This study investigates the nonlinear vibration characteristics of functionally-graded twisted bilayer graphene reinforced titanium (FG-TBLG-RT) cantilever trapezoidal laminated plates with variable thickness, targeting lightweight, and vibration-resistant structures for unmanned aerial vehicles (UAVs). A novel mechanical model is developed, aiming at coupling the functionally-graded material (FGM) distributions with a variable-thickness cantilevered trapezoidal geometry so as to represent lightweight UAV wing structures, and a comprehensive theoretical framework is established with the 1st-order shear deformation theory and von Kármán geometric nonlinearity. The governing equations are solved by the Rayleigh-Ritz method, Galerkin method, Runge-Kutta (R-K) method, and harmonic balance method (HBM). The accuracy of the proposed model is successfully validated by both the finite element analysis (FEA) and the experimental tests, demonstrating excellent agreement with a maximum deviation of less than 5%. A systematic analysis is conducted to reveal the effects of the twisted bilayer graphene (TBLG) weight fraction, distribution patterns, and geometric parameters on the natural frequencies. Furthermore, this work explicitly uncovers and experimentally validates the highly complex and pronounced nonlinear behaviors, including 1:1 internal resonance, bifurcation, and chaotic motions, under combined transverse and in-plane excitations. These original findings offer crucial and unprecedented theoretical guidance for the dynamic safety and robust design of low-altitude aerospace structures.