Large Amplitude Vibration of FG-GPL Reinforced Conical Shell Panels on Elastic Foundation

Abstract

Functionally graded (FG) composite structures reinforced by graphene platelets (GPL) have been widely adopted as a state-of-the-art structural element due to their preeminent properties and functional designability. However, most studies are confined to beams, plates, and cylindrical panels, relying on the numerical differential quadrature method (DQM) and the finite element numerical method. In this context, the current study intends to investigate the nonlinear free vibration of FG-GPL-reinforced composite (RC) conical panels resting on an elastic medium by developing a 2-D planar meshfree method-based nonlinear numerical method. The nonlinear free vibration problem is expressed by the first-order shell deformation theory and the von-Kármán nonlinearity. The complex conical neutral surface of the panel is transformed into a 2-D rectangular plane to avoid painstaking mathematical manipulation. The troublesome shear-membrane locking is suppressed by employing the MITC3+shell element, and the derived nonlinear modal equations are solved by introducing a three-step direct iterative scheme. The present method is compared with the DQM through the benchmark experiment, from which a good agreement between the two methods is observed. And, the nonlinear free vibration characteristics of FG-GPLRC conical panels on an elastic foundation are profoundly investigated, and it is found that those are significantly influenced by the foundation stiffness, the amount and dispersion pattern of GPLs, the panel geometry sizes, and the boundary condition.