## 4 Results  
The material properties of the GPL are summarized in Table 6. It was reported that the material properties of epoxy are functions of temperature \(T\). Therefore, Young's modulus, shear modulus, and thermal expansion coefficients of epoxy are also functions of temperature \(T\)[109]. Poly referred to as PMMA, is selected for the epoxy, and the material properties of which are assumed to be \(\rho_{M}=1150\) kg/m\({}^{3}\), \(v_{M}=0.34\), \(\alpha_{M}=45(1+0.0005\Delta T)\times 10^{-6}/K\), and \(E_{M}=(3.52-0.0034\)T) GPa, in which \(T=T_{0}\) + \(\Delta T\) (as mentioned earlier \(T_{0}\) is room temperature). Furthermore, the dimensions of the GPL are assumed to be \(l_{GPL}=2.5\,\upmu\)m, \(W_{GPL}=1.5\,\upmu\)m, and \(h_{GPL}=1.5\,\upmu\)m. In the current study, we consider the width of the panel equal to 20 \(\upmu\)m. Figures 3-6 face us with exposure about the influences of smaller aspect ratio (\(\mu\)/\(h\)) and nonlocal parameter to thickness ratio (\(\mu\)/\(h\)) on the vibration response of the structure subjected to the SSSS, CCCC, CSFS, and CFFF boundary conditions. \begin{table}
\begin{tabular}{c c} \hline \hline Material Properties: & GPL \\ \hline Young’s modulus (GPa) & 1010 \\ \hline Density (kg m\({}^{-3}\)) & 1062.5 \\ \hline Poisson’s ratio & 0.186 \\ \hline Thermal expansion coefficient (\(10^{-6}\)/K) & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Material properties of the GPL [110]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**H = a/15**} \\ \hline  & \multicolumn{2}{c}{**Numerical**} & \multicolumn{2}{c}{**Numerical**} & \multicolumn{2}{c}{**Numerical**} & \multicolumn{2}{c}{**Numerical**} & \multirow{2}{*}{
\begin{tabular}{c} **Numerical** \\ **Results** \\ **Results** \\ **Reference**Figure 4: The influences of \(a\)/\(h\) and \(\mu\)/\(h\) on the frequency for the CCCC boundary conditions with a/b = 5, 1 = h/5, \(\Delta\)T = 100K, NL = 10, g_GPL = 0.5%, and GPL-x. Figure 3: The influences of \(a\)/\(h\) and \(\mu\)/\(h\) on the frequency for the SSSS boundary conditions with a/b = 5, 1 = \(h/5\), \(\Delta T=\ 100\,K\), N\({}_{\rm L}\) = 10, \(g_{GPL}\) = 0.5% and GPL-x. According to Figures 3 and 4, for CCCC and SSSS boundary conditions, by enhancing the \(\mu/h\) parameter, the frequency response of the GPLRC panel decreases exponentially. An impressive result is that the impact of the \(a/h\) parameter on the frequency of the system is dependent on the value of the  
Figure 5: The effects of \(a/h\) and \(\mu/h\) on the frequency for the CSFS boundary conditions with a/b = 5, 1 = h/5, \(\Delta\)T = 100K, NL = 10, g_GPL = 0.5%, and GPL-x. Figure 6: The influences of \(a/h\) and \(\mu/h\) on the frequency for the CEFF boundary conditions with a/b = 5, 1 = h/5, \(\Delta\)T = 100K, NL = 10, g_GPL = 0.5%, and GPL-x. nonlocal parameter. For a better understanding, there is an indirect effect from \(a/h\) on the dynamics of the panel, and this phenomenon is more intense in the bigger value of the nonlocal parameter. Figures 5 and 6 present that for CSFS and CFFF boundary conditions. First, it can be seen that an increment in the nonlocal parameter leads to an enhancement in the natural frequency of the structure, as long as a maximum point appears. Then, an indirect relation between the \(\mu/h\) parameter and natural frequency of the structure can be seen. For more detail, at the lower value of the \(\mu/h\) parameter, there is a direct relation between it and natural frequency, but at the higher value, this relation changes from direct to indirect. Also, for CSFS and CFFF boundary conditions, there is an indirect effect of the \(a/h\) parameter on the dynamic response of the panel.