## 5 Numerical Calculation and Discussion  
Upon analyzing the above expressions, we observe that physical Equation (26) is a convergent infinite series function. When \(n=10\), the calculated results meet the required engineering accuracy. For our analysis, we selected CoFe\({}_{2}\)O\({}_{4}\) as the material of interest, with a relative material constant of [24]  
\[\begin{array}{l}\rho_{0}=5.35\times 10^{3}\ \mathrm{kg}\cdot\mathrm{m}^{-2},c_{ 44}=4.53\times 10^{10}\ \mathrm{N}\cdot\mathrm{m}^{-2},\\ h_{15}=550\ \mathrm{N}\cdot\mathrm{A}^{-1}\cdot\mathrm{m}^{-1},\ \mu_{11}=5.9\times 10^{-4} \ \mathrm{N}\cdot\mathrm{A}^{-2}.\end{array}\]  
For our numerical analysis, we consider the incident wave number \(ka\), the incidence angle \(\varphi\) of the SH wave, and the elliptical geometric parameters \(e=b/a\) as the characteristic parameters.  
Figure 2 illustrates the distribution of the DSCC during the incidence of SH waves along the major axis (\(\varphi=0\)) and minor axis (\(\varphi=\pi/2\)) of an elliptical opening with varying geometric parameters (\(e=0.3\), \(0.5\), \(0.7\), \(0.9\)). The symmetric shape of the elliptical opening in the incident direction results in a symmetric distribution of DSCC regions. Moreover, increasing the wave number leads to a decrease in the DSCC, particularly in the shadow region, where the decline is more pronounced. When waves are incident along the major axis of the elliptical opening, the DSCC attains its maximum value as the \(e\) value increases. However, the situation is reversed when waves are incident along the minor axis of the elliptical opening. Notably, waves incident from the minor axis exhibit a larger DSCC than those from the major axis.  
Figure 3 displays the distribution of the DSCC around the elliptical opening for various wave numbers of SH waves. When \(\mathrm{e}\) is small, the non-symmetric incidence of SH waves significantly affects the shape of DSCC, as depicted in Figure 3a. As \(e\) approaches 1, DSCC becomes symmetrically distributed around the incident direction, and the maximum value decreases. Furthermore, an increase in the incident angle results in an increase in DSCC at low wave numbers.  
Figure 4 displays the correlation between the DSCC and the dimensionless wave number. The solid line represents the incidence angle \(\varphi=\pi/6\), while the dashed line represents the incidence angle \(\varphi=\pi/3\). At the elliptical position \(\theta=\pi/2\), the DSCC decreases with an increase in the incidence angle, whereas the opposite trend is observed at \(\theta=0\). The DSCC attenuates with fluctuations in the wave number at both incidence angles. Notably, a lower wave number results in a larger DSCC.  
Figure 5 depicts the correlation between the DSCC and the incident angle. The solid line represents a low wave number \(ka=0.5\), while the dotted line represents a high wave number \(ka=3.0\). The trend reveals that the DSCC at elliptical positions \(\theta=0\) and \(\theta=\pi/2\) changes in opposite directions. In the low-wave-number case, the DSCC curve is monotonically increasing. The DSCC curve is lower than the low-wave-number case for high wave numbers and exhibits fluctuations. Notably, the DSCC change at elliptical position \(\theta=0\) is steeper than at elliptical position \(\theta=\pi/2\).  
Figure 3: Comparison of distribution of DSCC in elliptical openings under different wave numbers; incident angle \(\varphi\), wave number \(ka\) and elliptical geometric parameters \(e\).  
Figure 2: Comparison of distribution of DSCC in elliptical openings under different geometric parameters; incident angle \(\varphi\), wave number \(ka\) and elliptical geometric parameters \(e\).