# Research on Panel Flutter Considering the Effect of Convective Active Cooling
## 4 Flight Stability and Chatter Suppression  
The stability of a panel without an in-plane load at the same height but with different Mach numbers is discussed in this subsection. Figure 19 shows the variation in the critical dynamic pressure at the panel bifurcation point with a freestream Mach number for different pressure drop ratios. When \(P_{Gr}\) is valued less than 20.0, the critical dynamic pressure gradually increases as the Mach number increases. When \(P_{Gr}=20.0\), the critical dynamic pressure first decreases and then increases, but the variation is very small. When \(P_{Gr}=1.0,\ 2.0\), the panel bifurcates several times at a high Mach number. For example, when \(P_{Gr}=1.0,\ M_{\infty}=15.0\), the panel bifurcates from buckling motion to anharmonic periodic motion at \(\lambda=330.6\), bifurcates to buckling motion at \(\lambda=283.9\), and bifurcates to LCO at \(\lambda=432.7\), which greatly reduces the safe dynamic pressure of the flight. Figure 19 shows that when \(M_{\infty}<10.0\), the bifurcation does not occur more than once 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 of 344.0 at \(P_{Gr}=\infty\). Figure 20 shows the variation curves of the critical dynamic pressure of panel flutter with increasing Mach numbers for different coefficients of head-panel pressure. When \(\alpha=0.2,\ 0.6,\ 1.0\), the critical dynamic pressure increases with the increase in the Mach number. When \(\alpha=1.4,\ 1.8\), the critical dynamic pressure decreases with the increase in the Mach number. When \(\alpha=0.6,\ 1.0\), the panel bifurcates several times at a high Mach number. When \(M_{\infty}<13.7\), the critical dynamic pressure first decreases and then increases as the value of \(\alpha\) increases. Figure 19: Variation curve of critical dynamic pressure with freestream Mach number for different pressure drop ratios. Figures 21 and 22 show the variation curve of the critical dynamic pressure with increasing Mach numbers under inertial resistance and viscous resistance, respectively. It can be seen that all curves in Figures 21 and 22 show a gradually decreasing trend as the Mach number increases. As the inertial resistance increases, the critical dynamic pressure decreases gradually, which has an adverse effect on flight safety, but the effect is very small. 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. When the inertial resistance takes a value above 200.0, the curve is almost horizontal. As the viscous resistance increases, the critical dynamic pressure when panel bifurcation occurs increases significantly, which leads to an obvious suppression effect on the panel flutter. For \(M_{\infty}\)= 5.0, the critical dynamic pressures are 344.0 at \(C_{c2}=0.0\) and 502.8 at \(C_{c2}=20.0\) with 50.5% difference. Figure 21: Variation curve of critical dynamic pressure with freestream Mach number for bifurcation of panel under different inertial resistances. Figure 20: Variation curve of critical dynamic pressure with freestream Mach number for different coefficients of head-panel pressure. The panel shows significantly different stability characteristics under the action of coolant. Therefore, this paper proposes the following solutions to suppress fluttering. (1) Reduce the pressure drop ratio. However, it should be noted that the problem of the material strength limit caused by large flexural deformation of the structure must be considered under a small pressure drop ratio. If the deformation is required to belong \((-0.2,0)\) and actual flight dynamic pressure is required to reach 380.0, the pressure drop ratio must be less than 2.0. (2) Increase or decrease the coefficient of head-panel pressure (away from the value of 1.0).