For a deeper understanding of the physical phenomenology of shock-induced panel flutter, a theoretical model for analyzing aeroelastic stability of flexible panels subjected to an oblique shock has been developed. The von Kármán large deflection plate theory is used to account for the geometrical nonlinearity, and local first-order piston theory is employed to predict unsteady aerodynamic loading in shock-dominated flows. In order to consider the nonuniform static pressure differentials induced by the shock, we regard the final total displacement of the panel as the superposition of static deformation and dynamic displacement, which is in accord with the actual situation of physicality. The static deformation is obtained by solving the static aeroelastic equation, and then it is introduced into the dynamic aeroelastic equations in the form of the stiffness by the nonlinear induced loading. According to Lyapunov indirect method and the Routh–Hurwitz criterion, a theoretical solution for the aeroelastic stability boundaries of the flexible panel subjected to an oblique shock is derived. The results show that the presence of an impinging shock wave is found to produce panel flutter that is characteristically different from that with the shock-free condition. For a complex aeroelastic system in shock-dominated flows, there exists a game between the static pressure differential and the unsteady dynamic pressure. When the dynamic pressure gains the upper hand, the presence of shock reduces the aeroelastic stability of the panel. In contrast, when the static pressure difference has the upper hand, the presence of shock will enhance stability of the panel. The dimensionless aerodynamic parameter, which is the ratio of the non-dimensional static pressure to the non-dimensional dynamic pressure of the incoming flow, plays a significant role in aeroelastic stability of panels in shock-dominated flows. For different dimensionless aerodynamic parameters, the flutter boundaries will present different characteristics. As this dimensionless aerodynamic parameter increases, the non-dimensional critical flutter dynamic pressure will increase monotonously.

为了更深入地了解冲击引起的面板颤振的物理现象，开发了一种用于分析受到斜向冲击的柔性面板气动弹性稳定性的理论模型。von Kármán 大挠度板理论用于解释几何非线性，并采用局部一阶活塞理论来预测冲击主导流中的非定常气动载荷。为了考虑冲击引起的非均匀静压差，我们将面板的最终总位移视为静态变形和动态位移的叠加，符合物理实际情况。静态变形是通过求解静态气动弹性方程获得的，然后通过非线性诱导加载将其以刚度的形式引入到动态气动弹性方程中。根据Lyapunov间接法和Routh-Hurwitz判据，推导出了斜向冲击作用下柔性板气弹稳定边界的理论解。结果表明，发现撞击冲击波的存在会产生与无冲击条件下特征不同的面板颤振。对于以激波为主的流动中的复杂气动弹性系统，静压差和非定常动压之间存在博弈。当动态压力占上风时，冲击的存在会降低面板的气动弹性稳定性。相比之下，当静压差占上风时，冲击的存在将增强面板的稳定性。无量纲空气动力学参数，即无量纲静压与流入流的无量纲动压之比，在以冲击为主的流动中对面板的气动弹性稳定性起着重要作用。对于不同的无量纲气动参数，颤振边界会呈现不同的特征。随着这个无量纲气动参数的增加，无量纲临界颤振动压将单调增加。对于不同的无量纲气动参数，颤振边界会呈现不同的特征。随着这个无量纲气动参数的增加，无量纲临界颤振动压将单调增加。对于不同的无量纲气动参数，颤振边界会呈现不同的特征。随着这个无量纲气动参数的增加，无量纲临界颤振动压将单调增加。