# Research on Propagation Characteristics of Tire Cavity Resonance Noise in the Automobile Suspension
## 4 Power Flow Analysis of Tire Cavity Resonance Noise Propagation in a Suspension System  
According to the steps of calculating the power flow in the wheel [18], the Y-spoke aluminum alloy wheel and suspension system were simulated. The distribution of structural sound intensity in the system under the conditions of 4000 N load, 0.22 MPa inflation pressure, and 60 km/h speed could be obtained, as shown in Figure 7. It can be seen that there was a large degree of structural sound intensity at the local spokes. After the suspension system with a wheel had been studied, the real and imaginary values of stress and displacement at each point, the excitation frequency of the system response, and the point set data of the input and output surfaces were derived. The above txt format data were read by MATLAB R2014a, and the structural stress at each point in the wheel and the structural sound intensity of the input and output surfaces could be calculated according to the structural sound intensity formula. After obtaining the structural sound intensity and power flow, a vector diagram could be obtained by further programming. The contour of the structural sound intensity could be imported into the  
Figure 6: Stress and strain contour of a suspension system. (**a**) Stress contour of a suspension system. (**b**) Strain contour of a suspension system. simulation software through a program compiled in the Python language to realize the secondary development. Then, the contour of the structural sound intensity could be obtained. According to the steps described in ref. [18], the structural sound intensity vector distribution figures and a partial enlargement system in different planes could be obtained, as shown in Figure 8.  
As shown in Figure 8, the structural sound intensity distribution of the suspension system was uneven. In the partial enlargement of Figure 8, the length of the arrows represents the amplitude of structural sound intensity, and the direction of the arrows represents the direction of structural sound intensity. During the transmission of structural sound intensity vectors, structural sound intensities of different directions and sizes meet and merge into a whole vector toward the hub center. Structural sound intensity vectors with the same frequency and different phases propagate from the spokes to the hub and continuously converge and dissipate. For the Y-spoke aluminum alloy wheel and suspension system, data such as the sum of structural sound intensity and cross-sectional area at each point of the wheel input surface and output surface could be calculated. The power flow could be determined by formulas presented in ref. [18], and the results are shown in Table 3. Power flow is the product of the average structural sound intensity at the node and the corresponding cross-sectional area, as shown in Equation (8). \[P_{f}=\frac{\sum p_{si}}{N}S \tag{8}\]  
where \(P_{f}\) is the power flow of cross-section \(S,p_{si}\) is the structural sound intensity of point \(i\), \(S\) is the area of the corresponding section, and \(N\) is the number of points. The first output, second output, and third output in the table are the inner surface of the cylindrical auxiliary support and the front and rear bushing surfaces of the lower swing arm, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{3}{*}{**Load Condition**} & \multicolumn{2}{c}{**Sum of Structural**} & \multirow{3}{*}{**Number of Points**} & \multirow{3}{*}{**Cross Sectional**} & **Power Flow of Cross** \\  & & **Sound Intensity** & & & **Sectional Area (mm2)** & **Section (10\({}^{-3}\) W)** \\ \hline \multirow{3}{*}{4000 N} & Input & \(2.897\times 10^{-2}\) & 15,064 & 81,367 & \(1.565\times 10^{-1}\) \\  & First output & \(1.068\times 10^{-4}\) & 1840 & 7031 & \(4.081\times 10^{-4}\) \\ \cline{1-1}  & Second output & \(1.153\times 10^{-4}\) & 462 & 2797 & \(6.980\times 10^{-4}\) \\ \cline{1-1}  & Third output & \(1.808\times 10^{-5}\) & 350 & 1352 & \(0.698\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}