Particle　dampers　(PD)　are　safe,　economical,　and　effective　energy-dissipation　devices　for　structures.　However,　the　additional　mass　of　PD　must　be　sufficiently　large　to　provide　a　better　damping　effect,　and　the　initial　movement　condition　of　particles　has　a　significant　impact　on　the　damping　effect　of　PD.　In　this　study,　a　particle-inertial　damper　(PID)　is　proposed　to　overcome　these　problems,　and　its　mechanical　model　is　established　with　and　without　considering　particle　collision.　Subsequently,　the　influence　of　particle　rolling　friction　and　particle　collision　on　the　inertial　amplification　capacity　as　well　as　the　dynamic　response　of　a　single　degree　of　freedom　(SDOF)　structure　with　non-collision　and　collision　PID　(SDOF-PID)　are　systematically　analysed.　Finally,　the　control　effects　of　a　PID　and　a　tuned　mass　damper　(TMD)　are　compared　based　on　two　typical　optimisation　methods.　The　results　indicate　that　particle　rolling　friction　has　little　influence　on　the　inertia　amplification　effect　of　a　PID　and　the　displacement　response　of　a　SDOF-PID.　Under　harmonic　excitation,　particle　collision　significantly　affects　the　damping　mechanism　of　a　PID　by　its　equivalent　inertia　coefficient,　equivalent　damping　coefficient,　and　equivalent　stiffness　coefficient.　The　fixed-point　theory　and　‘performance-cost’　theory　can　be　used　to　optimise　the　PID　to　a　certain　extent.　The　damping　effect　of　a　PID　on　the　SDOF　under　the　most　severe　seismic　excitation　is　better　than　that　of　the　PID　under　white　noise　excitation.　With　respect　to　the　decreasing　ratio　of　40~50%,　the　additional　mass　of　the　PID　is　only　one　thousandth　that　of　the　TMD　under　the　same　damping　capacity　demand.　©　2023　by　the　authors.