Particle　damping　(PD)　technology　has　a　remarkable　effect　in　reducing　vibration　and　noise　for　high　frequency　vibration　such　as　mechanical　analysis　and　aviation,　and　has　been　widely　applied　in　some　engineering　practices.　However,　in　the　field　of　low　frequency　and　low　amplitude　vibration　control　for　building　structures,　the　research　and　application　of　particle　damper　technology　is　still　in　the　preliminary　stage.　The　deficiencies　and　problems　mainly　include　the　mechanical　model　of　PD　is　not　perfect　enough　and　the　mechanism　of　vibration　reduction　is　not　clear　enough.　In　the　light　of　the　shortcomings　of　the　existing　theoretical　model　of　the　PD,　a　mechanical　model　of　the　PD　with　friction　effect　between　the　particle　and　the　structure　is　proposed,　and　the　analytical　solution　of　the　displacement　response　for　the　mechanical　model　subjected　to　harmonic　excitation　is　obtained.　The　model　can　fully　represent　the　collision　and　non-collision　process　of　PD,　and　the　phase　trajectories　can　embody　the　complex　nonlinear　characteristics　of　PD.　The　theoretical　and　motion　characteristics　of　the　PD　are　verified　by　the　electromagnetic　shaking　table　test　of　a　single-story　steel　frame　with　PD,　which　proves　the　rationality　of　the　theoretical　model　and　the　correctness　of　the　analytical　results,　as　well　as　the　necessity　of　considering　the　friction　effect.　The　parameters　of　mass　ratio,　excitation　amplitude,　excitation　frequency　and　motion　gap　are　further　analyzed,　so　the　mechanism　of　vibration　reduction　is　clearer.　Finally,　compared　with　the　traditional　model　of　impact　damper,　it　is　obvious　that　the　mechanical　model　of　PD　with　friction　effect　can　more　reasonably　evaluate　the　damping　performance　in　practical　engineering.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.