## 3 Results and Discussion
### Investigating the Influence of Graphite Volume Fraction  
The total volume fraction of graphite in the core layer undoubtedly affects the natural frequency of the composite sandwich plate. Comparison of the natural frequencies of sandwich plates with 1% and 5% graphite volume fraction distribution in the core layer with negative gradient, uniform, and positive gradient distribution is shown in Figure 6.  
As can be seen in Figure 6, the natural frequency of the negative gradient distribution was less than the uniform distribution and then less than the positive gradient distribution, regardless of the volume fraction of 1% or 5%. The natural frequency of \(V\)g = 5% was more affected by different distribution forms than that of \(V\)g = 1%. This is because the increase of graphite content leads to the increase of the overall stiffness, which also magnifies the influence of gradient distribution on the sandwich plate.  
At a certain gradient parameter, the natural frequency of \(V\)g = 5% was higher than that of \(V\)g = 1% in a lower temperature range. Since the stiffness of the composite sandwich plate was dominated by the modulus of graphite that the increase in the graphite content in the core layer increases the stiffness  
Figure 5: Dimensionless natural frequencies vs. the positive gradient parameter (\(p_{+}\)) subjected to different temperatures.  
Figure 6: A comparison on dimensionless natural frequencies between the graphite volume fraction of 1% and 5% subjected to negative/non/positive gradient.  
of the sandwich plate. With the increase of temperature, the natural frequency of \(V\)g = 5% decreased rapidly, while the natural frequency of \(V\)g = 1% decreased first, then increased and then decreased slowly. This was due to the thermal stress produced by graphite in the core layer and the recovery stress produced by SMA in the surface layer playing a leading role, resulting in the rapid decline of stiffness of \(V\)g = 5%, while the stiffness of \(V\)g = 1% in the high temperature range decreased slowly and had a higher critical buckling temperature.  
Figure 7 shows that the dimensionless natural frequency of a sandwich composite plate varies with graphite volume fraction. In Figure 7, the natural frequency remains relatively stable with temperature changes when the volume fraction of graphite is between 1% and 2%. With the increase of graphite volume fraction, the natural frequency is more affected by temperature. For example, in the process of temperature rising from 25 \({}^{\circ}\)C to 100 \({}^{\circ}\)C, the dimensionless natural frequency of \(V_{g}\) = 10% decreased from 2.17 to 0.68, while the dimensionless natural frequency of \(V_{g}\) = 1% decreased from 1.17 to 0.82. Therefore, the increase of volume fraction of graphite increases the thermal stress generated by graphite in the core layer. Then the decrease of stiffness of the sandwich plate accelerates the decrease of the natural frequency. In addition, the natural frequency increases rapidly with the increase of graphite volume fraction in the core layer at 25 \({}^{\circ}\)C to 55 \({}^{\circ}\)C, while the influence of graphite volume fraction on the natural frequency is relatively weak at 70 \({}^{\circ}\)C to 100 \({}^{\circ}\)C.