为了解决超声速飞行过程中复合材料层压板层间应力集中导致的分层失效问题，提出了一种新型夹层功能梯度材料（functionally graded material，FGM）板结构。首先，基于Kirchhoff薄板理论和von Kármán大变形理论描述夹层FGM板的非线性几何关系，并通过三阶活塞理论模拟夹层FGM板受到的非线性气动力，根据Hamilton原理建立了超声速飞行时夹层FGM板的运动微分方程。然后，引入Galerkin法对夹层FGM板的运动微分方程在航向和展向上分别进行空间离散，得到对应的常微分方程组。最后，通过Runge-Kutta法对所得常微分方程组进行求解，得到夹层FGM板的动力学响应。结果表明，当夹芯层厚度不变时，夹芯层的梯度指数 n越小，颤振临界动压越大；当夹芯层的梯度指数 n小于1.0时，颤振临界动压随夹芯层的厚度占比增长而增大；另外，随着无量纲动压的变大，夹层FGM板的运动类型会由静稳定逐渐发展成为极限环运动。

To address the delamination failure issue in composite laminates caused by interlaminar stress concentration during supersonic flight，a novel sandwich functionally graded material （FGM） panel structure was proposed. First，the nonlinear geometric relationship of the sandwich FGM panel was formulated based on the Kirchhoff thin panel theory and the von Kármán large deformation theory. The nonlinear aerodynamic forces acting on the sandwich FGM panel were simulated using the third-order piston theory. The Hamilton principle was employed to derive the differential equations of motion for the sandwich FGM panel during supersonic flight. Subsequently，the Galerkin method was introduced to discretize these differential equations of motion spatially in both the streamwise and spanwise directions，yielding the corresponding system of ordinary differential equations. Finally，the dynamic response of the sandwich FGM panel was obtained by solving the derived ordinary differential equations using the Runge-Kutta method. The results indicate that，for a constant thickness of the sandwich core，a smaller gradient index n of the core material leads to a higher flutter critical dynamic pressure； When the gradient index n of the sandwich core is less than 1.0，the flutter critical dynamic pressure exhibits a monotonic increase as the thickness ratio of the sandwich core rises； Furthermore，as dimensionless dynamic pressure increases，the motion of the sandwich FGM panel transitions progressively from static stability to limit cycle oscillation.