## 3 Numerical Modelling and Analysis of Ultrasonic Inspection of Grounded Flat Steel  
### Simulation Modeling  
According to the principle of excitation of an electromagnetic ultrasonic SH guided wave transducer, when the coil is energized, a Lorentz force of equal magnitude is generated in the opposite direction under the two adjacent magnets. The Lorentz force causes horizontal shear vibration (y-direction offset vibration) inside the grounded flat steel, which excites the SH0 wave. As illustrated in Figure 4, a three-dimensional finite element simulation model was established using the actual parameters of the grounded flat steel of the transmission tower as the reference.  
In the model, the length of the grounded flat steel is 1000 mm, the width is 60 mm, and the thickness is 5.8 mm. Specifying the material parameters of the flat steel, the Young's modulus \(E\) is 210 GPa, the Poisson \(\
u\) is 0.33, and the density \(\rho\) is 7850 kg\(\cdot\)m\({}^{-3}\). On one side of the grounded flat steel model, a 25.2 mm \(\times\) 40 mm excitation loading area is divided into six pairs of minor loading areas (6.3 \(\times\) 20 mm). In order to imitate the actual vibration on the flat steel, the horizontal shear displacements are loaded in each loading zone using the specified displacement function under the COMSOL solid mechanics module, as shown in  
Figure 4: Grounded flat steel ultrasonic inspection 3D simulation model.  
Figure 3: Wave structure of SHD wave and displacement field in the direction of flat steel thickness: (a) SH0, (b) SH1, (c) SH2, (d) SH3.  
Figure 4. There is a 180\({}^{\circ}\) phase difference between the displacements loaded in adjacent regions in order to simulate the horizontal shear vibration generated by the electromagnetic ultrasonic transducer on the grounded flat steel in an actual situation.  
The simulation model's loading signal is then selected as a Gauss window-modulated sinusoidal signal with a center frequency of 250 kHz and applied with a specified displacement. The expression of the loading signal is  
\[f(t)=\ce^{-a(t-b)^{2}}\cos[2\pi f(t-b)] \tag{3}\]  
where \(c\) represents the signal amplitude coefficient, \(a\) is the bandwidth coefficient, \(b\) is the loading signal symmetry axis correlation coefficient, and \(f\) is the center frequency of the loading signal; for each parameter, the values are \(c\) = 1 \(\times\) 10\({}^{-7}\), \(a\) = 2 \(\times\) 10\({}^{10}\), and \(b\) = 2 \(\times\) 10\({}^{-5}\), respectively.  
The grid density determines the computational error o and impacts the efficiency and cost of numerical simulations. A 250 MHz electromagnetic ultrasound transducer was used in this study. It excites ultrasound guided waves with a wavelength of 6.3 mm and a wave speed of 3170 m/s. COMSOL officially recommends a meshing of approximately 1/6\(\lambda\) for ultrasound simulations. Therefore, we selected grid sizes of 1 mm, 2 mm, and 4 mm to evaluate the sensitivity of the grid on simulation results. When using different grid sizes, an error of only 2.1% for 2 mm grids was compared to the 1 mm grid, which is acceptable for ultrasonic simulations. However, when the grid size increased to 4 mm, the error exceeded 15%, indicating that a more extensive grid division would not be feasible. Thus, considering the convergence of the simulation model and computational cost, free tetrahedral cells were chosen to divide the model into grids, with a maximum cell size set at 1 mm and a calculation time step set at 4 \(\times\) 10\({}^{-8}\) s to ensure the accuracy of the calculation results.