## 4 Theoretical Study  
### Dispersion Curves  
GWT is an NDT technique that can be employed in this applicaton. Low-frequency waves can travel big distances without being significantly attenuated; however, their relatively large wavelength limits the size of defect that can be detected. A 10 mm length of defect was set as the minimum size defect that should be detected; considering that the wavelength should be smaller than the double of the minimum size defect, in this case the wavelength should be smaller than 20 mm. A SH\({}_{0}\) wave of 12 mm wavelength was introduced to this structure. As the wave propagates inside the specimen, it strikes at the boundaries of the medium, resulting in the change of its waveform. Consequently, there is an infinite number of possible wave modes that may appear in the material; their velocity changes in respect not only to the material properties of the specimen but to its geometry as well. Hence, the same mode at a different frequency may propagate with a different mode shape and velocity. This phenomenon is called dispersion; most of the wave modes in guided waves are dispersive Nevertheless, T(0,1) (or, alternatively, SH\({}_{0}\) on plates) is not dispersive, making the interpretation of the signal received less complicated. Its displacement is also in-plane, making it more suitable for this application, since the wave will propagate all along the pipe without it being affected by the working fluid that flows inside the pipe; T(0,1) cannot propagate in liquids. The number of wave modes that may appear in a plate is also smaller compared to a pipe and therefore the interpretation of the signal received from a plate may be less complicated as well. In this preliminary study, the EMAT is simulated and designed for exciting SH\({}_{0}\) waves, which will propagate axially on a 316 L stainless steel plate. The dispersion curves of a 3 mm thick, 316 L stainless steel plate of 8000 kg/m\({}^{3}\) density, 195 GPa Young's modulus, and 0.285 Poisson ratio have been calculated and demonstrated in Figure 3. This figure shows that the wavelength curve crosses the SH\({}_{0}\) curve at 256 kHz frequency and thus this should be the resonant frequency of the EMAT. The wavelength curve also crosses the S\({}_{0}\), A\({}_{0}\), and A\({}_{1}\) curves; Table 1 shows at which frequency the wavelength curve crosses each wave mode curve and their wave velocity at these frequencies. Hence, an EMAT designed to excite SH\({}_{0}\) of 12 mm wavelength should be driven with an AC current of  
Figure 2: Methodology schematic. 256 kHz frequency. Otherwise if the EMAT is tuned to any other frequency, it will be likely for it to excite Lamp waves instead of SHo. This is more possible if the coil design is meander instead of racetrack, for meander coils are used for Lamp waves as well. At 256 kHz, the SHo and the A0 have the same group velocity. As a result, both wave modes can be excited/received from the EMAT, simultaneously resulting in a more complicated signal, since A0 is dispersive at this frequency. Nevertheless, the orientation of the displacement of each wave mode is different; the SH0 has an in-plane displacement while the A0 has an out-of-plane displacement. Thus, a further study should be conducted regarding the wave mode, and more particularly the displacement to which the PPM EMAT is sensitive. Consequently, an electromagnetic simulation calculating and showing the amplitude and the direction of the wave modes generated by a PPM EMAT is needed. Material properties such as the Young's Modulus, Poisson ratio, and density of a specimen change with temperature rise as well, resulting in variations in the velocity of the propagating wave mode. The Young's modulus and density of the specimen decrease with an increase in temperature, while the Poisson ratio increases. These changes result in a decrease in the velocity of the SH0.