In　order　to　overcome　the　deficiencies　of　large　water　consumption　and　insufficient　damping　performance　of　the　traditional　tuned　liquid　damper　(TLD),　a　novel　tuned　liquid　inerter　damper　by　combining　a　rack　and　pinion　inerter　device　with　a　damping　net　and　sloped-bottom　tuned　liquid　damper　(DNS-TLD)　which　is　named　as　damping　net　and　sloped-bottom　tuned　liquid　inerter　damper　(DNS-TLID)　is　proposed.　The　damping　mechanism　of　DNS-TLID　is　analyzed　and　the　solution　formula　about　fundamental　frequency　is　derived,　then　a　mechanical　model　of　the　DNS-TLID-single-degree-of-freedom　(SDOF)　structural　system　is　established.　A　functional　solution　method　for　estimating　equivalent　liquid　motion　velocity　is　presented,　and　a　simplified　calculation　method　of　the　total　equivalent　damping　ratio　of　DNS-TLID　is　proposed.　The　accuracy　of　the　proposed　mechanical　model　and　the　calculation　formula　for　the　total　equivalent　damping　ratio　is　verified　through　the　shaking　table　tests　of　one　single-story　steel　frame　structure.　The　results　from　both　theoretical　analysis　and　experimental　investigation　demonstrate　that　DNS-TLID　can　effectively　achieve　lightweight　vibration　control　and　significantly　enhance　the　damping　performance　of　structures　subjected　to　ground　motions.　Compared　to　other　types　of　TLDs,　DNS-TLID　can　effectively　integrate　the　advantages　of　DNS-TLD　and　the　rack　and　pinion　inerter　device　and　exhibit　superior　performance　and　lightweight　control　effects.　Thus,　as　a　novel　advanced　combination　damper,　DNS-TLID　proves　to　be　highly　applicable　in　engineering　applications.　©　2024　Elsevier　Ltd