## 2 Simulation Method
### Vibration Energy Transmission Characteristics
The power flow input area was defined as the rim surface where the TACR energy first impacted the wheel, and the output area was defined as the bolt holes where the energy transferred into the suspension system. Then, as the power flow of the input and output areas in the wheel was calculated, the transmission efficiency of the TACR energy was defined as the ratio of the input and output power flow in this paper, which was calculated as  
Figure 11.0  
where \(P_{in}\) represents the power flow at the rim where excitation force is applied and \(P_{out}\) indicates the power flow at the bolt holes where the wheel and suspension connect. The transmission efficiency could help analyze and compare the energy transmission characteristics between wheels of different structures, as it could determine the ability of the structure to dissipate energy through the wheels and other structures intuitively and conveniently. Here, the power flow method was used in the TACR energy transmission characteristic investigation. The concept of using transmission efficiency to determine the structure energy dissipation ability could guide wheel structure optimization in further research. Additionally, later in this paper, this method is used to investigate the influence of several wheel design parameters on the TACR energy transmission characteristics. Table 3 shows the calculation results of the input and output power flow for the 14-inch and 15-inch aluminum alloy wheels. The transmission efficiencies of the 14-inch and 15-inch wheels were both low. The TACR energy entered the wheel from the rim to the hub, and most of the energy was dissipated by structure damping and wave interference. Since the elastic waves had the same frequency but different phases, they would interfere with each other during propagation in different positions in the wheels. Additionally, the much smaller output cross-sectional area compared with the input one also led to a low output efficiency. The huge difference shown in Table 3 can be explained from the perspective of the wheel structure difference. The locations of the structure intensity maximum values in the two sizes of the wheels are shown in Figure 16, and it can be seen that the maximum value in the 14-inch wheel was located at the bolt holes, while the maximum value in the 15-inch wheel was located at the rim outside, and the former was higher than the latter. For a 14-inch wheel, the TACR energy could propagate to the hub through the spokes, while \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{**Title 2**} & \multicolumn{2}{c}{**Title 3**} \\ \cline{2-5}  & **Input** & **Output** & **Input** & **Output** \\ \hline \(\sum\ p_{si}\) (\(10^{-3}\) W/mm\({}^{2}\)) & 48.26 & 3.94 & 145.4 & 0.58 \\ \(N\) & 14,580 & 480 & 18,868 & 600 \\ \(S\) (mm\({}^{2}\)) & 58,273 & 1214 & 64,004 & 1649 \\ \(P_{pf}\) (\(10^{-3}\) W) & 192.9 & 9.967 & 493.2 & 1.586 \\ \hline \(\varphi\) & \multicolumn{2}{c}{5.2\%} & \multicolumn{2}{c}{0.3\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Input and output power flow of the 14-inch and 15-inch wheels. for a 15-inch wheel, most of the energy could not reach the hub (for the wheels involved in this paper). This further shows that the wheel structure has a huge design space for suppressing the propagation of TACR energy, which is worth discussing.