# Propagation, Scattering and Defect Detection in a Circular Edge with Quasi-Edge Waves
## 1 Introduction
They found that the \(ES_{0}\) is suitable for long-distance inspections in the low range of the frequency to thickness value (\(FTV<5\)), while a strong amplitude modulation phenomenon due to the interaction with other wave modes was observed in the high FTV range, \(FTV=2\pi fH\) / C\({}_{T}\), where \(f\) is the linear frequency, \(H\) is the thickness of the waveguide (plate) and C\({}_{T}\) is the shear wave speed in the material. In recent publications, the semi-analytical finite element (SAFE) approach has been widely utilised to acquire the propagation characteristics of EGWs in isotropic [20] and anisotropic materials [21]. However, past studies of EGWs were conducted on flat or quasi-flat edge geometries. The effect of the waveguide curvature on the propagation characteristics of EGWs has not been investigated so far. Indeed, analytical approaches or SAFE are currently not available or suitable for the investigation of the characteristics of EGWs that propagate along curved edges due to the complexity of the geometry and associated boundary conditions. On the other hand, there has been a significant interest in using EGWs for non-destructive damage and defect detection. [PERSON] and [PERSON] [22] demonstrated the feasibility of \(ES_{0}\) for the detection of impact damage at the edge of a carbon-fibre-reinforced polymer (CFRP) plate. [PERSON] et al. [23] studied the effect of sharp and rounded corners on the propagation of \(ES_{0}\). They demonstrated that \(ES_{0}\) can propagate through sharp and rounded corners of plate- and shell-like structures, and that the nonlinear features of the \(ES_{0}\) wave mode can be used for locating defects and damage. All these features make the \(ES_{0}\) wave mode very suitable for inspecting inaccessible areas of the structure. [PERSON] et al. [24] investigated the scattering characteristics of \(ES_{0}\) in the presence of edge cracks located near a raccourse-shaped hole in a flat aluminium plate, which revealed that the amplitude of scattered waves can be utilised for detecting and quantifying edge defects. Despite these promising findings, relatively few studies have focused on damage detection in curved edges. Moreover, the potential of the EGWs in detecting defects along curved edges has not yet been explored despite the fact that these curved edges are often found in many designs, such as in the leading edge of an aircraft's engine inlet. To improve the understanding of EGWs in detecting damages in curved structural edges, this study aims to investigate the propagation of the fundamental mode of quasi-edge waves (\(QES_{0}\)) along curved edges and explore the scattering characteristics of the \(QES_{0}\) at notch-like edge defects. In contrast to previous studies on damage or defect detection using EGWs, this study not only focuses on the reflected and transmitted signals but also investigates scattered waves on the curved surface in various directions using the scatter directivity pattern (SDP) approach. Therefore, the outcome of this investigation can also be helpful for the selection and optimisation of sensor configuration for future NDT and SHM systems utilising the \(QES_{0}\) wave mode. This paper first presents a 3D FE approach for investigating the effect of waveguide curvature on the propagation characteristics of the \(QES_{0}\) wave mode in Section 2.1 and is followed by selected simulation results, which are described in Section 2.2. The details of the 3D FE model for investigating the scattering characteristic of \(QES_{0}\) at different edge defects are presented in Section 2.3. Section 3 is devoted to an experimental study, which is used to validate the developed FE model. The simulation results of the scattering study using the experimentally verified FE model are presented in Section 4. The conclusion and main findings are drawn in Section 5.