Bolted　joints　are　widely　used　in　mechanical　construction　due　to　their　ease　of　disassembly.　When　the　bolting　member　is　subjected　to　the　alternating　load,　the　pretightening　force　is　gradually　reduced,　which　may　cause　the　interface　contact　performance　to　decrease,　and　the　surface　may　be　microslipped.　Preload　relaxation　of　threaded　fasteners　is　the　main　factor　that　influences　the　joint　failure　under　normal　cyclic　loading,　but　it　is　difficult　to　monitor　the　energy　dissipation　between　the　interface　of　the　bolted　joint.　This　paper　presents　an　energy　dissipation　model　for　the　bolted　joint　based　on　two-degree-of-freedom　vibration　differential　mathematical　model.　The　parameters　of　the　model　is　calculated　by　using　the　fractal　theory　and　differential　operator　method.　The　efficiency　of　the　proposed　model　is　verified　by　experiments.　The　results　show　that　the　experimental　modal　shape　agrees　well　with　the　theoretical　modal　shape.　According　to　the　change　of　cyclic　load　and　vibration　frequency,　the　vibration　response　and　the　law　of　energy　dissipation　under　different　factors　can　be　obtained.　The　results　show　that　the　vibration　frequency　and　cyclic　load　are　the　main　factors　affecting　the　energy　dissipation　between　interfaces.　The　energy　dissipation　of　the　contact　surface　of　the　bolted　joints　account　for　the　main　part　of　the　energy　dissipation　of　the　bolted　structure.　The　results　provide　a　theoretical　basis　for　reducing　the　looseness　of　the　bolt　connection　and　ensuring　the　reliability　of　the　equipment.　©　2021　American　Society　of　Mechanical　Engineers　(ASME).　All　rights　reserved.