## 3 Results and Discussion  
### Prediction Calculation Result of Sound Absorption Coefficient  
The computational geometry is depicted in Figure 4. The modeled structure mimics a non-woven fabric with a fiber diameter of 10 \(\upmu\)m and a porosity of 99%, with a uniform unit  
Figure 3: High-airflow-resistance surface material laminated to this porous material mat. cell size of \(w=1000\) um (\(w_{x}=w_{y}=w_{z}=w\)) (Figure 4a). Particle A in the model presented in Figure 4b is a sphere with a diameter of 220 um, while particle B in Figure 4c is an ellipsoid measuring 440 \(\times\) 880 \(\times\) 27.5 um. Particles A and B have equivalent volumes. Figure 4d illustrates the geometry of Figure 4a augmented with a fiber mass equivalent to four particles A. The specific gravity of the fiber is assumed to be 1.38 g/cm\({}^{3}\) (PET), and that of particles A and B is 0.15 g/cm\({}^{3}\) (aerogel). The bulk densities of each configuration and the positions of the centers of gravity of the particles are detailed in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \begin{tabular}{c} **Fiber** \\ **Diameter** \\ **(\(\mu\)m)** \\ \end{tabular} & \begin{tabular}{c} **Density of** \\ **Fiber** \\ **(g/cm\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Density of** \\ **Particle** \\ **(g/cm\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Bulk** \\ **Density** \\ **(kg/m\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Particle** \\ **Content** \\ **(wt\%)** \\ \end{tabular} & \begin{tabular}{c} **Particle** \\ **Shape/pcs.** \\ **(x,y,z)** \\ \end{tabular} \\ \hline \hline \begin{tabular}{c} Non-woven fabric 1 \\ Figure 4a \\ \end{tabular} & 10 & 1.38 & - & 13.8 & - & -/0 & - \\ \hline \begin{tabular}{c} Composite 1 \\ Figure 4b \\ \end{tabular} & 10 & 1.38 & 0.15 & 16.8 & 19.5 & \begin{tabular}{c} Particle A \\ /4 \\ \end{tabular} & \begin{tabular}{c} **Center of** \\ **Gravity** \\ **(500,500,750)** \\ **(500,500,750)** \\ \end{tabular} \\ \hline \begin{tabular}{c} Composite 2 \\ Figure 4c \\ \end{tabular} & 10 & 1.38 & 0.15 & 16.8 & 19.5 & \begin{tabular}{c} Particle B \\ /4 \\ \end{tabular} & \
\begin{tabular}{c} (250,500,500) \\ (500,500,250) \\ (500,500,750) \\ \end{tabular} \\ \hline
\begin{tabular}{c} Non-woven fabric 2 \\ Figure 4d \\ \end{tabular} & 10 & 1.38 & - & 16.7 & - & -/0 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculation conditions. Figure 4: Computational geometry: (**a**) non-woven fabric 1; (**b**) composite 1 (particle A mixed non-woven fabric); (**c**) composite 2 (particle B mixed non-woven fabric); (**d**) non-woven fabric 2. The predictive analysis of the sound absorption coefficient spectrum for a specimen thickness of 10 mm across 1/3-octave bands is illustrated in Figure 5. Table 2 presents the results, showing average sound absorption coefficients derived from the spectra between 500-1600 Hz, 500-3150 Hz, and 1000-5000 Hz. The sound absorption spectra of non-woven fabric 1 and composite 1 were nearly identical. However, a divergence in sound absorption coefficients between non-woven fabric 1 and composite 2 became evident above 400 Hz, with composite 2 demonstrating enhanced sound absorption, particularly in the frequency band above 1000 Hz. This indicates that spherical particles in a non-woven fabric with a bulk density of approximately 13.8 kg/m\({}^{3}\) and a particle content rate of about 20 wt% minimally affect the sound absorption coefficient. In contrast, the inclusion of elliptical flattened particles of equivalent weight and volume significantly improves sound absorption. This suggests that particle shape plays a crucial role in influencing the sound absorption coefficient. Comparing non-woven fabric 2 and composite 2, composite 2 exhibited superior sound absorption, particularly in the higher-frequency range. It was observed that the inclusion of elliptical flattened particles may enhance the sound absorption effect relative to the weight, compared to materials composed solely of fibers.