On the Use of Finite Differences for Vibration-Based Damage Localization in Laminated Composite Plates

Laminated 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, as these materials develop inherently unique failure modes. This thesis aims to further the study of the use of modal shapes and their spatial derivatives to damage localization in laminated composite rectangular plates. ANSYS® Parametric Design Language (APDL) is used to perform Finite Element simulations of plates with several damage scenarios and damage mechanics models. MATLAB® is used to postprocess these simulations results, namely by calculating the derivatives using the Finite Difference Method, applying three different Damage Detection Methods, including one that is being proposed here. To mimic experimental conditions and testing the resilience of the derivative orders, different noise levels are introduced in the results of the Finite Element simulations. A Quality Index is employed to quantitatively evaluate the solutions, mainly regarding the response to the introduced noise. The results show that the different Damage Detection Methods tested have comparable results in terms of quality. These results also show that the damage detectability 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.