This study investigates harvesting energy from systems made of Functionally Graded Magneto-Electro-Elastic Materials (FGMEEM) undergoing impact acceleration. Using the Ritz method together with the Euler-Bernoulli beam theory, the reduced governing equations of motion associated with the system are obtained. Subsequently, neglecting the effect of the terms related to the magneto-electro-elastic layer and leading the gradient index to infinity, the presented results are compared and verified by those available in the literature. Then, using the mass-spring shock spectrum diagram, the influence of shock duration on the amounts of harvested power is investigated and the optimal duration is determined. The results indicate that although employing the shock spectrum diagram associated with a mass-spring system can predict the optimal duration with relatively good accuracy, to have more accurate results, one should hire the shock spectrum diagram associated with the harvested power. Finally, a parametric study is also conducted to investigate the effect of the gradient index on the maximum amount of voltages and powers that can be scavenged from the environment. The results indicate that increasing the gradient index by reducing the volume fraction of the magneto-electro-elastic material in the electric energy generator layer makes a decrease in the harvested power.