# Dynamic Response of Outer Windshield Structure in Different Schemes under Aerodynamic Load
## 4 Results and Discussion
### Time- and Frequency-Domain Analysis of Vibration Displacement
#### 4.2.1 Time-Domain Analysis  
Figure 12 shows the displacement curve for the measuring points at different positions along the y-axis with time when the aerodynamic response of the three rubber external windshield schemes occurs under the aerodynamic load. To better analyze the time-domain characteristics of the aerodynamic response for the rubber external windshield, the amplitude change in the displacement time-history curve was divided into two stages (0\(\sim\)1 s and 1\(\sim\)4 s). The mean displacement of different vibration stages and the root mean square (RMS) value of time-domain displacement are analyzed, as shown in Table 2. The RMS of the time-domain displacement signal is calculated without using a window function and filter; the formula is as follows:  
Figure 10: Average flow-field structure of the cross-section under the initial flow-field state. \[RMS=\sqrt{\frac{1}{k+1}\sum_{i=0}^{k}y_{i}^{2}} \tag{11}\]  
Calculate the sum of squares of all amplitudes of the time series, divide by the total number of sample points, and finally take the square root, where k + 1 represents the total number of sample points in the calculated interval. Figure 11: Monitoring points. Figure 12: Displacement time-history curve: (a) d1, (b) d2, (c) d3, (d) d4. By comparing the displacement time-history curves for the rubber external windshield structure, the vibration displacement state of the three schemes can be observed. It can be seen from Figure 12 that the vibration displacement and amplitude of the external windshield structure in Case 1 along the direction perpendicular to the vehicle body surface are significantly greater than those in Case 2 and Case 3. As the thickness of the straight walls on both sides of the outer windshield capsule is greater than the arc top, and the straight walls on both sides of the capsule are connected with the mounting bracket, the fluctuating amplitude of points d1 and d2 is smaller than that of points d3 and d4 in the middle of the arc of the U-shaped capsule. At the initial stage of the dynamic response of the outer windshield, there is not yet a dynamic balance stage between aerodynamic force, inertial force, and elastic force, which causes the vibration amplitude to change significantly with time, such as within 0-1 s of the vibration stage. When the interaction among aerodynamic force, inertial force, and elastic force reaches a dynamic balance, the amplitude and period of vibration remains relatively stable. Table 3 shows the average and RMS values for the displacement measuring points in the two dynamic response stages, and quantitatively compares the displacement and vibration intensity between the three external windshield schemes. According to the data in the table, the maximum displacement of external windshield d3 in Case 1 is 15.1 mm, the maximum displacement of outer windshield d4 in Case 3 is 15.8 mm, and the maximum displacement of outer windshield in Case 2 is 10.4 mm, less than that in Case 1 and Case 3. The vibration displacement direction of the rubber external windshield can be judged by the positive and negative displacement measuring points. For example, in the two stages of vibration response of the external windshield in Case 1 and Case 2, the measuring points d1 and d3 are both negative values, and the measuring points d2 and d4 are both positive values, Therefore, W1 is displaced from the initial state to the exterior of the vehicle body, and W2 is displaced from the initial state to the inside of the vehicle body, that is, phase displacement movement is generated. In Case 3, the deformation laws of W1 and W2 are the same as those of Case 1 and Case 2 in the initial stage of vibration. In the stage of vibration stability, however, W1 and W2 in Case 3 both move toward the inner side of the vehicle body. For RMS amplitude, the dynamic response starting stage of the rubber external windshield is greater than the dynamic response stability stage. In the dynamic response starting stage, the maximum RMS amplitude of d3 on W1 on the leeward side is 15.6 mm.