Nonlinear supersonic flutter study of porous 2D curved panels including graphene platelets reinforcement effect using trigonometric shear deformable finite element

Abstract 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.