IMPACT VIBRATION ABSORBER OF PENDULUM TYPE

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1 7h Ieaioa DAAAM Baic Cofeece "INDUSTIAL ENGINEEING -4 Ai, Tai, Esoia IMPACT VIBATION ABSOBE OF PENDULUM TYPE Poukoshko, S.; Boyko A.; Kooova, O,; Sokoova, S. & Jevsigejev, V. Absac: I his wok he iac vibaio absobe of eduu ye is eaied. I iss of eduu wih oio iiig sos aached o he vibaig syse. Peduu vibaio absobes ae widey used i acice. The ifuece of eduu aaees o he ossibiiy of suessio of vibaios of he basic syse ude haoic eciaio is discussed i his sudy. Key wods: vibaio, absobe, aiude, eduu, fequecy.. INTODUCTION Vibaio is a eeiive, eiodic o osciaoy esose of echaica syse. Sice os of achies ad sucues udego soe degee of vibaios, egiees have o ide he esus of vibaios i he desigig ocess [ 4 ], [ 8 ]. I is usuay equied o coo he vibaios because i causes faigue ad faiue of he vibaig eees ad discofo fo he eoe. Oe of he os effecive assive coo ehods is addig a iac vibaio absobe IVA o he syse ude eciaio [ ], [ ], [ 5 ]. IVA iss of iac ass which is aced o basic vibaig ass so, ha eiodicay coides wih i. The asfe of oeu o he iac ass fo he ai ass ad dissiaio of eegy i evey iac ovide educio i aiude esose of he ai ass. IVA ae fufied wih oe, wo ad oe degees of feedo; ocooabe ad eguaed; wih uiaea o wih biaea ais. I accodace wih sucua ye iac vibaio absobes ay be sig Fig., foaig Fig. ad edua Fig.. a oue b ie Fig..a-b. Sig iac absobes a sige ui b ui ui Fig..a-b. Foaig iac absobes Fig.. Peduu iac absobes I his wok he iac absobe of eduu ye is eaied. I iss of eduu wih oio iiig sos aached o he vibaig syse. Peduu vibaio absobes ae used i acice fo deceasig of vibaio eve of diffee egieeig sucues: fue ies, eevisio owes, bidges, high-ise buidigs, aeia ass, fo shaf auobaacig ad ohes [ ], [ 6 ], [ 8 ]. The uose of his eseach is o sudy he ifuece of aaees of he eduu

2 o ossibiiy of vibaio suessio of he basic syse ude haoic eciaio, ad he effec of he syse aaees o syse dyaics. This ivoved deeiaio he effec of ass aio, eciaio aiude, ad ceaace bewee iac so was. A eduu wih oe ad wo iacs duig he eiod is ideed. Deedece of suessio abiiy of absobe o eduu egh, coefficie of esiuio a iac, ass aio of he basic syse ad eduu, ad ga size ae foud.. ANALITICAL MODEL OF ABSOBE. Maheaica ode I Fig.4 he odes of sige ad doube iac eduu absobes ae eseed. a sige-iac absobe ode b doube iacs absobe ode Fig.4. Mode of he eduu iac absobe Paaees of syse: ass of he ai body; - ass of he dae; μ / - ass aio; d ihee daig coefficie of he ai syse; k siffess coefficie of ai syse; - coefficie of esiuio of he veociy afe iac; - aua fequecy of he ai syse; ω he fequecy of eduu; - egh of eduu; c size of ga; α - a age fo wo-iacs absobe, a α c / ; The syse is ideed ude haoic eciaio: P P si Ω, P - aiude of eciaio foce; Ω fequecy of eciaio.. The equaios of oio of he syse Usig Lagage s equaios he equaio of oio of he eaied syse is deived: k d si P si Ω S T ; g si S T whee: S - iac iuse, T dea fucio, T eiod of coisios. The seeoechaica heoy of iac is used fo iac iuse defiiio [ 7 ]: S v v whee v ad v - veociy of ai body ad veociy of iaco jus befoe iac. The veociy of iaco iss of asaioa veociy ad eaive veociy: v v v v v, hee he agua veociy is eduu veociy jus befoe iac, T. Takig io accou iac iuse ay be eeseed as: S. 4 Afe eaagee of equaio of syse ad akig io accou 4 syse ay be wie:

3 Ω si ; si si T T T T b ω whee: k, d b, P, g ω.. Aayica souio of he siified equaios of oio Fo he siified vaia of equaios of oio of he syse wihou akig io accou dissiaio ad ieias foces: Ω, si T S T S P k ω 6 whee, wih he of ehod of fiig a aayica souio is foud [ 6 ]. Puey foced vibaios of he syse ad absobe fo a ie doai, Т bewee iacs ude codiios of uig: ΩT; ω Ω fo esoace codiio /μ Ω:, si 4 ~, si 4 si ~ whee he oaios ae as ageed above..4 Nueica souio of equaios of oio I his wok he ueica souio of syse 5 was obaied wih he of Eue ehod usig he kieaics codiios e-iac ad os- iac veociies of ovig bodies if coefficie of esiuio is kow. The veociy of he ai body v ad veociy of iaco v jus afe iac ae: v v. 8 v v. 9 Agoih of Eue s ehod fo he sieiac dae, akig io accou 8,9:, b if if if si si,,,,,, Ω si Eue ehod gives good esus if ie ieva Δ is sa. The equaios of oio ae soved ueicay wih he of Macad oga. The eceived esus eabe o aayze a aaees of oio of he syse. Eaes of he souio of oio ae eseed beow fo sige ad wo-iac absobes.. NUMEICAL EXAMPLE Fo he uea souio e vaue of aaees ae acceed.5, b.,.5. Paaees vaues ae chose fo civi egieeig codiios. The sucue is odeed as sige-degee of feedo 5 7

