## 2 Methodology  
Tubular composite pressure vessels are designed in a way that failure mainly happens in their cylindrical part. There, axial (longitudinal) cracks in the metal liner, as well as fibre fracture and epoxy matrix cracks in the CFRP overwrap, can occur [14; 37; 38]. These types of damage, together with an impact damage [39; 40], which may happen too, are the most critical and crucial issues with regard to a safe use of the COPV. In the work presented here and for reasons of simplification, the end caps of the vessel are neglected, and wave propagation is modelled in the circumferential (hoop) direction only. This will not only allow to detect axial cracks but also to concentrate on the circumferential CFRP plies, which are holding most of the pressure in the vessel. Furthermore, it allows damage detectability in such a hybrid material to be studied still under less complex loading conditions before moving to the more complex ones. In terms of the GW propagation, the cylindrical structure is therefore approximated to a plate, being allowed if the ratio of radius to thickness is larger than 10:1 [41]. The scope of this paper is merely to investigate the GW propagation in a multi-layered plate first while cylindrical structures need to be discussed in some future paper later. Figure 2 shows the configuration used. The numerical model considered consists of a plate made of a 4 mm CFRP laminate with a [90/0/90/0] layup (from top to bottom), followed by a 2 mm aluminium layer. Modelling was performed under the two-dimensional plain strain assumption. The CFRP plies were modelled separately as a stack in accordance to their lamination direction being transversally isotropic with a 1 mm thickness of each. Material properties from the ANSYS database were used in the model and are listed in Tables 1 and 2, where \(\rho\) is density, \(E\) is [PERSON]'s modulus, \(G\) is shear modulus, and \(\upsilon\) is [PERSON]'s ratio. Due to the production process of COPVs, a firm connection between the aluminium liner and CFRP overwrap is achieved, which allows a firm bonding between the two parts of the structure  
Figure 1: Schematic discretisation of: (**a**) an unbounded (infinite) domain in the scaled boundaty finite element method (SBFEM) (**b**); a domain in the SBFEM; and (**c**) in classical FEM. Figure 2: Sketch of a simplified structure of a COPV with corresponding sensor placement, adapted from [13]. to be considered. To calculate the dispersion curves and mode shapes, the plate thickness has been approximated using finite elements of the eighth order, whereas the domain in the wave propagation direction is described analytically, as shown in Figure 1a. For the analysis of wave propagation, an excitation domain, an evaluation domain, a damage domain and two unbounded domains at both ends of the plate were used. The schematic of the numerical model is shown in Figure 3.  
When actuating/deflecting the laminate at virtually any location over its cross-section, different mode shapes will be generated in accordance to the frequency being applied. To minimise the effect of dispersion by minimising a change in group velocities, some centre operation frequencies can be chosen, which have been marked with circles in Figure 4. For those, the mode shapes have been determined for which examples are shown in Figure 6. These mode shapes have further been used as the excitation to simulate a respective mode within the laminate and to understand the resulting consequences. The excitation was performed in both horizontal and vertical directions where the load distribution over the plate has been in accordance to the shape of the mode having been considered. These were pre-calculated using the unbounded domain in the SBFEM, for which an example is shown in Figure 1a. Even though such an excitation can be hardly realised in real application it has been used here for reasons of simplification and validation only and mainly to study the behaviour of a single respective mode.