Nonlinear vibration and dynamic buckling responses of stiffened functionally graded graphene‐reinforced cylindrical, parabolic, and sinusoid panels using the higher‐order shear deformation theory
Tran Quang Minh, Vũ Hoài Nam, Vu Minh Duc, Vu Tho Hung, Le Ngoc Ly, Nguyen Thi Phuong
Abstract
Abstract The nonlinear vibration and dynamic responses of functionally graded graphene‐reinforced composite (FG‐GRC) laminated cylindrical, parabolic, and sinusoid panels stiffened by FG‐GRC stiffeners in the uniformly distributed temperature variation are presented in this paper. An improved smeared stiffener technique is used to model the added stiffnesses of stiffeners to the total stiffnesses of panels. The higher‐order shear deformation shell theory (HSDT) with the geometrical nonlinearities of von Kármán is applied to establish the governing formulations. The stress function form is estimated using the approximated technique for complex curvature panels. Lagrange function and Euler‐Lagrange equations are applied, and the Rayleigh dissipation function is taken into account to obtain the nonlinear equation of motion. Numerical examples are investigated using the Runge‐Kutta method to obtain the dynamic responses of panels, and the critical dynamic buckling loads of panels are considered using the Budiansky‐Roth criterion. Some significant remarks on the nonlinear vibration and dynamic buckling responses of three types of stiffened panels can be recognized from the numerical examples.