The nonlinear panel flutter behaviour of two-dimensional porous curved panel reinforced by graphene platelets exposed to a supersonic flow is investigated. A curved beam element developed based on the trigonometric shear deformation theory is employed. The formulation integrates the geometric nonlinearity with von Karman’s approximation. The effort to model the fluid–structure interaction is reduced by implementing the first-order form of piston theory aerodynamics to describe the flow and accounting for the influence of static aerodynamic load due to the inherent geometric curvature of the panel. The nonlinear governing equations are formulated adopting the Lagrangian formulation. The panel deflection under the static aerodynamic load is evaluated using the Newton–Raphson iteration method. The flutter behaviour is analysed with reference to the large deflection equilibrium state through an eigenvalue analysis and by tracing the complex eigenvalues and identifying the first coalescence of any two vibratory modes. The flutter dynamic pressure is also predicted iteratively using the eigenvalue approach for the selected range of limit cycle amplitudes. The influence of static aerodynamic load and vibration amplitude on the flutter characteristics is brought out for both isotropic and graphene reinforced composite panels with different boundary conditions. The pre-flutter static deflection shape of the panel is also examined. The material parameters such as porosity level in the metal foam and the graphene platelet content are assessed on the nonlinear flutter features of 2D panels.

研究了暴露于超音速流中的石墨烯薄片增强的二维多孔弯曲面板的非线性面板颤动行为。采用基于三角剪切变形理论开发的弯曲梁单元。该公式将几何非线性与von Karman近似相结合。通过实现活塞理论空气动力学的一阶形式来描述流动并考虑由于面板固有的几何曲率而产生的静态空气动力学载荷的影响，减少了对流体-结构相互作用进行建模的工作。非线性控制方程采用拉格朗日公式表示。使用牛顿-拉夫森迭代法评估静态空气动力载荷下的面板挠度。通过特征值分析并跟踪复杂的特征值并识别任意两个振动模式的第一个合并，可以参考大挠度平衡状态来分析颤振行为。对于选定的极限循环幅度范围，还可使用特征值方法来迭代地预测颤动动压。分别针对各向同性和石墨烯增强复合板在不同边界条件下的静态气动载荷和振动幅度对颤振特性的影响。还检查了面板的预颤振静态变形形状。材料参数（例如金属泡沫中的孔隙度和石墨烯血小板含量）是根据2D面板的非线性颤动特征评估的。