## 3 Numerical Results
\begin{table}
\begin{tabular}{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}{*}{2.5} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 34.120 & 37.223 & 51.078 & 84.182 & 94.212 & 98.824 \\  & & & present & 34.971 & 37.777 & 51.337 & 84.426 & 96.432 & 100.298 \\ \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & **27.338** & **30.640** & **45.603** & **79.122** & **80.206** & **83.922** \\  & & & present & **31.090** & **33.962** & **47.974** & **81.840** & **86.763** & **90.744** \\ \cline{2-10}  & \multirow{2}{*}{10000} & \multirow{2}{*}{0.00003} & [16] & 15.532 & 20.385 & 39.013 & 62.406 & 68.005 & 76.640 \\  & & & present & 15.455 & 20.144 & 38.607 & 62.080 & 67.221 & 76.162 \\ \hline \multirow{4}{*}{3} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 37.396 & 40.291 & 53.393 & 85.647 & 103.258 & 107.638 \\  & & & present & 38.433 & 41.011 & 53.797 & 86.002 & 105.969 & 109.509 \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & **29. At last, the influence of different degrees of rotational restraints on the mode shapes was investigated. Figure 3 shows the first, second and third mode shapes of R-F-R-F orthotropic square plates with three different values of rotational fixity factors (0, 0.5 and 0.9999). The mode shapes can be found to be significantly altered by the rotational restraints. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{D_{x}/H}\)} & \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}{*}{3} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 37.329 & 47.184 & 103.032 & 114.635 & 117.697 & 193.554 \\  & & & present & 38.361 & 47.801 & 105.744 & 114.263 & 119.417 & 181.325 \\ \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & **29.901** & **40.317** & **86.506** & **101.984** & **110.698** & **175.531** \\  & & & present & **34.663** & **44.176** & **96.379** & **110.262** & **111.896** & **173.447** \\ \cline{2-10}  & \multirow{2}{*}{10000} & \multirow{2}{*}{0.00003} & [16] & 16.956 & 31.180 & 68.166 & 86.296 & 107.266 & 154.272 \\  & & & present & 16.891 & 30.816 & 67.830 & 85.271 & 106.321 & 152.957 \\ \hline \multirow{4}{*}{3.5} & \multirow{2}{*}{0.01} & \multirow{2}{*}{0.97087} & [16] & 40.345 & 49.653 & 111.351 & 115.728 & 125.250 & 190.216 \\  & & & present & 41.543 & 50.418 & 114.511 & 115.467 & 127.275 & 186.716 \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{0.1} & \multirow{2}{*}{0.76923} & [16] & **32.326** & **42.179** & **93.507** & **108.072** & **111.416** & **183.912** \\  & & & present & **38.001** & **46.927** & **105.437** & **113.152** & **118.355** & **178.938** \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{10000} & \multirow{2}{*}{0.00003} & [16] & 18.353 & 31.977 & 73.713 & 90.806 & 107.501 & 166.512 \\  & & & present & 18.277 & 31.596 & 73.350 & 89.725 & 106.550 & 159.394 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont_. Figure 3: Mode shapes of a square orthotropic plate with different rotational restraints. (**a**) first mode; (**b**) second mode; (**c**) third mode.