A Reduced-Order Model for the Nonlinear Vibration of CNT-Reinforced Functionally Graded Composite Plates Using Orthogonal Trial Functions

The nonlinear forced vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is investigated using a mesh-free semi-analytical technique. Three distribution patterns of nanotubes in the thickness direction are considered: Uniform, FG-X, and FG-O. The equations of motion based on the classical plate theory with von Karman nonlinearity are developed and discretized using Galerkin’s approach. The axial displacements are eliminated by adopting orthogonal trial functions for the displacement field, and a reduced, yet complete, model is obtained. Two boundary conditions are considered: immovable simply supported (SS) and clamped. The nonlinear boundary conditions are exactly satisfied. The Runge–Kutta method in combination with MatCont bifurcation software is used to numerically solve the equations of motion. Results are validated for the nonlinear forced vibration of plates available in the literature. The nonlinear forced vibration of FG-CNTRC plates is analyzed through the frequency–response, time-history, and phase portrait. Effects of the volume fraction, the distribution pattern of nanotubes, and the aspect ratio of the plate are investigated.