The　dynamic　vibration　absorber　(DVA)　is　widely　used　in　engineering　models　with　complex　vibration　modes.　The　research　on　the　stability　and　periodic　motions　of　the　DVA　model　plays　an　important　role　in　revealing　its　complex　vibration　modes　and　energy　transfer.　The　aim　of　this　paper　is　to　study　the　stability　and　periodic　motions　of　a　two-degrees-of-freedom　system　coupled　with　an　encapsulated　nonsmooth　dynamic　vibration　absorber　under　low-frequency　forced　excitation.　Based　on　the　slow-fast　method,　the　model　is　transformed　into　a　six-dimensional　piecewise　smooth　system　coupling　two　time　scales.　The　existence　and　stability　of　the　admissible　equilibrium　points　for　the　model　are　discussed　under　different　parameter　conditions.　Based　on　the　first　integrals,　the　Melnikov　vector　function　of　the　nonsmooth　dynamic　vibration　absorber　model　is　calculated.　The　existence　and　number　of　periodic　orbits　bifurcated　from　a　family　of　periodic　orbits　under　different　parameters　are　discussed.　The　phase　diagram　configuration　of　periodic　orbits　is　given　based　on　numerical　simulation.　The　results　obtained　in　this　paper　offer　a　new　perspective　for　vibration　analysis　and　parameter　control　for　nonsmooth　dynamic　vibration　absorbers.