# Research on Panel Flutter Considering the Effect of Convective Active Cooling
## 5 Discussion and Conclusions  
Based on [PERSON]'s large deformation thin plate theory and the Kirchhoff-Love hypothesis, the dynamics model of panel flutter under the action of coolant is established. The accuracy of the analysis model was verified. On this basis, the effects of the head  
Figure 22: Variation curve of critical dynamic pressure with freestream Mach number for bifurcation of wall plate under different viscous resistances. panel pressure of coolant, the pressure drop ratio, the coolant injection direction, and the inertial resistance and viscous resistance on panel stability and flight stability were studied, respectively; these are considered to be significant for panel flutter analysis, and the suppression method of panel flutter is proposed. The follow conclusions can be drawn from these results:  
(1) The pressure drop ratio determines the pressure difference distribution on the upper and lower surfaces of the panel. A low pressure drop ratio causes multiple bifurcations of the panel with a large in-plane load, and, in general, the critical dynamic pressure when bifurcation occurs under a low pressure drop ratio is larger than that under a high pressure drop ratio. When \(M_{\infty}<10.0\), the bifurcation occurs no more than one time and the critical dynamic pressure decreases as the pressure drop ratio increases. For \(M_{\infty}=5.0\), the largest critical dynamic pressure is 420.1 at \(P_{Gr}=1.0\), which is 22.1% higher than the least critical dynamic pressure valued at 344.0 at \(P_{Gr}=\infty\). Multiple bifurcations occur at a low Mach number, which greatly reduces the critical dynamic pressure. As the pressure drop ratio decreases, the flexural deformation of the panel when bifurcation occurs increases, so the strength limit of the wall plate material is also considered. (2) The coefficient of head-panel pressure determines the pressure difference on the upper and lower surfaces of the panel. Values far away from 1.0 can cause a large critical dynamic pressure and avoid multiple bifurcations at high Mach numbers. Moreover, the large panel flexural deformation should be considered. (3) The coolant injection direction changes the critical dynamic pressure. At low head-panel pressure, the critical dynamic pressure under forward injection is larger than that under reverse injection, while at large head-panel pressure, the result is opposite. (4) Inertial resistance slows down the convergence process of the panel response, while viscous resistance speeds up this process. Inertial resistance reduces the critical dynamic pressure but not obviously, while viscous resistance significantly improves the critical dynamic pressure. For example, when \(M_{\infty}\)= 5.0, the critical dynamic pressures are 344.0 at \(C_{c1}=0.0\) and 343.06 at \(C_{c1}=200.0\) with 0.27% difference, while critical dynamic pressures are 344.0 at \(C_{c2}=0.0\) and 502.8 at \(C_{c2}=20.0\) with 50.5% difference. The critical dynamic pressure gradually decreases as the Mach number increases. (5) By analyzing the flutter characteristics of the panel under the action of coolant, the suppression strategy of panel flutter is proposed. Reducing the pressure drop ratio, increasing or decreasing the coefficient of head-panel pressure (away from the value of 1.0), and adjusting the coolant injection direction can play a role. When changing these parameters, the problem of the material strength limit caused by large flexural deformation of the structure must be considered. Reducing inertia resistance and improving viscous resistance can also suppress the flutter. Considering the definitions of inertial resistance and viscous resistance, a coolant with a small concentration or large viscosity coefficient can be selected. Conceptualization, J.H., G.Z., and G.Y. ; formal analysis J.H. ; writing--original draft preparation, J.H. ; writing--review and editing, W.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.