## 3 Simulation Analysis
### Simulation Results  
#### 3.3.1 Two-Layer Model  
The two-layer model is built to study the structure-borne sound's propagation law indoors and the vibration strength distributions when vibration propagates along the beam, brick, and wall units. Apply the excitation quantity as measured on the field site to the model as shown in Figure 11 which shows the vibration spectrum of the transformer. Although the vibration of the transformer will be different under different working conditions, for the simulation analysis, considering the vibration propagation law of the transformer, the intensity of the vibration does not affect its propagation law. In the actual measured vibration values given in Figure 11, we use the vibration curve under no-load condition. The specific parameters of Power Spectral Density (PSD) acceleration which applies to the equivalent rectangular box's upper surface are shown in the Figure 12.  
Take the transformer that is placed at position #3 as an example to study the propagation law. The unit in Figure 13 is meter. In the nephogram, the displacement is used as an indicator, and the blue region indicates the vibration intensity is relatively low, while the red region indicates more severely-affected areas. The displacement is the sum of the components of different frequencies. As is shown in Figure 13, the vibration propagates upward along columns and beams. In the process of transmission, the floor structure of the house is relatively stable and less affected by the vibration, but the amplitude of the surrounding walls is relatively large. The amplitude of the vibration reaches the peak at the wall edge on sides of the \(X\)-direction of the house, and the vibration amplitude of the four walls along the longitudinal direction of the house (\(Z\)-direction in the Figure 13) is also large. Structure-borne sound wave will be attenuated when propagating in the building structure, and the amount of attenuation when propagating to the floor is greater than that to the wall. Location #3 is at the center, where the impact of the transformer as a vibration source on the entire house structure is significant. Figure 11: Acceleration spectrum of the transformer’s vibration: (**a**) No-load; (**b**) Short-circuit; (**c**) Load. In detail, we can further obtain the response spectrum of the typical monitoring point. We use the frequency-acceleration curve to learn more about the vibration. In the range of 800 Hz, the response spectrum of vibration at point 1 is shown in Figure 14. The monitoring value can be shown in \(X\), \(Y\), \(Z\) directions. Figure 14: The transformer is at position #3, and the response spectrum of monitoring point No. 1 in the two-layer model. Figure 12: Specific parameters of Power Spectral Density (PSD) acceleration. Figure 13: Displacement nephogram in two-layer model when the transformer is at position #3. The response spectrum is mainly around 100 Hz, and the response spectrum at high frequencies can be negligible. In order to dramatically display the result, the data should be filtered, only considering the value within 150 Hz, and adjusting the \(X\)-coordinate. The corresponding response spectrum curve is shown in Figure 15.  
Considering that the vibrations in the three directions are almost of the same magnitude, and in practice, the vibration of the transformer is mainly up and down [19], when the excitation is applied, only the vibration in the \(Y\) direction will be analyzed. The transformer's position remains unchanged, and the response curve of 1-6 test points at the front side is shown in Figure 16.  
It can be seen that the vibrations of point 2 and point 5 are relatively stronger than other points, which coincides with the result in the displacement nephogram. From Figure 16, we can find that in \(X\)-coordinate, with the distance to the transformer increasing, the amplitude of vibration has a decreasing trend, but this rule is not quite obvious.