Multi-particle　dampers　have　a　good　application　prospect　in　the　field　of　civil　engineering　structures　because　of　their　good　damping　efficiency　and　wide　frequency　band.　However,　the　highly　complex　nonlinear　mechanical　properties　and　the　lack　of　a　reasonable　mechanical　model　limit　its　application　and　development　in　practical　engineering.　In　view　of　this,　an　equivalent　single-particle　mechanical　model　with　inerter　was　established　without　considering　the　accumulation　of　particles.　The　introduction　of　inerter　further　considered　the　influence　of　particle　rolling　on　the　damping　mechanism　and　effect.　Then,　the　theoretical　analysis　of　a　single-degree-of-freedom　structure　with　a　multi-particle　damper　was　carried　out.　The　influence　of　inertance　on　the　frequency　response　curve　of　displacement　in　the　non-collision　stage　and　the　steady-state　analytical　solution　of　periodic　collision　after　collision　were　analyzed　emphatically.　Numerical　simulation　and　experimental　research　were　also　carried　out　to　verify　the　correctness　of　the　theoretical　analysis.　The　results　show　that　the　equivalent　model　proposed　can　further　clarify　the　nonlinear　characteristics　of　the　multi-particle　damper　after　considering　the　inerter.　The　inertia　coefficient　has　a　significant　influence　on　the　frequency　response　curve　of　the　controlled　structure　in　the　non-collision　stage　and　the　analytical　solution　(boundary　and　stability)　of　the　periodic　motion　after　collision.　The　steady-state　analytical　solution　of　periodic　motion　provides　a　theoretical　basis　for　further　parameter　influence　analysis　and　for　damping　mechanism　analysis　of　particle　dampers.　Copyright　©2021　Engineering　Mechanics.　All　rights　reserved.