Additional　damping　ratio　(ADR)　is　an　important　performance　parameter　in　the　design　of　energy　dissipation　system.　The　ratio　of　the　hysteretic　energy　dissipation　of　the　damper　to　the　total　strain　energy　of　the　damping　system　is　used　as　the　quantitative　ADR　in　the　traditional　method,　and　the　bi-linear　model　is　usually　used　to　calculate　the　hysteretic　energy　dissipation　of　the　buckling-restrained　brace　(BRB).　The　accuracy　of　the　above　calculation　methods　is　low.　The　explicit　analytical　expression　of　the　hysteretic　energy　of　Bouc-Wen　model　which　can　accurately　characterize　the　hysteretic　performance　of　the　damper　is　derived　by　integral　method,　and　time-varying　ADR　calculation　methods　based　on　the　strain　energy　method　and　the　modal　damping　energy　dissipation　method　are　proposed.　In　order　to　accurately　achieve　the　damping　ratio　of　the　damping　system,　the　inter-story　displacement　angle　and　damping　ratio　of　the　damping　system　are　taken　as　the　control　objectives,　and　the　layout　scheme　and　damping　force　of　the　damper　are　taken　as　the　design　variables.　The　design　method　of　damping　ratio-displacement　double　objective　is　proposed.　The　iterative　design　and　analysis　of　a　RC　frame　damping　system　are　carried　out.　The　reasonable　length　of　time　interval　for　calculating　time-varying　hysteretic　energy　is　determined,　and　different　calculation　methods　of　time-varying　ADR　are　compared.　The　results　show　that　the　ADR　based　on　the　strain　energy　method　is　larger,　which　is　not　conducive　to　the　structural　safety.　It　is　suggested　to　use　the　average　value　of　modal　damping　energy　dissipation　method　to　characterize　ADR.　The　double　objective　design　method　is　reasonable,　and　the　performance　requirements　are　more　detailed　and　accurate.　©　2022,　Editorial　Board　of　Journal　of　Vibration　Engineering.　All　right　reserved.