With　the　aim　of　characterizing　the　forces　and　movement　of　a　bolted　structure　under　axial　loading,　a　two-degree-of-freedom　energy　dissipation　model　is　proposed.　The　model　is　based　on　forced　vibrations　of　a　two-degree-of-freedom　bolted　structure.　The　finite　element　method　and　fractal　theory　were　combined　to　analyze　the　contact　surface　strains　and　pressure　changes　and　to　calculate　an　analytical　solution　for　energy　dissipation.　Parameters　of　the　model,　such　as　the　damping　ratio,　load,　preload,　and　loading　frequency,　were　varied,　and　numerical　simulations　were　performed　in　MATLAB　to　determine　the　influence　of　the　parameters　on　energy　dissipation.　Increasing　the　load　results　in　greater　energy　dissipation,　while　reducing　the　pre-tightening　force　first　slowly　increases　the　energy　dissipation　followed　by　a　more　rapid　increase.　As　the　loading　frequency　increases,　energy　dissipation　at　the　interfaces　gradually　increases.　Moreover,　higher　vibration　frequencies　lead　to　increased　energy　dissipation,　suggesting　that　loading　frequency　is　the　main　parameter　affecting　bolt　relaxation.　In　addition,　increasing　the　damping　ratio　does　not　significantly　increase　energy　dissipation,　therefore,　damping　ratio　is　not　a　key　factor　in　energy　dissipation.　©　2019,　Computers　and　Industrial　Engineering.　All　rights　reserved.