## 3 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(D_{\mathbf{x}}\)/\(H\)} & \multirow{2}{*}{\(\boldsymbol{\Phi}\)} & \multirow{2}{*}{\(\boldsymbol{r}\)} & \multirow{2}{*}{**Results**} & \multicolumn{6}{c}{**Mode**} \\ \cline{5-10}  & & & & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \multirow{4}{*}{1} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 21.357 & 35.537 & 58.967 & 81.294 & 109.976 & 115.987 \\  & & & present & 21.366 & 35.170 & 58.966 & 80.416 & 108.770 & 115.971 \\ \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & 17.094 & 31.760 & 49.427 & 72.700 & 100.455 & 107.749 \\  & & & present & 17.060 & 31.389 & 49.249 & 71.823 & 100.058 & 106.691 \\ \cline{2-10}  & \multirow{2}{*}{10000} & \multirow{2}{*}{0.00003} & [16] & 9.570 & 27.810 & 38.712 & 65.210 & 87.729 & 106.456 \\  & & & present & 9.512 & 27.473 & 38.519 & 64.452 & 87.266 & 105.401 \\ \hline \multirow{4}{*}{1.5} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 26.279 & 38.807 & 72.541 & 91.761 & 111.206 & 142.856 \\  & & & present & 26.637 & 38.797 & 73.461 & 91.802 & 110.322 & 144.289 \\ \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & 21.051 & 34.121 & 60.857 & 81.023 & 108.491 & 123.765 \\  & & & present & 22.418 & 34.861 & 63.462 & 82.477 & 107.974 & 127.221 \\ \cline{2-10}  & \multirow{2}{*}{10000} & \multirow{2}{*}{0.00003} & [16] & 11.866 & 28.692 & 47.810 & 71.071 & 106.570 & 108.108 \\  & & & present & 11.798 & 28.346 & 47.571 & 70.237 & 105.632 & 107.520 \\ \hline \multirow{4}{*}{2.5} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 30.412 & 41.798 & 83.941 & 101.146 & 112.381 & 165.514 \\  & & & present & 31.037 & 42.042 & 85.572 & 101.866 & 111.714 & 167.983 \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & **24.370** & **36.315** & **70.446** & **88.559** & 109.239 & **143.418** \\  & & & present & **26.989** & **38.162** & **75.681** & **92.409** & 109.298 & **150.643** \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{10000} & \multirow{2}{*}{0.00003} & [16] & 13.753 & 29.538 & 55.431 & 76.482 & 106.800 & 125.350 \\  & & & present & 13.707 & 29.192 & 55.157 & 75.582 & 105.862 & 124.522 \\ \hline \multirow{4}{*}{3.5} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 34.046 & 44.576 & 93.972 & 109.733 & 113.520 & 184.433 \\  & & & present & 34.890 & 45.022 & 96.185 & 110.996 & 113.017 & 175.721 \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & **27.268** & **38.364** & **78.885** & **95.905** & **109.972** & **160.741** \\  & & & present & **31.022** & **41.261** & **86.535** & **101.642** & **110.610** & **167.809** \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{10000} & \multirow{2}{*}{0.00003} & [16] & 15.439 & 30.372 & 62.126 & 81.537 & 107.033 & 140.538 \\  & & & present & 15.382 & 30.015 & 61.819 & 80.572 & 106.092 & 139.466 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: First six frequency parameters \(\Omega=\omega a^{2}\sqrt{\rho h/H}\) for orthotropic plates with various flexural stiffness and different rotational fixity factors (\(D_{y}/H=1\), \(\
u=0.3\), and \(a/b=0.5\)).