Nonlinear flutter analysis of functionally graded carbon

Abstract

In this paper, geometrical nonlinear flutter analysis of functionally graded carbon nanotube-reinforced composite plates is presented. The governing equations of the system are obtained using the Mindlin plate theory and von Karman geometric nonlinearity. The linear piston theory is utilized to determine the aerodynamic pressure. Applying the Hamilton principle, equations of motion of a system are derived in the matrix form, and then the finite element method is used to obtain the discretized equations. Application of Newmark’s time integration and Newton–Raphson method are used to solve the nonlinear oscillation equations for determining the nonlinear flutter response and critical flow velocity. To check the validity of the present formulation, numerical results are compared with the previous data in the literature. The effects of stiffeners, type carbon nanotube (CNT) and angle of attack of airflow, thickness (ratio h/a) of the plate on critical airflow velocity and nonlinear dynamic response of the SFG-CNTRC plates are studied.