In this paper, the dynamic modeling of functionally graded beams subjected to a mobile mass is studied using modal analyzes. The material properties are assumed to vary continuously in the transverse direction according to an exponential law. A new simple shear deformation beam theory (SFPSDBT) has been formulated and employed in the study, taking into account the effect of the material inhomogeneity and as well the inertia of moving mass. The governing equations are derived using Hamilton's principle combined with a Galerkin weighted residual approach. The forced dynamics are solved by using the implicit Newmark method via the MATLAB program. Detailed analysis is performed to determine the impact of; material properties distribution, charging speed, the inertia of traveling mass, slenderness ratio, and mass weight on the dynamic responses. We can state that the above-mentioned effects should be considered in mathematical modeling, as they play a very important role in the forced vibration of functionally graded beams undergoing mobile mass.