## 5 Results and Discussion  
### Mode Analysis  
The first four mode shapes combined with the corresponding natural frequencies of the glass fiber corrugated panels (GFCPs) and carbon fiber corrugated panels (CFCPs) are shown in Figure 5a. To provide a clear comparative study, the comparison results, i.e., glass fiber vs. carbon fiber and experiments vs. simulation, are plotted in Figure 5b-e, respectively. The error between two results is expressed by:  
\[Error=\frac{M_{i}-Mref_{i}}{Mref_{i}} \tag{7}\]  
where \(Mref_{i}\) is the \(i\)-th mode frequency, which is used as the reference value for comparison, and \(M_{i}\) is the \(i\)-th mode frequency which is compared to the reference frequency. As shown in Figure 5b, the experimental mode of GFP is the reference value, and it can be found that the mode frequencies of GFP were larger than those of the GFP, and the  
Figure 4: The FE model of the corrugated sandwich panel. (**a**) The assembly of the FE model. (**b**) Typical components of the FE model. fourth experimental mode error was the highest. The simulation mode analysis is shown in Figure 5c, and the simulation mode of GFP is the reference value. The simulation results show the same law as the experimental results. In Figure 5d,e, the experimental modes of panels are the reference values. The errors between the experimental and the simulation modes were all less than 6%, which indicates that the results obtained from the proposed FE model showed very good agreement with the experimental results. Comparing the mode characteristics of the two panels, it was found that for the first four modes, the GFCPs and the CFCPs provided similar mode shapes, i.e., bending deformation, as shown in Figure 5a. It is worth noting that the first mode shapes of the corrugated panels were diagonally bent rather than perpendicular to the direction of the foam strip, which is consistent with those of the homogeneous panels. This indicates that the foam is not a main factor for influencing the first mode, i.e., the bending stiffness, of the corrugated panels, even though the foam strips have a clear direction in the panel structures. This is mainly attributed to their low Young's modulus and closer location to the inside of the panel compared to the fiber reinforcements and epoxy resin. Figure 5: (**a**) Experimental and numerical mode results of the studied GFCPs and CFCPs. (**b**) Comparison of experimental modes of different corrugated panels. (**c**) Comparison of numerical modes of different corrugated panels. (**d**) Comparison of experimental and numerical modes of the GFCPs. (**e**) Comparison of experimental and numerical modes of the CFCPs. Comparing the experimental modes of GFCP and CFCP, as shown in Figure 5b,c, it was found that the mode frequency of the CFCP was basically greater than that of the GFCP. Although the difference was neglected in the lower-order vibration, it became more obvious for the higher mode levels. One should note that the bending stiffness of composite panels is predominantly affected by the outer layer material [47]. The surface resin layer and the fiber cloth are subjected to tension and compression and play predominant roles in the low-order vibration. The surface resin layer and fiber cloth can be considered as two springs in series, and the Young's modulus of the fiber is much greater than that of the resin. Therefore, the bending stiffness of the surface layer, and finally, of the entire panel, is mainly determined by the resin. Since the main difference between the GFCP and CFCP is the fiber rather than the surface resin layer, the difference in natural frequencies of GFCP and CFCP is small. It should be noted that carbon fiber has a lower density than that of glass fiber, which is likely the main contributing factor for the slightly higher mode frequency of the CFCP compared to the GFCP counterparts.