## 3 Model Calculation Based on Actual Parameters of True Transformer
### Displacement and Acceleration Variation Law of Disks at Different Frequencies  
Figure 5 shows winding displacement changes in steady-state condition (t = 0.15 s) at 0-250 Hz. In the low-frequency region, the displacement is large and the amplitude is very high, distributed in an 'arch' shape, while in the high-frequency region, the displacement amplitude is small, but fluctuation is increasing. The theory in the previous section proves the zero nodes of high-order vibration mode increase, but the amplitude change decreases; obviously, the displacement change in Figure 5 conforms to the above theory. To better observe the displacement distribution at different frequencies, take the displacement change at 0-40 Hz as a separate observation. As shown in Figure 5a, at 0-20 Hz, the displacement  
Figure 4: The first four modes.  
Figure 3: Natural frequencies of each order.  
is distributed in a 'U' shape on the winding, which is the same as the first vibration mode. With an increase of frequency from 20 Hz to 40 Hz, the displacement shape gradually turns into multiple \"arches\" from the 'U' shape, but the displacement peak decreases gradually. As shown in Figure 5b, in the winding displacement distribution at 40-100 Hz, the displacement fluctuation amplitude decreases consistently, the maximum displacement amplitude gradually approaches the head and end of the winding, fluctuation in the middle part tends to be gentle, and fluctuation in the middle part is almost zero with an increase of frequency. The winding displacement distribution gradually changes from \"M\" shape distribution to \"three-arch\" and \"four-arch\" shapes, which is also consistent with the distribution of vibration modes from third-order vibration modes to high-order vibration modes. As shown in Figure 5c, as frequency increases from 100 Hz to 250 Hz, displacement amplitude continues to decrease in a terraced manner, gradually close to zero, and displacement fluctuation also slowly decreases to zero.  
Figure 6 shows the winding acceleration changes at 0-250 Hz. In the low-frequency region, the acceleration is large and the amplitude is high, distributed by the above vibration mode law, while in the high-frequency region, the acceleration amplitude changes little and gently.  
Figure 5: Displacement of each disk at 0–250 Hz. (a) Displacement of each disk at 0–40 Hz; (b) 40–100 Hz; and (c) 100–250 Hz.  
Moreover, all disks have the same acceleration distribution as above. As shown in Figure 6a, at 0-20 Hz, vibration acceleration is distributed in a 'U' shape on the winding, consistent with the distribution law of the first vibration mode on the winding. As the frequency increases from 20 Hz to 40 Hz, the displacement shape changes from 'U' to 'double-arch' and then to 'M', consistent with the distribution law from the first-order vibration mode to the third-order vibration mode. Different from the displacement, the peak acceleration in each disk increases gradually with an increase in applied frequency.  
As the conclusion of the above analysis, as shown in Figure 6b, the acceleration distribution of each disk is consistent with the shape change law of the vibration mode, while the amplitude does not continue to decay, but changes around a fixed value, and peak acceleration still appears near both ends of the winding.  
On the contrary, as shown in Figure 6c, as the frequency increases from 100 Hz to 250 Hz, the acceleration of each disk at each resonance frequency remains at a fixed value except at both ends, and the peak value appears closer and closer to both ends of the winding.