# Static and Dynamic Response of FG-CNT-Reinforced Rhombic Laminates
## 5 Numerical Results and Discussion
### Results and Discussion
#### 5.2.1 Free Vibration Analysis  
Tables 10 and 11 represent the first six dimensionless frequency parameter of UD-CNT- and FG-CNT-reinforced rhombic plate for the three different types of CNT volume fraction \(\left(V^{*}_{\text{CNT}}=0.11,\ 0.14\ \text{and}\ 0.17\right)\) and four different skew angles \(\left(\alpha=15^{\circ},\ 30^{\circ},\ 45^{\circ}\ \text{and}\ 60^{\circ}\right)\). The results were tabulated for simply supported and clamped boundary condition, respectively. It was noticed that an increase in the skew angle results in an increase in dimensionless frequency parameter for all types of CNTs distribution and all considered CNT volume fractions. An approximately 6% increase was noticed in the dimensionless fundamental frequency parameter of functionally graded CNTRC rhombic plate when skew angle changes from \(15^{\circ}\) to \(30^{\circ}\), \(22\%\) and \(60\%\) increase was noticed for \(15^{\circ}\) to \(45^{\circ}\) and for \(15^{\circ}\) to \(60^{\circ}\). Table 12 shows the dimensionless frequency parameter of FG-CNTR-reinforced rhombic plate for CCSS-, CSCS-, CCFF-, and CFCF-type boundary support. For the all considered boundary conditions and skew angles, the FG-O distribution retains the minimum dimensionless frequency parameter while the FG-X distribution shows maximum values of dimensionless frequency parameter among other kinds of distribution. Additional distribution of CNTs should be provided at the top and the bottom section rather than at the mid-section for attaining maximum stiffness. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**BC**} & \multirow{2}{*}{\(V^{*}\)**CNT**} & \multicolumn{2}{c}{_a/h = 10_} & \multicolumn{2}{c}{_a/h = 20_} & \multicolumn{2}{c}{_a/h = 50_} \\ \cline{3-8}  & & **[PERSON] et al. [5]** & **Present** & **[PERSON] et al. [5]** & **Present** & **[PERSON] et al. [5]** & **Present** \\ \hline CCCC & 0.11 & 0.00222 & 0.00207 & 0.01339 & 0.01257 & 0.2618 & 0.24056 \\  & 0.14 & 0.00208 & 0.00192 & 0.01188 & 0.01115 & 0.2131 & 0.19644 \\ \hline SSSS & 0.11 & 0.00373 & 0.00354 & 0.03628 & 0.03352 & 1.1550 & 1.04729 \\  & 0.14 & 0.00330 & 0.00314 & 0.03001 & 0.02779 & 0.9175 & 0.83205 \\ \hline SCSC & 0.11 & 0.00332 & 0.00313 & 0.03393 & 0.03127 & 1.0990 & 0.99624 \\  & 0.14 & 0.00297 & 0.00281 & 0.02852 & 0.02634 & 0.8890 & 0.80555 \\ \hline SPSF & 0.11 & 0.00344 & 0.0039 & 0.03341 & 0.03223 & 1.0680 & 1.01428 \\  & 0.14 & 0.00302 & 0.00297 & 0.02760 & 0.02654 & 0.8505 & 0.80295 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison study of non-dimensional maximum deflection of various volume fraction of UD CNT-reinforced composite plate. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**BC**} & \multirow{2}{*}{\(V^{*}\)**CNT**} & \multicolumn{2}{c}{_a/h = 10_} & \multicolumn{2}{c}{_a/h = 20_} & \multicolumn{2}{c}{_a/h = 50_} \\ \cline{3-8}  & & **[PERSON] et al. [5]** & **Present** & **[PERSON] et al. [5]** & **Present** & **[PERSON] et al. [5]** & **Present** \\ \hline CCCC & 0.11 & 0.00211 & 0.00191 & 0.01150 & 0.01052 & 0.18940 & 0.16721 \\  & 0.14 & 0.00198 & 0.00179 & 0.01036 & 0.00954 & 0.15600 & 0.13941 \\ \hline SSSS & 0.11 & 0.00318 & 0.00294 & 0.02701 & 0.02398 & 0.79000 & 0.67655 \\  & 0.14 & 0.00284 & 0.00266 & 0.02256 & 0.02021 & 0.62710 & 0.53777 \\ \hline SCSC & 0.11 & 0.00286 & 0.00264 & 0.02587 & 0.02297 & 0.77280 & 0.66351 \\  & 0.14 & 0.00258 & 0.00240 & 0.02184 & 0.01955 & 0.62060 & 0.53313 \\ \hline SPSF & 0.11 & 0.00290 & 0.00276 & 0.02484 & 0.02281 & 0.73380 & 0.70308 \\  & 0.14 & 0.00259 & 0.00248 & 0.02078 & 0.01916 & 0.58540 & 0.54605 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison study of non-dimensional maximum deflection of various volume fraction of UD CNT-reinforced composite plate. Therefore, the FG-X and FG-O distributions yield maximum and minimum stiffness, respectively.