Abstract:　Here,　a　TID　was　adopted　for　aseismic　control　of　structures.　The　analytical　formulas　of　optimal　damping　parameters　and　optimal　stiffness　ones　for　a　single　DOF　structure　with　TID　and　a　multi-DOF　structure　with　TID　subjected　to　ground　white　noise　excitation　were　deduced,　and　the　corresponding　aseismic　effects　and　application　in　multi-DOF　systems　were　presented.　The　results　showed　that　the　optimal　parameters＇　analytical　formulas　keep　higher　accuracy　when　the　structure　damping　is　considered,　the　smaller　the　structural　damping　ratio,　the　smaller　their　errors　and　the　higher　their　accuracy,　the　aseismic　effect　of　TID　is　more　obvious;　if　the　damping　ratio　of　a　structure　is　larger,　the　larger　mass　ratio　can　be　adopted　to　improve　its　vibration　reduction　effect;　under　random　seismic　excitations,　although　the　damping　ratio　of　vibration　isolation　layer　is　smaller　than　that　of　a　common　vibration　isolation　structure,　after　installed　with　TID　or　TMD,　it　is　possible　for　a　structure　to　get　better　vibration　reduction　effect;　compared　with　TMD,　it　is　better　for　TID　to　be　installed　at　bottom　of　a　structure　and　get　the　better　effect,　but　in　case　of　the　same　mass　ratio,　TID＇s　effect　on　structure＇s　top　layer　response　is　poorer;　considering　the　mass　amplification　effect　of　TID,　it　can　be　improved　until　its　aseismic　effect　exceeds　TMD＇s,　TID　can　be　made　with　a　rod＇s　shape　for　easy　installation.　©　2018,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.