# Development of a Drone's Vibration, Shock, and Atmospheric Profiles
## 3 Results and Discussion
### Consolidated PSD Vibration Spectrum  
The PSD plots from the data loggers show that the shapes of the curves were similar to each other for each drone. The vibration intensities at the higher frequency range are generally higher than those observed in the lower frequency region (Figures 6 and 7). All of the PSD plots are characterized by three distinctive vibration regions. Region 1 (1.56 to 10 Hz) shows the interaction between the quadcopter frame (around 10 Hz and below) and the airflow caused by the drone's rotating and moving around of the quadcopter (around 1.56 Hz and above). Region 2 (10-70 Hz) represents the RPM of the motor shaft and 2-blade rotations between the minimum stable throttle to 50-60% of the throttle. The vibration frequency of the motor shaft is the RPM divided by 60. For example, a 600 RPM will have a 10 Hz vibration frequency, and the 2-blade vibration frequency is twice that of the motor shaft. Region 3 (70-230 Hz) the excitation frequencies were a function of the motors and 2-blade propeller at the high rotations per minute (RPM). The motor shaft generated  
Figure 5: Exemplary vibration events during the turning of the drone.  
vibration frequency can be estimated using (Motor RPM)/60 Hz. The 2-blade propellers' corresponding vibration frequency can be estimated using (Motor RPM)/30 Hz.  
Figure 6: Consolidated PSD profiles of the **top** and **bottom** part of the DJI Matrice 600 Pro.  
Comparing the PSD spectra of the DJI Matrice 600 Pro to that of the DJI Matrice 100, the shapes are similar in the higher frequency range, reflecting the characteristics of the motor and two-blade propeller structure. However, they differ in the lower frequency regions for all three directions on the vibration intensities. The PSD plot of the DJI Matrice 100 showed higher vibration intensities in the low-frequency region than that of the DJI 600 Pro at the horizontal level, alluding to the fact that the DJI Matrice 100 is more susceptible to fluttering--a dynamic instability of flight vehicle associated with the interaction of aerodynamic, elastic, and inertial forces [25]--and rotation by airflow due to its relatively light weight. In contrast, the DJI Matrice 600 Pro exhibited higher vibration intensities in low frequency only in the vertical direction.  
Tables 3 and 4 illustrated the major frequencies and PSD breakpoints corresponding to Figures 6 and 7. These were selected after smoothing the PSD curves and to allow for the ability to be used by vibration test systems to represent this type of package delivery method.  
Figure 7: The consolidated PSD air profiles of the **top** and **bottom** part of the DJI Matrice 100.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{5}{c}{**Frequency and PSD breakpoints for DJI Matrice 100 top**} \\ \hline \multicolumn{5}{c}{**X-Axis (Lateral)**} & \multicolumn{2}{c}{**Y-Axis (Longitudinal)**} & \multicolumn{2}{c}{**Z-Axis (Vertical)**} \\ \hline Frequency (Hz) & PSD (\(\mathrm{g^{2}}/\mathrm{Hz}\)) & Frequency (Hz) & PSD (\(\mathrm{g^{2}}/\mathrm{Hz}\)) & Frequency (Hz) & PSD (\(\mathrm{g^{2}}/\mathrm{Hz}\)) \\ \hline
1.56 & 0.000196 & 1.56 & 0.000095 & 1.56 & 0.002401 \\
7.03 & 0.000203 & 9.38 & 0.000172 & 6.25 & 0.001030 \\
14.84 & 0.000282 & 19.53 & 0.000266 & 9.38 & 0.001658 \\
19.53 & 0.000236 & 27.34 & 0.000360 & 44.53 & 0.001255 \\
25.78 & 0.000331 & 81.25 & 0.001338 & 91.41 & 0.001667 \\
72.66 & 0.000432 & 96.88 & 0.002042 & 117.97 & 0.002057 \\
98.44 & 0.012128 & 164.06 & 0.016571 & 169.53 & 0.003886 \\
165.63 & 0.024107 & & 194.53 & 0.009995 \\
189.84 & 0.013427 & & & \\ \hline \multicolumn{5}{c}{**Frequency and PSD breakpoints for DJI Matrice 100 bottom**} \\ \hline \multicolumn{5}{c}{**X-Axis (Lateral)**} & \multicolumn{2}{c}{**Y-Axis (Longitudinal)**} & \multicolumn{2}{c}{**Z-Axis (Vertical)**} \\ \hline Frequency (Hz) & PSD (\(\mathrm{g^{2}}/\mathrm{Hz}\)) & Frequency (Hz) & PSD (\(\mathrm{g^{2}}/\mathrm{Hz}\)) & Frequency (Hz) & PSD (\(\mathrm{g^{2}}/\mathrm{Hz}\)) \\ \hline
3.13 & 0.000377 & 1.56 & 0.001820 & 1.56 &