## 3 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{r}\)} & \multirow{2}{*}{\(D_{\mathbf{x}}/D_{\mathbf{y}}\)} & \multirow{2}{*}{\(\mathbf{H}/D_{\mathbf{y}}\)} & \multirow{2}{*}{\(\mathbf{\
u}_{\mathbf{x}}\)} & \multirow{2}{*}{**Results**} & \multicolumn{6}{c}{**Mode**} \\ \cline{5-10}  & & & & & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \multirow{4}{*}{0} & \multirow{4}{*}{0.5} & \multirow{4}{*}{0.3} & [29] & 9.1507 & 13.511 & 37.46 & 40.4704 & 42.3718 & 68.5419 \\  & & & present & 9.1484 & 13.4905 & 37.4421 & 40.4343 & 42.3186 & 68.4430 \\ \cline{2-10}  & & \multirow{2}{*}{1} & \multirow{2}{*}{0.3} & [29] & 9.3871 & 20.5731 & 38.404 & 50.9914 & 53.0128 & 87.1387 \\  & & & present & 9.3835 & 20.5387 & 38.3858 & 50.9049 & 52.9419 & 87.0934 \\ \cline{2-10}  & & \multirow{2}{*}{2} & \multirow{2}{*}{0.3} & [29] & 9.55 & 29.4576 & 38.8208 & 66.6428 & 67.3417 & 87.8272 \\  & & & present & 9.5461 & 29.4211 & 38.8042 & 66.5191 & 67.2802 & 87.7881 \\ \hline \multirow{2}{*}{0.5} & \multirow{2}{*}{0.5} & \multirow{2}{*}{2} & \multirow{2}{*}{0.3} & [16] & 13.5354 & 31.0445 & 43.5971 & 67.3021 & 70.2325 & 92.9605 \\ \cline{2-10}  & & & & [30] & 22.369 & 22.695 & 24.49 & 30.2 & 42.1 & 60.49 \\ \cline{2-10}  & & & & [29] & 22.5461 & 22.8694 & 24.6502 & 30.3287 & 42.1714 & 60.5361 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: First six frequency parameters \(\Omega=\omega a^{2}\sqrt{\rho h/D_{x}}\) for orthotropic square plates (\(b/a=1\)) with three different rotational fixity factors. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{D_{\mathbf{x}}}/H\)} & \multirow{2}{*}{\(\mathbf{\Phi}\)} & \multirow{2}{*}{\(\mathbf{r}\)} & \multirow{2}{*}{**Results**} & \multicolumn{6}{c}{**Mode**} \\ \cline{5-10}  & & & & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{0.1} & \multirow{4}{*}{0.97087} & [16] & 21.476 & 25.914 & 43.323 & 59.327 & 65.800 & 80.462 \\  & & & present & 21.495 & 25.712 & 42.896 & 59.356 & 65.331 & 79.174 \\ \cline{2-10}  & & & & [16] & 17.192 & 21.908 & 40.141 & 49.776 & 56.630 & 78.336 \\  & & & present & 17.157 & 21.686 & 39.721 & 49.607 & 56.055 & 76.882 \\ \cline{2-10}  & & & & [16] & 9.678 & 16.302 & 37.026 & 39.143 & 47.228 & 72.508 \\  & & & present & 9.630 & 16.113 & 36.666 & 38.936 & 46.698 & 70.629 \\ \hline \multirow{4}{*}{1.5} & \multirow{4}{*}{0.01} & \multirow{4}{*}{0.97087} & [16] & 26.373 & 30.161 & 46.075 & 72.836 & 78.355 & 81.195 \\  & & & present & 26.742 & 30.281 & 45.946 & 73.780 & 78.720 & 81.058 \\ \cline{2-10}  & & & [16] & 21.112 & 25.159 & 42.051 & 61.145 & 66.971 & 78.812 \\  & & & present & 22.501 & 26.206 & 42.548 & 63.752 & 68.960 & 78.524 \\ \cline{2-10}  & & & [16] & 11.952 & 17.768 & 37.700 & 48.164 & 55.034 & 76.631 \\  & & & present & 11.893 & 17.560 & 37.324 & 47.909 & 54.406 & 75.520 \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{0.01} & \multirow{4}{*}{0.97087} & [16] & 30.494 & 33.877 & 48.647 & 82.683 & 84.205 & 89.170 \\  & & & present & 31.127 & 34.237 & 48.733 & 82.787 & 85.849 & 90.154 \\ \cline{1-1} \cline{2-10}  & & & [16] & **24.428** & **28.034** & **43.865** & **70.707** & **75.917** & **79.278** \\ \cline{1-1} \cline{2-10}  & & & present & **27.062** & **30.272** & **45.315** & **75.934** & **80.192** & **80.409** \\ \cline{1-1} \cline{2-10}  & & & [16] & 13.858 & 19.121 & 38.362 & 55.742 & 61.681 & 77.413 \\ \cline{1-1} \cline{2-10}  & & & present & 13.790 & 18.896 & 37.971 & 55.449 & 61.150 & 75.842 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 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 \(a/b=1\)).