result, many indices based on the mode shapes complexity have been formulated in the literature to measure the damping nonproportionality of a vibrating system through experimental or operational modal analyses [3], [13], [24], [30]. Some of these indices have also been used to numerically estimate the damage evolution path in framed structures with a typical shear-type behaviour [21], assuming the (1.11)…”

“…The system was discretized into 40 straight beam elements (element no. 9 of the NOSA-ITACA library [39]) for a total of 41 nodes and 246 degrees of freedom, allowing to obtain a simple yet refined baseline model far different from the reduced order models usually adopted in the literature to address the problem of modal complexity [23], [24].…”

“…Based on these considerations, over the last decades several contributions have spread in the literature trying to verify the relationship between damage and modal complexity in order to exploit this information for structural health monitoring of existing artefacts. Worth of mention are the pioneering work of Kawiecki [18], who tried to use the modal damping characteristics of a tested structure for damage detection; the investigations carried out by Iezzi et al [22], [23], [24], who applied and validated the effectiveness of a measurable complexity index to detect the presence of damage in framed structures having a typical "shear-type" behaviour; the study of Masciotta et al [14], who embarked on the analysis of the real and imaginary components of complex eigenvectors for damage localization; and the very recent study of Lofrano et al [21], who proposed a numerical approach based on a perturbation method to detect, locate and quantify the damage in framed structures by exploiting state-of-the-art complexity indices. Despite the scientific robustness of the developed approaches and the consensus reached on the pivotal role that complex eigenmodes can play as a measure of structural damage, the applicative counterparts have shown some limitations.…”