## 3 Key Components Design
### Vibration Mechanism
#### 3.1.2 Finite Element Modeling Analysis of Jujube Trees  
The typical high-quality production of jujube trees after pruning and shaping are free spindles, natural open heart, stratified evacuation, and natural round head. Among them, the free spindle-shaped frame is firm, the shaping is simple, the yield is easy, the management is convenient, is suitable for close planting and cultivation, therefore the free spindle-shaped shaping method has been widely used in the jujube tree planting process. After shaping, tree height is 2.8-3.3 m, 5-8 a central dry evenly on the center stem, spread outward in 70-80\({}^{\circ}\) angle, and the distance between the adjacent two main branches is 30 cm. In this experiment, the free spindle-shaped jujube tree was selected for SolidWorks 3D modeling [14], and simplify the jujube tree model. In general, the higher the height of the jujube tree, the greater the displacement caused by the same vibration. The height of the normal winter jujube tree is about 2.8-3.2 m, and the typical height we selected during the modeling process is 3 m, and center of the lower trunk is cylindrical. The main branch above 1.5\({}^{\circ}\) in the draft, five main branches are evenly distributed on top of it. Each main branch is stretched outward at a distance of 30 cm at an angle of 75\({}^{\circ}\), and its length and diameter are equally distributed. When performing finite element analysis, the elastic modulus of the jujube is 10 GPa. Due to the high-water content of the living tree, the material density is 1000 kg/m\({}^{3}\), regardless of the external force, the damping coefficient is taken as 0 [15; 16]. First, consider the influence of trunk diameter \(D\) on vibration displacement, respectively, take \(D=150\), \(D=175\), \(D=200\), \(D=225\), \(D=250\) mm, and make a modal analysis of jujube tree model. The DC motor used in this paper is continuously adjustable under the remote control of the Bluetooth module, and the vibration speed can be continuously adjusted within 0-1500 r/min. Therefore, the vibration mechanism can provide the vibration frequency of 0-25 Hz. In this frequency range, the natural frequency of jujube vibration of different diameters is shown in Table 1.  
Resonance is a phenomenon in which the amplitude of the system increases significantly when the excitation frequency of the system is close to the natural frequency of the system. However, when the excitation frequency and the natural frequency are close, resonance does not always occur [17; 18]. Therefore, it is necessary to further explore the excitation frequency that causes the jujube to resonate according to the natural frequency. If the test of each mode is a complicated and cumbersome work, this paper adopts the harmonic analysis of the jujube tree model to find the resonance point within the required range at one time. Any complex wave can be composed of many sinusoidal components with different frequencies, amplitudes and phases, and the harmonic analysis is to decompose them. In the trunk of the jujube tree 1 m away from the ground, the exciting force is applied, and all suitable frequencies are swept one by one. The obtained harmonic analysis diagram is shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Order**} & \multicolumn{5}{c}{**Natural Frequency/Hz**} \\ \cline{2-5}  & \(D\) = 150 mm & \(D\) = 175 mm & \(D\) = 200 mm & \(D\) = 225 mm & \(D\) = 250 mm \\ \hline
1 & 3.4804 & 3.8818 & 4.6748 & 5.477 & 6.2831 \\
2 & 3.5338 & 3.9212 & 4.7147 & 5.5163 & 6.3217 \\
3 & 12.495 & 15.006 & 17.107 & 18.752 & 19.987 \\
4 & 16.107 & 17.918 & 20.70 & 21.36 & 21.851 \\
5 & 16.911 & 18.501 & 21.116 & 24.066 & \\
6 & 19.19 & 20.139 & 21.508 & 24.324 & \\
7 & 23.201 & 24.52 & & & \\
8 & 24.483 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Natural frequency table of jujube trees with different diameters. Figure 3: _Cont._  
It can be seen from Figure 3 that not all-natural frequencies will cause the jujube to resonate.