S. S. Patil, S.B.Javheri, C.G.Konapure. Main structure

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1 ISSN: ISO 900:008 Ceriied Inernaional Journal o Engineering and Innovaive Technology (IJEIT) Volume, Iue 6, June0 Eecivene o Muliple Tuned Ma Damper S. S. Pail, S.B.Javheri, C.G.Konapure Abrac The eimic wave caued by an earhquake way rucure like E.S.R ank, bridge, building in variou way depending on he requency & direcion o ground moion, and he heigh o he rucure. In order o reduce he way o rucure, i i imporan o place large damper ino heir deign o inerrup he requency. Variou parameer like ma raio, damping raio and ine o rucure are conidered. The objecive o reearch paper i o prove ha, he ue muliple uned ma damper(mtmd) raher han ingle uned ma damper(stmd) can reduce he way o rucure wihin limi. For hi a cae udy o R.C.C. ESR having capaciy o 40m 3 i conidered. Index Term Tuned Ma Damper,Dampin Raio,Sine,Ma Raio,Muliple Tuned Ma Damper, Single Tuned Ma Damper. I. INTRODUCTION The eimic wave caued by an earhquake make rucure o way and ocillae in variou way depending on he requency and direcion o ground moion and heigh o rucure. In order o enhance he rucural eimic perormance, a proper rucure deign i ormulaed engaging variou eimic vibraion conrol echnologie. Tuned ma damper i a claical device coniing o an aborber ma, pring and vicou damper aached o main yem. Today TMD are exenively ued in civil engineering rucure o uppre vibraion due o wind and earhquake orce. A cae udy o ESR waer ank having capaciy 40 m 3 i conidered or he comparaive udy o muliple uned ma damper (MTMD) and ingle uned ma damper (STMD). II. TUNED MASS DAMPER (TMD) A TMD coni o a ma mouned on a rucure via a pring yem and a vicou damper, preerably in a locaion where he rucure delecion are greae. The pring and ma are uned o a o have a naural requency cloe o ha o he primary rucure. When properly uned, he TMD ma ocillae in he oppoie direcion rom he primary rucure. The moion o he ma relaive o he main rucure can be very large when he yem i properly uned and hi provide an opporuniy o diipae a ubanial amoun o energy in he damper linking he ma o he main rucure. The opimum coniguraion o he pring yem will vary depending on he applicaion. The TMD principle alo applie o individual componen prone o vibraion uch a lender column, ru member and ru. The muliple uned damper ma have been propoed abou a decade ago a a beer opion or ingle TMD. The baic coniguraion o MTMD rucure yem comprie a number o TMD aached o he main rucure a hown in he igure. Main rucure Fig Idealized Srucural model o TMD III. THEROTICAL FORMULATION (A) Srucure wih Single Tuned Ma Damper For rucure aached wih STMD (Single uned ma damper).conider a rucure aached wih ingle uned ma damper. Le, m, k, c, and R are he properie o main rucure. Similarly, m,, R, c, are he properie o ingle uned ma damper aached o he rucure. Fig Idealized Srucural model or STMD. Fig 3 Mahemaical model o rucure wih STMD m + c + k x c ( - ) k (x -x ) = F () - () 78

2 ISSN: ISO 900:008 Ceriied Inernaional Journal o Engineering and Innovaive Technology (IJEIT) Volume, Iue 6, June0 m + (c +c ) + (k +k ) x c k x = F = (B) Srucure wih Muliple Tuned Ma Damper Fo e i x = x = x i e i e i () = x i e i = - x e i e i or x = x i = e i x = - x e i Fig 5 Idealized Srucural model or MTMD c = R.c c c = R. (m ) c = R m c = R m = k/m m m = ; = a; = r Fig 6 mahemaical model or rucure wih MTMD m +c +k x (x - x ) k ( )c F (x x 3 )k ( - )c = () x = x = x i e i e i = x i e i = - x e i c = R.c c c = R. (m ) c = R m x = Fig 4 Mahemaical Model or STMD F 0 / m Re x iim (z) Re z - [ k a ][r k(r k-a )+(R k r k a) ] [(r k - a ) + (R k r k a) ] ii m ( ) = (R k r k a) ]) R R + ( k r k R k ) ([(r k - a ) + Where, and ii m (z) are real and imaginary number repecively. We have, x x c = R m = k/m m m = ; = a; = r, = r r r a 4R r a ir r a r a Rr a 4 3 r r a 4 R r a i R r a 4 3 x r a Rra 79

