Dynamic damage identification using complex mode shapes

Abstract

Damage, be it a material or a geometric degradation, modifies some features of the response foreseen by the original structural design. These variations, once the dependence on the damage causing them is established, can be used for identification purposes. In the literature, vibration-based approaches usually compare some responses of linear elastic structures with dissipative properties that are assumed proportional to the mass and stiffness measures. However, such an assumption is reasonable for new, undamaged structures, but can be unreliable in existing, potentially damaged structures, particularly for damages localised in narrow areas. The eigenmodes of a proportionally damped system can be reduced to the real ones of the relevant ideal undamped system. On the other hand, non-proportional damping exhibits complex eigenmodes that cannot be reduced to those of the ideal, or of the proportionally damped, structure. Thus, we may assume the complexity of the eigenmodes as a measure of nonproportional damping, hence of damage. On this basis, some contributions in the literature verified the relationship among presence of damage and amount of complexity. Here, we propose a perturbation approach and an objective function able to identify presence, location and amplitude of localised damages, intended as sources of non-proportionality in viscously damped linear systems. A prototype naturally discrete structure with four degrees-of-freedom is chosen to test and show capability and accuracy of the proposed method.

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

“…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)…”

“…To implicitly account for information associated with nonproportional damping arising from local damage phenomena, the scientific community has recently shifted the focus of its research activity towards the effects that non-uniform energy dissipation mechanisms cause to the mode shapes of a vibrating system. The hypothesis underlying this research trend is that undamaged structures exhibit proportional damping and their eigenmodes can be reduced to the real ones P r e p r i n t of the corresponding ideal undamped systems, whereas damaged structures exhibit nonproportional damping and their eigenmodes are lists of complex quantities associated to the amount of damage present in the system [21].…”

“…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.…”

A streamline approach to multiaxial fatigue monitoring using virtual sensing

“…19 Further examples on the application of filter-type techniques can be found in the literature. [20][21][22][23][24][25][26][27][28][29] Substituting the KF with these successors can improve the accuracy of fatigue monitoring methodology. Recently, the DKF has been applied to estimate the system state with aims to compute fatigue damage accumulation.…”

Optimal Sensors Placement in Dynamic Damage Detection of Beams Using a Statistical Approach

“…In this work, non-localized damages are adopted, which are in general more difficult to identify than narrow damages [36,37]. Damages are modeled as a perturbation of the healthy system and therefore a perturbation approach can properly describe the effect of the damage, both for standard [38] and state-space dynamic analysis [39,40]. In [41], a perturbation method has been proposed by some of the authors to derive the asymptotic eigensolution of a vibrating beam with uncertain damage.…”