Nonlinear Vibration and Dynamic Buckling of Complex Curved Functionally Graded Graphene Panels Reinforced with Inclined Stiffeners

This paper presents a new semi-analytical approach for the nonlinear vibration and dynamic responses of functionally graded graphene platelet-reinforced composite (FG-GPLRC) panels with complex curvature reinforced by orthogonal and/or inclined stiffeners in the thermal environment resting on the nonlinear viscoelastic foundation with the nonlinearities of von Kármán in the framework of the higher-order shear deformation theory (HSDT). The three curvature types of complexly curved panels are considered to be cylindrical, sinusoid, and parabola panels. Orthogonal and/or inclined stiffeners are modeled utilizing an improved smeared stiffener technique. The stress function form is estimated by applying the like-Galerkin method for complexly curved panels. By applying the Lagrange function and Euler–Lagrange equation, the nonlinear equations of motion of the panels are obtained. The viscous damping effects of the viscoelastic foundation are considered by utilizing the Rayleigh dissipation function. Numerical results are examined utilizing the Runge–Kutta method to acquire the time-deflection curves, and by utilizing the Budiansky–Roth criterion, the critical dynamic buckling loads are determined. From the investigated results, it is possible to evaluate the nonlinear vibration and buckling dynamic responses of three forms of panels with stiffeners.