## 3 Numerical Examples and Results
### Coupled Fluid-Structure-Thermal Analysis
#### 3.3.1 Parameter Study under Uniform Temperature Field  
The effects of geometric and material parameters on critical dynamic pressure of the HCS plates in a uniform temperature field are investigated. The HCS plates are made of Ti-6 Al-4V filled with Rohacell 31 foam. The reference geometric parameters are nc = 25, \(a/h=50\), \(b/a=1\), \(h_{1}=h_{3}=h_{t}=0.1h\), \(t=0.1h\).  
1. Effects of aspect ratio and airflow direction  
Figure 10 illustrates the effects of aspect ratio \(b/a\) and airflow direction on the dimensionless critical dynamic pressure. The aspect ratio takes the value of 0.5, 1.0, 1.5 and the airflow direction is parallel or perpendicular to machine direction (_MD_) of the corrugated plate. It is shown that with an increasing aspect ratio, the critical dynamic pressure decreases regardless of the airflow direction. Meanwhile, the streamwise has a limited influence on the critical dynamic pressure and the critical dynamic pressure is slightly higher when it is parallel to _MD_ as opposed to perpendicular to _MD_.  
2. Effects of number of unit cell and inclined angle  
Figure 11 illustrates the effects of number of unit cells \(n_{c}\) and inclined angle \(\theta\) on the dimensionless critical dynamic pressure. The number of unit cells varies from 15 to 45 and the inclined angle varies from 30\({}^{\circ}\) to 75\({}^{\circ}\). The critical dynamic pressure increases with the increase in the number of unit cells  
Figure 10: Effects of (**a**) aspect ratio and (**b**) airflow direction on dimensionless critical dynamic pressure against temperature change.  
or the inclined angle. Within a smaller range of temperature change, the discrepancy of the critical dynamic pressure between different numbers of unit cells or different corrugation angles is quite evident. However, for a larger temperature change, the critical dynamic pressure does not change much with these two changing parameters.  
3. Effects of thickness of face sheets and corrugated members  
Figure 12 illustrates the effects of the thickness of the face sheets \(h_{f}\) and the corrugated members \(t\) on the dimensionless critical dynamic pressure with temperature change \(\Delta T=100\). The thickness of face sheets takes the value of 0.05, 0.10, 0.20 and the thickness of corrugated members varies from 0.02 to 0.20. It is clearly seen that increasing either the facesheet or corrugation thickness can both improve the critical dynamic pressure. Moreover, the stability enhancement for the HCS plates is more obvious when thickening the facesheet thickness as opposed to the corrugation thickness.  
4. Effects of Material properties  
Material properties of the foam and corrugated sandwich plates are also taken into consideration. Table 3 shows the effects of the material combination of the foam and base structures on the critical temperature change and dimensionless critical dynamic pressure with temperature change \(\Delta T=100\). Ti, Steel and Al denote Ti-6 Al-4V, 304 stainless steel and Aluminum 1050 for the base structures,  
Figure 11: Effects of (**a**) number of unit cell and (**b**) inclined angle on dimensionless critical dynamic pressure against temperature change.  
Figure 12: Effect of thickness of face sheets and corrugated members on dimensionless critical dynamic pressure with temperature change \(\Delta T=100\).  
respectively. RC31, RC51, RC71, AC and empty denote the corrugated sandwich plate filled with Rohacell 31, Rohacell 51, Rohacell 71, aluminum foam (Alporas) and no filler, respectively. The material properties are given in Tables 1 and 2.  
It is shown that the base materials of the face sheets and the corrugated members have a much greater influence on the critical dynamic pressure than the foam material. The filling foam increases both the critical temperature change and dynamic pressure to a certain degree compared to the unfilled cases. The HCS plates made of Ti-6 Al-4V and filled with Rohacell 51 foam have the best performance for both static and dynamic stabilities.