## 3 Comprehensive Frequency Parameter and Mode Shape Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(r\)} & \multicolumn{1}{c}{\multicolumn{1}{c}{**Mode**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Mode**}} & \multicolumn{1}{c}{\multirow{2}{*}{**F**}} & \multicolumn{1}{c}{**First**} & \multicolumn{1}{c}{**Second**} & \multicolumn{1}{c}{**Third**} & \multicolumn{1}{c}{**Fourth**} & \multicolumn{1}{c}{**Firth**} & \multicolumn{1}{c}{**Sixth**} & \multicolumn{1}{c}{**Seventh**} & \multicolumn{1}{c}{**Eighth**} & \multicolumn{1}{c}{**Ninth**} & \multicolumn{1}{c}{**Tenth**} \\ \hline
0.1 & Present & 4.3770 & 18.259 & 20.678 & 39.456 & 52.080 & 55.200 & 74.159 & 76.145 & 105.79 & 109.09 \\  & FEM & 4.3769 & 18.257 & 20.675 & 39.453 & 52.077 & 55.200 & 74.149 & 76.137 & 105.78 & 109.08 \\  & Present & 4.5172 & 18.481 & 20.789 & 39.628 & 52.371 & 55.294 & 74.370 & 76.301 & 106.10 & 109.17 \\  & FEM & 4.5168 & 18.480 & 20.781 & 39.622 & 52.366 & 55.290 & 74.351 & 76.287 & 106.08 & 109.16 \\  & Present & 4.6651 & 18.723 & 20.933 & 39.832 & 52.699 & 55.425 & 74.618 & 76.499 & 106.46 & 109.29 \\  & FEM & 4.6684 & 18.720 & 20.931 & 39.825 & 52.693 & 55.421 & 74.609 & 74.845 & 106.45 & 109.27 \\  & Present & 4.8214 & 18.981 & 21.232 & 40.078 & 53.064 & 55.622 & 74.910 & 76.758 & 106.87 & 109.49 \\  & FEM & 4.8211 & 18.979 & 21.122 & 40.073 & 53.060 & 55.620 & 74.899 & 76.736 & 108.86 & 109.48 \\  & Present & 4.9870 & 19.251 & 21.381 & 40.379 & 53.451 & 55.936 & 75.257 & 77.108 & 107.31 & 109.83 \\  & FEM & 4.9867 & 19.250 & 21.380 & 40.374 & 53.446 & 55.932 & 75.247 & 77.101 & 107.30 & 109.82 \\  & Present & 5.1627 & 19.525 & 21.377 & 40.755 & 53.829 & 56.453 & 75.670 & 77.602 & 107.74 & 110.44 \\  & FEM & 5.1623 & 19.521 & 21.735 & 40.750 & 53.827 & 56.450 & 75.655 & 77.589 & 107.72 & 110.43 \\  & Present & 5.3496 & 19.797 & 22.228 & 41.240 & 54.161 & 57.300 & 76.171 & 78.332 & 108.09 & 111.54 \\  & FEM & 5.3493 & 19.755 & 22.222 & 41.236 & 54.157 & 57.295 & 76.156 & 78.322 & 108.07 & 111.53 \\  & Present & 5.5487 & 20.065 & 22.897 & 41.885 & 54.438 & 58.638 & 76.802 & 79.454 & 108.36 & 113.40 \\  & FEM & 5.5482 & 20.063 & 22.896 & 41.883 & 54.435 & 58.632 & 76.788 & 79.437 & 108.33 & 113.39 \\  & Present & 5.7614 & 20.340 & 23.797 & 42.778 & 54.866 & 60.699 & 77.874 & 81.256 & 108.58 & 116.55 \\  & FEM & 5.7611 & 20.337 & 23.792 & 42.775 & 54.680 & 60.691 & 77.760 & 81.244 & 108.57 & 116.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Frequency parameter \(\phi\) of square REFP plates with the defined rotational fatty factors \(r_{00}=0.5\) and \(r_{00}=r\) changing from 0.1 to 0.9. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(Ma\)} & \multicolumn{1}{c}{\multirow{2}{*}{**s**}} & \multicolumn{1}{c}{\multirow{2}{*}{**F**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Second**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Third**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Fourth**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Firth**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Sixth**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Seventh**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Eighth**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Ninth**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Tenth**}} \\ \hline
0.5 & 30 & 17.116 & 36.377 & 73.408 & 90.929 & 115.23 & 131.63 & 159.01 & 208.76 & 219.46 & 248.47 \\  & 50 & 17.117 & 36.374 & 73.405 & 90.915 & 115.21 & 131.63 & 158.99 & 208.75 & 219.44 & 248.46 \\
0.5 & 100 & 17.118 & 36.372 & 73.403 & 90.906 & 115.20 & 131.62 & 158.98 & 208.74 & 219.43 & 248.45 \\  & 150 & 17.118 & 36.372 & 73.402 & 90.902 & 115.20 & 131.62 & 158.9