This　article　explores　the　dynamic　behavior　of　a　two-degree-of　freedom　dry　friction　coupled　vibration　system.　By　constructing　a　generalized　Poincaré　map　and　obtaining　the　necessary　and　sufficient　conditions　for　the　existence　of　invariant　cone　in　the　system,　the　linearization　principle　of　Poincaré　map　is　equivalently　replaced　by　the　study　of　a　global　monodromy　matrix.　Based　on　the　Floquet　theory,　the　stability　of　the　invariant　cone　consists　of　periodic　orbits　is　proved,　and　the　bifurcation　phenomenon　and　persistence　of　the　invariant　cone　under　parameter　changes　are　explored.　The　distribution　configuration　of　the　trajectory　is　given　through　numerical　simulation,　verifying　the　accuracy　of　the　theory.　This　provides　a　theoretical　basis　for　parameter　optimization　and　vibration　control　of　high-dimensional　dry　friction　vibration　systems　in　practical　engineering　applications.　©　2024　Institute　of　Physics　Publishing.　All　rights　reserved.