Low-frequency　excitation　is　often　challenging　to　fully　absorb　through　internal　energy　dissipation　systems,　while　grounding　damping　can　effectively　leverage　the　stability　of　the　ground　to　absorb　low-frequency　energy,　thereby　mitigating　the　effects　of　low-frequency　excitation　on　the　primary　structure.　In　this　paper,　the　response　mechanism　of　a　grounded　damping　nonlinear　energy　sink　(GNES)　is　investigated　based　on　the　complexification-averaging　and　multi-scale　method.　Furthermore,　the　impact　of　external　excitation　amplitude　on　the　amplitude　frequency　curves　is　analyzed　under　two　different　primary　system　damping　ratios,　and　the　frequency　threshold　at　which　the　GNES　exhibits　damping　effect　is　identified.　Besides,　the　vibration　suppression　region　within　the　two-dimensional　parameter　space　is　partitioned　into　four　distinct　zones:　the　invalid　region,　saddle-node　bifurcation　region,　effective　damping　region,　and　deterioration　region.　An　in-depth　analysis　is　conducted　on　the　effects　of　varying　system　parameters　on　the　damping　region.　Compared　to　the　classical　NES　model,　the　numerical　simulation　results　indicate　that　GNES　achieves　superior　vibration　reduction　over　a　broader　range　of　excitation　frequencies.　This　finding　holds　substantial　significance　in　enhancing　the　applicability　of　NES　in　broadband　excitation　environments.