## 1 Introduction  
Structural health monitoring (SHM) in the aerospace sector has the potential to reduce costs and increase reliability [1]. A number of nondestructive inspection techniques are already applied in the aerospace industry such as radiography [2], acoustic emission [3], eddy current [4], and ultrasonic inspection [5]. The use of advanced composite structures has also introduced an added layer of complexity where the failure modes are complex [6] and damage may occur between layers. Guided waves present a suitable SHM technique for thin structures [7; 8; 9]. They can travel large distances and interact with defects. Hence, they can be used for detection, localisation, and identification of damage [10; 11]. Ultrasonic guided waves are guided by the traction free top and bottom surfaces of thin plate-like structures. They are generated due to the constructive and destructive interference and superposition of pressure waves and shear vertical waves undergoing multiple reflections from the boundaries [12]. Guided waves in plates can be classified into three broad categories based on their polarisation [13]: (a) symmetric (S) waves polarised perpendicular to the plane of the plate with the plate surfaces displacing out of phase, (b) anti-symmetric (A) waves polarised perpendicular to the plane of the plate with the plate surfaces displacing in phase, and (c) shear horizontal (SH) waves polarised in the plane of the plate. SH waves can also be symmetric or anti-symmetric with respect to the mid-plane of the plate. In theory, an infinite number of guided wave modes can propagate in a plate. Hence, the conventional notation used to represent them is with a subscript n, where n = \(0,1,2,3\dots\), i.e., \(\text{S}_{\text{n}}\) and \(\text{A}_{\text{n}}\). For \(\text{SH}_{\text{n}}\), an even n denotes symmetric and an odd n denotes anti-symmetric waves. In multilayered structures, the elastic anisotropy results in quasi-Lamb waves and quasi-SH waves, which are mutually coupled, and the distinction is not as clear as in isotropic structures. It is still standard practice to adopt the nomenclature for guided waves in isotropic structures, which is followed here. Guided wave dispersion curves provide important insight into the wave propagation in a structure. The group velocity curve shows the value of velocity versus the frequency. It is, however, important to calculate the change in the propagation direction of the group velocity versus the phase velocity for anisotropic materials. For isotropic plates with constant thickness, the group and phase velocities do not have angular dependence and the 2D profile is circular. This quickly becomes non-trivial in complex multilayered structures where the directions of wave propagation and energy propagation are different. The directional nature of composite structures creates another increase in complexity, where the 2D profile can take any shape depending on the composite layup. Nevertheless, identifying these characteristics is important for applications that use guided waves. There are two main approaches for computing the dispersion properties: (a) analytical and (b) semi-analytical. The analytical methods consist of solving the governing differential equations by applying the appropriate boundary condition. They can further be divided into exact methods based on 3D elasticity theory and semi-exact methods based on approximate plate theories. The 3D elasticity method was used to calculate the phase velocity of composite lamina and laminate [14,15]. The exact methods are computationally intensive due to the transcendental equations used for multilayered composites. Therefore, approximate plate theories are employed to ensure the solutions are practical [16,17]. Recently, [PERSON]'s general energy expression was applied to derive the group velocity vector of elastodynamic guided waves [18] in arbitrary layered structures. The semi-analytical methods use finite element (FE) approaches to model part of the structure and impose wave solutions in the propagation directions.