## 4 Result and Discussion
Figure 7.8 Analytical and numerical comparison of radiation efficiency (\(\sigma_{\rm mn}\)) for Case I plate with four point masses having parabolic decreasing thickness variation for taper ratio \(\rm T_{x}\) = 0.75. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Type**} & **Plate Thickness** & \multicolumn{2}{c}{**Plate with One Point Mass**} & \multicolumn{2}{c}{**Plate with Two Point Masses**} & \multicolumn{2}{c}{**Plate with Four Point Masses**} \\  & **Variation** & **SPL (dB)** & **RE (\(\sigma_{\rm mn}\))** & **SPL (dB)** & **RE (\(\sigma_{\rm mn}\))** & **SPL (dB)** & **RE (\(\sigma_{\rm mn}\))** \\ \hline \multirow{3}{*}{Point masses} & Case I & 82 & 1.058 & 78 & 1.007 & 77 & 0.994 \\  & Case II & 81 & 1.045 & 83 & 1.079 & 77 & 0.994 \\ \cline{1-1}  & Case III & 79 & 1.020 & 77 & 0.994 & 76 & 0.935 \\ \hline \end{tabular}
\end{table} 
Table 7: Comparison of peak sound power level and radiation efficiency of plate having different parabolically varying thickness with different combinations of point masses for \(\rm T_{x}\) = 0.75. Figure 13: Numerical comparison of sound power level for Case III plate having parabolic increasing decreasing thickness variation for different combinations of point masses for taper ratio \(\rm T_{x}\) = 0.75. Figure 15: Numerical comparison of radiation efficiency (\(\sigma_{\rm mn}\)) of Case I plate for parabolically decreasing thickness variation with different combination of point masses combinations for taper ratio \(\rm T_{x}=0.75\). Peak Sound Power Level Variation with Different Taper Ratios for All Combinations of Point Masses Attached to a Plate  
In this numerical simulation, the peak sound power level is calculated. The different cases of plate with different parabolically varying thickness are considered. The different combinations of point mass are taken and different taper ratios are considered as shown in Figure 18. We are aiming at the highest peak sound power level for different combinations of point mass attached to a plate which is reported at first peak which corresponds to (0, 0) mode of the plate. In this numerical simulation, different cases of plate are investigated with point mass combination. For the Case I plate with one point mass combination, it is seen that peak sound power level increases for increasing value of taper ratio. For two point masses and four point masses combinations, there seems to be the variation of peak sound power levels for increasing value of taper ratio as evident from Figure 18. For Case I plate  
Figure 16: Numerical comparison of radiation efficiency (\(\sigma_{\rm{mm}}\)) for Case I plate with two point masses combinations having different parabolic thickness variation for taper ratio \(\rm{T_{x}=0.75}\). Figure 17: Numerical comparison of sound power level (dB) for Case I plate with two point masses combinations having different parabolic thickness variation for taper ratio \(\rm{T_{x}=0.75}\). it is seen that peak is maximum for taper ratio, \(\rm T_{x}=0.75\) for plate with one point mass combination and peak is minimum for taper ratio, \(\rm T_{x}=0.75\) for four point masses combination. It is further noticed that for Case II plate the highest peak is seen for taper ratio, \(\rm T_{x}=0.75\) for two point masses combination. Similarly, it is seen that for Case III plate lowest peak is observed for taper ratio, \(\rm T_{x}=0.75\) for plate with four point masses combination. Thus from the simulation result, it is quite obvious that peak sound power level corresponds to (0, 0) mode is deeply affected by different combinations of point masses. It is observed that plate with different combinations of point masses with different taper ratios provide us design options for peak sound power level. As for example, for peak sound power reduction, taper ratios, \(\rm T_{x}=0.75\) with four point mass combination and taper ratio, \(\rm T_{x}=0.75\) with two point masses combination, for Case III plate may be the options.