# Propagation, Scattering and Defect Detection in a Circular Edge with Quasi-Edge Waves
## 1 Introduction  
Free edges are common features in various engineering components, and these structural features are often subjected to residual stress and are prone to manufacturing defects. As a result, fatigue cracks and other mechanical damage are predominantly initiated and propagate from free edges. Therefore, the defect monitoring of these structural features is of great practical interest. Ultrasonic-guided waves (UGWs) are considered one of the most effective techniques in non-destructive testing (NDT) and structural health monitoring (SHM). Over the past several decades, the application of UGWs has attracted significant attention to damage and defect detection and monitoring. One main advantage of UGWs is that these waves can propagate in various materials over long distances without significant decay and inspect large areas with a limited number of sensors, which is a prerequisite for SHM systems. In addition, it has been well documented that UGWs can effectively detect various types of damage, such as crack [1; 2; 3], corrosion [4; 5; 6] and delamination [7; 8; 9]. Most studies of UGWs are performed on relatively simple geometries, whereas real structures normally contain many structural features, such as edges, holes, weld seams and other geometric discontinuities, which represent a challenge for defect detection and monitoring. These structure features are normally associated with scattering andreflection, which induce extra difficulty in the interpretation of the damage signatures. In recent years, several studies indicated that some structural features can also be utilised as a waveguide for NDT or SHM purposes [10; 11; 12]. Ultrasonic waves that propagate along those structural features are known as feature-guided waves (FGWs). One main characteristic of FGWs is the concentration of wave energy in the vicinity of the waveguide or structural feature [13; 14; 15]. This concentration phenomenon (energy trapping effect) often results in almost lossless signal amplitude, enabling long propagation distance inspection and monitoring, e.g., inaccessible locations. Moreover, it also allows guided waves to inspect specific parts of the structure instead of the entire area to achieve a cost-effective structural integrity inspection [13]. The feasibility of the application of FGWs in damage and defect detection has been widely demonstrated. [PERSON] et al. [14] and [PERSON] et al. [13] investigated the propagation of FGWs along the stiffer, which bonded with an aluminium and composite plate, respectively. Their experimental results demonstrated that the feature-guided shear horizontal wave propagates along a stiffener can be utilised for monitoring the integrity of the bond. [PERSON] et al. [16] theoretically and numerically studied the generation of combined harmonic using an FGW mode propagating in a weld seam. They reported that the generation of a cumulative combined harmonic can be observed in the wave mixing zone, and this phenomenon can be utilised to monitor the progression of material degradation. Edge-guided waves (EGWs) are a type of FGWs, which are analogous to conventional Rayleigh waves. EGWs propagate along the surface of free edges and are guided by the apex of the plate structure, with a relatively low effective depth of penetration, and hence, they are less affected by the internal features of plate and shell components. In the literature, it has been found that two fundamental wave modes can propagate along these waveguides in an elastic material, namely extensional (\(ES_{0}\))- and flexural (\(EA_{0}\))-mode edge-guided waves [17; 18]. [PERSON] et al. [19] proposed a semi-analytical method to obtain the dispersion curve and mode shapes of EGWs propagated in isotropic materials. [PERSON] et al. [12] conducted an experimental and numerical study on the propagation of \(ES_{0}\).