Here,　the　phase　formulas　of　a　TMD　control　system　were　derived.　The　effects　of　parameters　on　phase　difference　and　vibration　reduction　result　were　investigated.　Both　the　frequency　band　of　vibration　reduction　and　the　distribution　of　phase　difference　change　with　parameters　were　indicated.　The　results　showed　that　the　comprehensive　optimal　control　effect　of　TMD　is　obtained　with　the　optimal　damping　ratio　and　the　optimal　frequency　ratio;　the　increase　in　mass　ratio　of　TMD　can　improve　both　the　control　performance　and　control　robustness.　In　addition,　the　theory　of　phase　energy　combined　with　the　principle　of　energy　dissipation　was　employed　to　obtain　the　equivalent　damping　ratio　of　TMD.　It　was　shown　that　the　proposed　equivalent　damping　ratio　is　more　reasonable　than　that　deduced　under　the　excitation　of　white　noise.　©,　2015,　Chinese　Vibration　Engineering　Society.　All　right　reserved.