## 4 Results
The influences of different graphene distribution patterns and \(R_{1}/a\) on the frequency of the structure subjected to the (SSSS), (CSFS) and (CCCC) boundary conditions are presented in Figure 7, Figure 8, and Figure 9.  
Figure 8: The effects of \(R_{1}\!/\!u\) and GPLRC’s pattern on the frequency for the CFSF boundary conditions (a/b = 5, h = b/10, R2 = 5a, \(\Delta T\ =\ 100K\), \(g_{GPL}\) = 0.5%, N\({}_{\rm L}\) = 10, \(\mu\ =\ h/10\), \(l\ =\ h/5\)). When pattern 2 and pattern 3 are employed to reinforce the structure, the structure encounters the highest and lowest dimensionless frequency, respectively. This behavior stems from the mathematical function, which was presented in the previous section. The alteration of the critical temperature (\(\Delta T^{*}{}_{Cr}\)) based on the changes of \(R_{1}/a\) for different values of \(g_{GPL}\) and various types of boundary conditions are presented in Figure 10, Figure 11, and Figure 12.  
Figure 9: The effects of \(R_{j}\)/\(a\) and GPLRC’s pattern on the frequency for the CCCC boundary conditions (a/b = 5, h = b/10, R2 = 5a, \(\Delta T\ =\ 100K\), \(g_{GPL}\) = 0.5%, N\({}_{\rm L}\) = 10, \(\mu\ =\ h/10,\ l\ =\ h/5\)). Figure 11: The effects of g_GPL and R_1/a on the critical temperature of a GPLRC panel for the CSSS boundary conditions (b/a = 4, h = a/10, NL = 10, R2 = 5b, \(\mu\) = h/10, l = h/5, and GPL-O). Figure 4:0 The effects of \(g_{GPL}\) and \(R_{1}/a\) on the critical temperature of the GPLRC panel for the SSSS boundary conditions (b/a = 4, h = a/10, R2 = 5b, NL = 10, \(\mu\ =\ h/10,\ l\ =\ h/5\), and GPL-O). As expected, \(g_{GPL}\) plays an important role and has a direct influence on the static behavior of the structure. As can be observed from figures, an increment in the \(R_{1}/a\) parameter can be seen to exponentially increase in the buckling load at the lower value of the \(R_{1}/a\). While this trend changes at the higher values of the \(R_{1}/a\), it means at the higher values of the \(R_{1}/a\), there are no considerable changes in the temperature due to enhancement in the \(R_{1}/a\) parameter. It should be noted that the effect of the \(g_{GPL}\) parameter on the critical temperature is more noticeable at the higher values of \(R_{1}/a\) compared to at the lower value of that parameter. In another work, by increasing the \(R_{1}/a\) parameter, the panel tends to be plate without any imperfection. Thus, the dimensionless critical temperature increases. Figure 13, Figure 14, and Figure 15 indicate the influences of the length scale (\(\ll\)\(h\)) and \(R_{1}/a\) of the panel on the vibrational characteristics of the structure for various types of boundary conditions such as SSSS, CSSS, and CCCC. Figure 4:1 The effects of g_GPL and R_1/a on the critical temperature of a GPLRC panel for the CCCC boundary conditions (b/a = 4, h = a/10, NL = 10, R2 = 5b, \(\mu\) = h/10, l = h/5, and GPL-O). Figure 4:2 The effects of \(|\)/\(h\) and \(R_{1}\)/\(a\) parameters on the critical temperature of the GPLRC panel subjected to CSSS boundary conditions (b/a = 4, h = a/10, R2 = 5b, N\({}_{\rm L}\) = 10, \(\mu\ =\ h/10\), \(g_{GPL}\) = 1%, and GPL-O). Figure 4:3 The effects of \(|\)/\(h\) and \(R_{1}\)/\(a\) parameters on the critical temperature of the GPLRC panel subjected to SSSS boundary conditions (b/a = 4, h = a/10, R2 = 5b, N\({}_{\rm L}\) = 10, \(\mu\ =\ h/10\), \(g_{GPL}\) = 1%, and GPL-O). It can be observed from Figure 13, Figure 14, and Figure 15 that \(l\)/\(h\) and \(R_{1}/a\) parameters have direct influences on the critical temperature of the GPLRC panel. For better comprehension, an increment in the length scale and \(R_{1}/a\) parameters provide an increase in the critical temperature of the GPLRC panel. Also, the influences of the length scale parameter on the critical temperature are affected by the \(R_{1}/a\) parameter. Furthermore, the influence of the \(l\)/\(h\) parameter on the critical temperature is more considerable at the higher value of \(R_{1}/a\) in comparison with the lower ones.