## 3 Establishment of the Finite Element Model and Simulation Results
### Finite Element Simulation Results
#### 3.2.1 Vertical Incident Simulation Results  
Taking the Q235-rubber structure with a single air layer as an example, the reflection characteristics of the air layer under different incident conditions were analyzed using the finite element model shown in Figure 4. The frequency of the incident sound wave was set to \(1\) MHz, and the incident angle was set to \(90^{\circ}\). The parameter scan function was used to set the angle scanning range from \(0\) to \(90^{\circ}\) and the frequency scanning range from \(0\) to \(2\) MHz.  
When the incident wave enters the upper surface of the flange perpendicularly through the background pressure field, part of the sound waves will be scattered, and most of the sound waves will penetrate into the flange, as shown in Figure 6, which shows the sound field maps of the background pressure field and the interface reflection sound field map, respectively.  
Figure 5: The influence of relative error and calculation time on mesh size [26]. Adapted with permission from Ref. [Research on Ultrasonic Testing Method of Adhesive Quality of Multilayer Structure Based on COMSOL]. 2021, [PERSON].  
From Figure 6, it can be seen that the maximum sound pressure amplitude of the incident wave is 1 and it enters the upper flange to form a standing wave. The arrow indicates the incident angle of the sound field. When the incident sound field of the upper flange enters the silicone gasket, scattering and transmission occur. When the sound wave propagates in the upper flange, a small amount of sound waves undergo transmission, and most of the sound waves undergo reflection, which is consistent with the actual situation.  
Set the thickness of the air layer as 0 \(\upmu\)m, 30 \(\upmu\)m, 50 \(\upmu\)m, 70 \(\upmu\)m, 90 \(\upmu\)m, and 110 \(\upmu\)m. Since the reflected wave is greatly attenuated in the air layer, it is necessary to use the ratio of the incident signal to the reflected signal of the flange and the silicone gasket to determine the reflection coefficient when the incident wave amplitude cannot be determined. A corresponding vertical incidence measurement simulation model is established, and the relationship between the ultrasonic reflection coefficient and the frequency under different air layer thicknesses and incident angles is plotted, as shown in Figure 7.  
The above figure shows that there is a clear regularity between different air layer thicknesses and their resonance frequencies. When the air layer thickness increases, the minimum value of the first-order resonance frequency shifts towards the low-frequency direction. As the separation distance between the flange and the silicone gasket increases, the shift amount of the first-order resonance frequency minimum value becomes larger. Therefore, it is feasible to analyze the contact state between the silicone gasket and the flange by analyzing the trend of the minimum value of the resonance frequency.  
Figure 6: f = 1 MHz, \(\theta\) = 0\({}^{\circ}\). Acoustic field map: (**a**) incident sound field, (**b**) reflected sound field.  
Figure 7: Vertical incidence measurement model reflection coefficient curve.