# Propagation, Scattering and Defect Detection in a Circular Edge with Quasi-Edge Waves
## 5 Conclusions  
An investigation of the propagation and scattering characteristics of the \(QES_{0}\) wave mode in circular edges of structural components was presented in this paper. In the first part of this article, the effect of waveguide curvature on the attenuation and mode shapes of \(QES_{0}\) was investigated using the FE approach. The FE models were constructed for a wide range of R/T ratios, ranging from 10 to 100, covering most curvatures in practical applications. The FE simulation results indicated that the coefficient of attenuation exponentially increased with the waveguide curvature. In addition, from the analysis of the mode shapes, it was found that the normal displacement of \(QES_{0}\) at the top edge, close to the outer-side surface, was larger than that of the corresponding location close to the inner-side surface. This characteristic can be used for improving signal-to-noise ratio in practical applications of the \(QES_{0}\) wave mode, specifically for relatively thick components. In the second part of this study, the reflection-and-transmission ratio of \(QES_{0}\) at edge defects was first experimentally and numerically investigated. The outcomes indicated that the 3D FE approach is capable of accurately predicting the interaction between the \(QES_{0}\) wave mode and different dimension's edge defects. The experimentally validated3D FE model was further employed to explore the scattering characteristics of the \(QES_{0}\) wave mode for various geometries of edge defects, representing possible edge defects. The results indicated that the scattered waves have relatively large amplitudes in both forward and perpendicular directions with respect to the incident wave propagation direction. Meanwhile, compared to the type I (inner side) partially through-thickness edge defect, the \(QES_{0}\) at the type II (outer side) edge defect has a relatively strong scattered wave component between the forward and normal directions of incident wave direction. Although the results are promising, underlying assumptions of the developed FE model should be considered when comparing experimental results with numerical simulations. The effect of material damping was not modelled; therefore, only the effect of waveguide curvature on the attenuation of \(QES_{0}\) was revealed in the FE simulations. To fully understand the propagation characteristics of \(QES_{0}\), future studies can incorporate the effect of material damping on the propagation of the \(QES_{0}\) wave mode. Moreover, it is assumed in the FE model that the surfaces of the specimen are perfectly smooth, which is not the case for real structural components. Since EGWs are surface waves, the roughness of surfaces could significantly affect the propagation of the \(QES_{0}\) wave mode, specifically when the wavelength becomes comparable with the characteristic size of the asperities or other structural imperfections. In addition, the contact condition between the interfaces of the wedge and specimen in the FE model is defined as a 'Tie' constraint, which may differ from the conditions in actual measurements. In summary, this study provided fundamental insights into the propagation of \(QES_{0}\) in a curved waveguide, and the scattering characteristics of \(QES_{0}\) at various shapes of edge defects. The main practical outcome of this work is the demonstration of the high sensitivity of the \(QES_{0}\) wave mode to different types of edge defects and its ability to propagate over long distances (at high R/T ratios, i.e., above 20). This capability can be utilised for inspecting defects in inaccessible areas of structures. Overall, the outcomes highlight the significant potential of this guided wave mode for future NDT and SHM systems in detecting and characterising damage along the curved edges of structural components. Conceptualisation, P.L. and A.K. ; software, P.L. ; validation, P.L., A.K. and C.T.N. ; investigation, P.L. ; resources, A.K. and C.T.N. ; writing--original draft preparation, P.L. ; writing--review and editing, A.K. and C.T.N.