## 5 Acoustic-Structural Coupling Analysis of the Muffler
### Analysis of Acoustic Attenuation Performance  
Figure 17 illustrates a comparative diagram of transmission loss. As shown in Figure 17, the experimental results exhibit closer agreement with the transmission loss considering sound-structure coupling effects than with the transmission loss neglecting these effects. Furthermore, the overall trends demonstrate better consistency, suggesting that the inclusion of sound-structure coupling effects enhances the accuracy of the finite element prediction of transmission loss. The above results can be analyzed as follows: The acoustic-structure coupling effect accurately reflected the interaction of acoustic waves  
Figure 16: Comparison of some acoustic cavity modes with coupled modes. (**a**) 6 th order coupled mode (426.62 Hz), (**b**) 2 nd order acoustic cavity mode (427.04 Hz), (**c**) 8 th order coupled mode (570.78 Hz), (**d**) 3 rd order acoustic cavity mode (571.1 Hz). Figure 15: Comparison of some structural modes with coupled modes. (**a**) 2 nd order coupled mode (82.38 Hz), (**b**) 1 st order structural mode (82.43 Hz), (**c**) 7 th order coupled mode (139.97 Hz), (**d**) 4 th order structural mode (140.23 Hz). during transmission between solid and air and captured resonance phenomena in the structure, as well as the frequency-dependent energy transmission patterns. These capabilities enabled a more precise description of the transmission loss characteristics. Moreover, the coupling model better simulated the complex boundary conditions in the test and showed particularly high prediction accuracy in both low-frequency and high-frequency bands. Although the transmission loss under the acoustic-structure coupling effect aligned well with the test results, some discrepancies still existed. This discrepancy could be attributed to the simplifications made in the simulation, including geometric details, material properties, and boundary conditions, which did not fully capture the practical conditions of the test. Additionally, test data might contain inherent errors owing to equipment accuracy and environmental noise. An observation of the transmission loss curve comparison diagram reveals that the transmission loss curve neglecting sound-structure coupling effects exhibits a similar trend to the curve considering these effects. However, the distinction lies in the fact that the transmission loss peaks for the case with sound-structure coupling are generally lower than those for the case without it. This finding was consistent with most studies on the acoustic-structure coupling effect on mufflers [31,32]. Moreover, the mean transmission loss under coupled conditions is 8.98 dB, a decrease of 0.56 dB compared to the 9.54 dB under uncoupled conditions, corresponding to a reduction of 6.24%. At most frequencies, the sound pressure level considering sound-structure coupling effects is generally lower than the sound pressure level neglecting these effects. This is primarily because the presence of sound-structure coupling facilitates energy exchange between acoustic waves and the solid structure, resulting in a portion of the acoustic energy being either absorbed by the solid or transmitted through it, consequently diminishing the intensity of the acoustic waves. As shown in Table 6, the variation trend of transmission loss considering sound-structure coupling effects at 3500 Hz deviates from that observed at other frequencies. In contrast to the scenario neglecting sound-structure coupling effects, its peak not only undergoes a shift towards lower frequencies, diminishing from 3510 Hz to 3500 Hz, but also exhibits a greater transmission loss. An observation of the sound pressure maps in Figure 18 reveals that at a frequency of 3050 Hz, the peak sound pressure level considering sound-structure coupling effects is lower than the peak sound pressure level neglecting these effects.