Moving mass-induced transient response of functionally graded and functionally graded graphene nanoplatelet-reinforced composite curved beams via quasi-3D finite element analysis

The transient response of functionally graded (FG) and graphene nanoplatelet-reinforced composite (GPLRC) curved beams under moving mass excitation is investigated using a quasi-3D finite element formulation. Such excitation is relevant to curved structural components carrying travelling vehicles, payloads, or mechanical devices, for which the inertia of the moving body interacts with the structure. The model extends a five-variable shear and normal deformation theory to the moving mass problem and incorporates the associated inertia, Coriolis, and centrifugal effects together with Newmark time integration. Parametric studies are conducted to evaluate the effects of speed ratio, beam curvature, slenderness ratio, material gradation, and graphene reinforcement on the dynamic amplification factor. The moving mass model consistently predicts higher amplification than the moving load idealisation, with differences of 2–5% due to inertia interaction between the travelling mass and the structure. The maximum response occurs when the moving mass travels at approximately half the critical speed. Curvature has a pronounced influence on the response, while increasing slenderness reduces the response. The power-law index significantly affects the response at low values, where rapid changes occur during the material transition. Among reinforcement patterns, the X-type distribution yields the lowest amplification, whereas the O-type produces the highest. These findings clarify the combined effects of beam curvature, material gradation, and moving mass inertia on the transient behaviour of advanced curved composite beams.