## 2 Materials and Methods
### Lamb Waves
#### 2.2.1 Calculation of the Dispersion Curves  
The WTB example is used to better understand and explain the unusual limitations of Lamb waves and show the difficulties encountered in performing defect measurements. First, in order to understand the structure of the analysed object and its complexity, the geometry parameters of the WTB should be presented. The cross-sectional view of the WTB structure is sown in Figure 4a, the simplified model of the structure in Figure 4b.  
Figure 3: The schematic diagram of the safety and quality assurance of wind turbine blades (**a**), SHM example (**b**), NDT example (**c**).  
The whole WTB is made of a composite structure, which consists of several material layers with different geometry and material properties. Generally, the WTB consists of the surface layer, epoxy, and unidirectional GFRP. Each main layer is of a different thickness Figure 4b. Other features: the WTB skin and main spar consist of several GFRP plies, with orientations of 0\({}^{\circ}\)/90\({}^{\circ}\)/+45\({}^{\circ}\)/\(-\)45\({}^{\circ}\)/0\({}^{\circ}\) and +45\({}^{\circ}\)/\(-\)45\({}^{\circ}\), respectively. Thus, the second parameter that is especially important and is used in the study of WTB is the elastic properties of the whole object. The elastic properties are used to describe the theoretical dispersion curves, which are used to obtain comparable results. The main parameters are density (\(\rho\)) and elastic constants as Young's modulus (E) and Poisson's ratio (v). Generally, the manufacturers provide the elastic properties of the individual layers, as presented in Table 1[53]. Then, using the analytical or semianalytical methods, the Lamb waves dispersion features of the whole object are obtained.  
The dispersion curves of the phase and group velocities of Lamb waves propagating in the WTB are theoretically calculated by the SAFE method according to the given elastic properties (Table 1) and geometry parameters (Figure 4b). The SAFE method, in more detail, is presented by other authors [54; 55] and is based on the plane wave propagation in a plate using one-dimensional discretisation.  
The plate is divided into a finite number of layers, each of which is described by three nodes in the one axis direction. In the second axis direction, it is assumed that the plate is infinite. The calculation is carried out up to 250 kHz for both phase and group velocities and presented in Figure 5a,b accordingly.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Numerical Value** \\ \hline \hline \multicolumn{1}{c}{Paint (Surface layer):} & \multicolumn{1}{c}{Density (\(\rho\))} & 1270 kg/m\({}^{3}\) \\  & Young’s modulus (E) & 4.2 GPa \\  & Poisson’s ratio (v) & 0.35 \\ Unidirectional GFRP layer: & \multicolumn{1}{c}{Density (\(\rho\))} & 1828 kg/m\({}^{3}\) \\  & [PERSON]’s modulus (E1) & 42.5 GPa \\  & [PERSON]’s modulus (E2) & 10 GPa \\  & [PERSON]’s ratio (v12) & 0.26 \\  & [PERSON]’s ratio (v23) & 0.4 \\  & In-plane shear modulus (G12) & 4.3 GPa \\ Epoxy: & \multicolumn{1}{c}{Density (\(\rho\))} & 1260 kg/m\({}^{3}\) \\  & [PERSON]’s modulus (E) & 3.6 GPa \\  & [PERSON]’s ratio (v) & 0.35 \\ \hline \hline \end{tabular}
\end{table}
Table 1: GFRP material properties used in modelling.  
Figure 4: The real WTB sample (**a**) and graphical representation of the composite structure (**b**).  
The calculated dispersion curves clearly show the dispersion phenomenon (the velocity is a function of frequency) and the existence of an infinite number of Lamb wave modes. At the lower frequency, two dispersive modes A\({}_{0}\) and S\({}_{0}\) are clearly visible and distinguishable, as seen in Figure 5a,b. However, other modes are difficult to identify.  
In order to better understand the dispersion influence for the measurements, the signals of the Lamb waves need to be presented. The experimental study is conducted, and the obtained results are presented in the next section.