4 syse, afe addig he eduu absobe i becoes wo feedo degees, he eiig foce is haoic. Paaees of oio of sige-iac absobe ae eseed i Fig. 5 a-e, uiiac absobes - i Fig. 6 a-e, 7a-e. Pos i Fig.5-7: a - disacee of ass, b φφ - oaio age of eduu, c v v - eaive veociy of ass, d vv - veociy of ass, as fucios of ie, e vv - veociy of ass as fucio of ass disacee. a a b φφ b φφ c v v c v v d vv d vv e vv Fig.5.a-e. Pos of deedece of oio aaees o ie ad hase a fo oeiac absobe i case of: Ω.5,.5, ω,75, μ.4, e.6 e vv Fig.6.a-e. Pos of deedece of oio aaees o ie ad hase a fo doube-iac absobe i case of: Ω.5,.5, ω.75, α., μ.4, e.6

5 The absobe wih aaees ω. α. aeas ui-iacs i shows fou iacs duig eiod Fig.7. a b φ φ Fig.8. Maia aiude Aa i eaio o eiig foce fequecy Ω fo diffee uiiacs eduu fequecies ad α, μ.4,.6 c v v d vv Fig.9. Maia aiude Aa i eaio o eiig foce fequecies Ω fo sige iac eduu absobe μ.4,.6 e vv Fig.7.a-e. Pos of deedece of oio aaees o ie ad hase a fo he case of Ω.5,.5, ω., μ.4, α. e.6 Pos of aia aiude A a of ai body i eaio o eiig foce fequecy Ω fo diffee eduu fequeces ω ae eseed i Fig.8-9, os of A a dedig o ass aio μ i Fig., deedig o age α i Fig.. Fig.. Maia aiude Aa deedig o μ aio fo ui-iac absobe ω.75,.6, α.5

6 5. EFEENCES Fig.. Maia aiude Aa deedig o eduu ceaace age α ω.75, μ.4,.6 4. CONCLUSION The diffeeia equaios of oio of he vibaig syse ae deived o he basis of Lagage s equaio of he secod ye. The iacs i he syse ae descibed as iacs of efecy igid bodies akig io accou he coefficie of esiuio. The equaios of oio ae soved ueicay wih he of Macad oga, usig Eue s ehod. Nueica souio aows cacuaig o oy he aaees of oio i he seady-sae ode, bu aso i a asiioa ocess. A aaees of asie oio ad seadysae oio wee defied, esus wee aayzed. Deedeces of aiude of vibaios ae show gahicay o coeaio of he asses, aia of eduu Aiude i he gahs is show aia, isead of aiude of he se oio. Fo a oe-iac absobe, adjused o esoace fequecy, aeuaio abiiy is geae, bu veociy of coisios is gea, ha ca esu i he daage of aeia. I fuue i is ecessay o ake io accou esiie oeies of iac coacs usig he dyaics codiios o add he coac foces i iac coac oi..cheg Jiaia, Hui Xu. Ie ass iac dae fo aeuaig sucue vibaio. Ieaioa Joua of Soids ad Sucues. 6, 4, Issue 7, , C.C., Wag J.Y. Fee vibaio aaysis of a esiie iac dae. Ieaioa Joua of Mechaica Scieces., 45, Chua Sy G., Pacheco B.M., Fujuio Y. ad Io M. Cassica iac dae ad eduu iac dae fo oeia civi egieeig aicaio. Sucua Eg./Eahquake Eg.99,7, No,-. 4.Caece W. de Siva. Vibaio. Fudaea ad Pacice. CC Pess LLC, New-Yok,. 5. Ea S., Maui E. A fudaea sudy o iac daes, Ieaioa Joua of Machie Toos ad Maufacues. 996, 6, Koeev B.G., ezikov L.M. Dyaic vibaio absobe. Nauka, Moscow, 988. i ussia 7. Viba J. Oiisaio ad syesis of vibo-iac ashies. Ziae, iga 988. i ussia 8. Vibaios i egieeig: V.6. Poecio fo vibaios ad iacs. Foov, K.F., edio, Mashiosoeie, Moscow, 995. i ussia 6. COESPONDING AUTHO Sveaa Poukoshko, D. sc.ig., eadig eseache, Egieeig eseach Cee Vesis Uivesiy Coege Addess: Izeieu see, Vesis, LV-6, Lavia, Phoe: E-ai: o.sve@ibo.v