## 3 Results and Discussion
### Investigating the Influence of Gradient Parameter  
The continuous variation of graphite in the core layer of the composite sandwich plate along the thickness direction is based on the distribution function of graphite volume fraction. There are 3 distribution forms of graphite volume fraction in the core: positive gradient distribution, uniform distribution, and negative gradient distribution. In this section, the influence of three distribution forms on the natural frequency of composite sandwich panel was comparable. The gradient parameter \(p_{+}/p_{-}\) of gradient distribution was considered to be 0.5, 1, and 2 as representative parameters of continuous gradient distribution for comparison calculation. In addition, the physical parameter \(p\) of uniform distribution was 0. Figure 3 shows the relative volume fraction of graphite along the Z coordinates reflecting the distribution function of Equation (1) to Equation (3). The subscripts '\(-\)' and '\(+\)' of the gradient parameters represent the negative and positive gradient distribution of the graphite volume fraction respectively. The abscissa is the Z coordinate of the core layer. The vertical coordinate is the ratio of the volume fraction of graphite for unit thickness layer of Z coordinates to the volume fraction of graphite in the core layer. From the depiction in Figure 3, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Surface Sheets (SMA-Epoxy)**} & \multicolumn{2}{c}{**Core (Graphite-Epoxy)**} \\ \multicolumn{2}{c}{**SMA**} & \multicolumn{2}{c}{**Epoxy**} & \multicolumn{2}{c}{**Graphite**} \\ \hline \(E_{s}(GPa)\) & From Figure 2 & \(E_{e}(GPa)\) & 3.43 & \(E_{g}(GPa)\) & 275.6 \\ \(\sigma_{r}(MPa)\) & From Figure 2 & \(G_{e}(GPa)\) & 1.27 & \(G_{g}(GPa)\) & 114.8 \\ \(\upsilon_{s}\) & 0.3 & \(\upsilon_{e}\) & 0.35 & \(\upsilon_{g}\) & 0.2 \\ \(\rho_{s}(kg\cdot m^{3})\) & 6450 & \(\rho_{e}(kg\cdot m^{3})\) & 1250 & \(\rho_{g}(kg\cdot m^{3})\) & 1900 \\ \(\alpha_{s}(1/^{\circ}\mathrm{C})\) & \(10.26\times 10^{-6}\) & \(\alpha_{e}(1/^{\circ}\mathrm{C})\) & \(64.80\times 10^{-6}\) & \(\alpha_{g}(1/^{\circ}\mathrm{C})\) & \(24.40\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties of surface sheets and core. Figure 3: The relative volume fraction of graphite along the Z coordinates. the negative gradient distribution of graphite is more distributed in the central region of the core layer, while the positive gradient distribution of graphite is more distributed in the upper and lower edge regions of the core layer. The dimensionless natural frequencies vary with temperature subjected to different gradient parameter (\(p\)) value as shown in Figure 4.  
In Figure 4, the natural frequency of negative gradient distribution of graphite volume fraction is smaller than that of uniform gradient distribution, and the natural frequency of positive gradient distribution is larger than that of uniform distribution. When the distribution form shows a negative gradient, the increase in gradient parameter \(p_{-}\) causes the natural frequency and the critical buckling temperature to decrease. When the distribution form shows a positive gradient, the increase in the gradient parameter \(p_{+}\) leads to an increase in natural frequency and critical buckling temperature. With a certain total content of graphite in the core layer, the positive gradient distribution causes more graphite to distribute at the upper and lower edges of the core layer which increases the bending stiffness \(D_{ij}\) of the composite sandwich plate, while the negative gradient distribution causes more graphite to distribute at the center of the core layer which decreases the bending stiffness \(D_{ij}\). The variation of the gradient parameter, i.e., the distribution of graphite, affects the bending stiffness of the sandwich plate, and thus the natural frequency. Figure 5 depicts the dimensionless natural frequency of sandwich composite plate varies with positive gradient parameters (\(p_{+}\)).