## 7 Conclusions  
This study focuses on a split-stream rushing exhaust muffler as its subject of investigation, employing numerical simulation and experimental testing methodologies to examine the sound attenuation performance of the muffler while considering sound-structure coupling effects, and its structural parameters underwent optimization informed by the findings of the single-factor investigation into sound-structure coupling. The main conclusions are as follows:  
1. The muffler underwent structural modal, acoustic cavity modal, and sound-structure coupled modal analyses using the finite element method, and the transmission loss under sound-structure coupling conditions was computed. The findings indicate that novel coupled modes arise from the frequency hybridization and interaction between the structural modes and acoustic cavity modes. The sound-structure coupling effect results in a reduction of the transmission loss peaks across the majority of the frequency spectrum, with a notable exception at 3500 Hz, where the transmission loss exhibits a substantial increase. The findings indicate that this phenomenon stems from the resonance occurring between the solid structure and acoustic wave induced by the sound-structure coupling effect at this specific frequency. The phenomenon of  
Figure 26: Transmission loss of the muffler before and after optimization under acoustic-structure coupling. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Average Transmission Loss (dB)**} \\
**Before Optimization** & **After Optimization** & **Increase in the Value** \\ \hline
9.1 & 11.78 & 29.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Mean transmission loss of the muffler before and after optimization under acoustic-structure coupling. resonance causes an amplification of sound pressure levels, consequently augmenting the scattering of acoustic waves at the structural surface and elevating the reflection coefficient of acoustic waves, culminating in an augmented transmission loss. 2. A two-load test of the split-stream rushing muffler was conducted. The findings indicate that the transmission loss analysis incorporating sound-structure coupling effects aligns more closely with actual conditions, thereby validating the accuracy and reliability of the simulation model. 3. The impacts of the wall thickness, inner pipe diameter, and inner pipe length on the acoustic performance of the muffler, considering sound-structure coupling effects, was investigated by employing the single-factor experimental methodology. The findings indicate that the wall thickness exhibits a negligible influence. The inner pipe diameter exhibits a relatively significant influence, with transmission loss escalating in correlation with an increase in diameter. The effect of the inner pipe length on transmission loss is characterized by a downward shift in the frequency spectrum of transmission loss and a reduction in its mean value with increasing inner pipe length. Subsequently, the structural parameters of the muffler underwent optimization. Numerical computations indicate that the optimization outcomes are favorable. Conceptualization, P.H. and P.W. ; methodology, P.H. ; software, P.H. and Y.G. ; validation, P.H. and P.W. ; formal analysis, P.H. ; investigation, P.H. ; resources, P.W. and H.S. ; data curation, P.H., H.Z., J.X. and Y.Z. ; writing--original draft preparation, P.H. ; writing--review and editing, P.H. and P.W. ; visualization, P.H. ; supervision, P.W. ; project administration, P.W. ; funding acquisition, P.W. and H.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the Natural Science Foundation of Inner Mongolia Autonomous Region, grant number 2023 MS05022; the Basic Research Fund for Institutions of Inner Mongolia Autonomous Region, grant number BR230155; the Natural Science Foundation of Inner Mongolia Autonomous Region, grant number 2024 MS05039; and the Huzhou Natural Science Foundation, grant number 2023 YZ01. Not applicable.