On the use of finite differences for vibration-based damage localization in laminated composite plates

PurposeLaminated composite materials are a staple of modern material development, with extremely strong fibers being combined with resins to form versatile and efficient engineering structures. However, the advancements in material development must be accompanied by equally advanced methods for damage detection, localization and quantification, as these materials develop inherently unique failure modes. This paper aims to further the study of the use of modal shapes and their spatial derivatives to localize damage in laminated composite rectangular plates. Exploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates.Design/methodology/approachANSYS® Parametric Design Language (APDL) is used to perform finite element analysis of plates with several damage scenarios and damage mechanics models. MATLAB® is used to post-process these simulation results, namely by calculating the derivatives using finite differences, applying three distinct sets of damage indices, including one that is presently proposed. To mimic experimental conditions and test the resilience of the derivative orders, different noise levels are introduced into the results of the finite element analysis. A quality index is employed to quantitatively evaluate the solutions, mainly regarding the response to the introduced noise.FindingsThe results show that the applied damage localization methods have comparable results in terms of quality. These results also show that the quality of the damage localizations is higher when the damaged areas coincide with high displacement/curvature areas of the mode shapes and that higher noise levels have a more noticeable negative impact when employing higher-order derivatives.Originality/valueExploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates. The influence of a specific damage layer on the order of derivatives of modal response is evaluated, showing promising results concerning its identification.