3 Where, Rez ISSN: ISO 900:008 Ceriied Inernaional Journal o Engineering and Innovaive Technology (IJEIT) Volume, Iue 6, June0 Laeral orce = W x (αh)= x r a R r a n mka rk rk a Rkrka k k k k iim z = R m r R a n 5 k k k k rk a Rkrka IV. COMPARATIVE STUDY OF STMD & MTMD A. R.C.C ESR waer ank having ollowing daa. ) Capaciy:-40m 3 ) L.D.L:-.0 3) Free board :-0.3m 4) S.B.C o oil:-5 MT/ m 3 5) Seimic zone: IV = 376 kg Uing concep F = k δ k= F / δ = 3760/0.37 = N/m So he required inormaion i Ma o rucure= kg Sine o rucure= N/m. B Uing ESR rucure aached wih STMD and MTMD ollowing reul are obained. Table 4. (I) For Rd=0.05 Diplacemen in (mm) Ma Raio STMD MTMD Fig 7. Waer Tank (ESR) Elevaion Uing I. S Conider R= Damping o rucure = 5% = 0.05 Laeral diplacemen a op δ = m Period T = π x (0.37/9.8)=.ec Re I.S.893, Fig No 5 wih 5% criical damping Sa/g = 0.09 αh =.0 x.5 x 0.5 x 0.09 = Graph or Rd=0.05 Table 4. (II) For Rd=0.06 Diplacemen in (mm) Ma Raio STMD MTMD

4 ISSN: ISO 900:008 Ceriied Inernaional Journal o Engineering and Innovaive Technology (IJEIT) Volume, Iue 6, June0 Graph 4 or Rd = Table 4. (V) or Rd=0.09 Graph or Rd=0.06 Table 4. (III) or Rd=0.07 Diplacemen in (mm) Ma Raio TMD MTMD Diplacemen in (mm) Ma Raio TMD MTMD Graph 5 or Rd = 0.09 Graph 3 or Rd = 0.07 Table 4. (IV) or Rd=0.08 Diplacemen in (mm) Ma Raio STMD MTMD C. Table or Comparaive Sudy o Diplacemen For Main Srucure and Srucure wih MTMD Table 4.3 (I) or ma raio =0. Damping raio Diplacemen %reducion w.r. or damper due o MTMD in (mm) rucure Rd = Rd = Rd= Rd= Rd=

5 Damping raio or damper ISSN: ISO 900:008 Ceriied Inernaional Journal o Engineering and Innovaive Technology (IJEIT) Volume, Iue 6, June0 V. CONCLUSION Table.4.3 (II) For Ma Raio =0.5 Diplacemen due o MTMD in ( mm) % reducion w.r. rucure Rd = Rd = Rd= Rd= Rd= Damping or damper Table.4.3 (III) For Ma Raio =0.0 raio Diplacemen due o MTMD in mm %reducion w.r. rucure Rd = Rd = Rd= Rd= Rd= Damping or damper raio Table.4.3 (IV) For Ma Raio =0.5 Diplacemen due o MTMD in mm %reducion w.r. rucure Rd = Rd = Rd= Rd= Rd= Damping or damper raio Table.4.3 (V) For Ma Raio =0.30 Diplacemen due o MTMD in mm %reducion w.r. rucure Rd = Rd = Rd= Rd= Rd= The analye o vibraion o an ESR rucure wih TMD Inallaion, which are uned o eleced mode o vibraion, have been udied in hi dieraion. The diplacemen o a rucure wih MTMD were deermined. Thee calculaion were compared wih he diplacemen o he ame rucure wih convenional TMD inalled. From he comparaive reul, i i noiced ha, a ma raio increae rom 0% o 30% repone or diplacemen o he rucure i alo reduced. For Rd = 0.09, MTMD give 37.96% reducion in diplacemen han uing STMD only. (Table 4. V) 3 For he ame ma raio and variaion in damping raio, i ha been oberved ha diplacemen o he rucure reduce uing MTMD. 4 For Rd = 0.09 and ma raio 0.3 give maximum reducion in diplacemen and i i 9.40% when compared wih original rucure. (Table.4.3 V) 5 Hence, rom he comparaive udy i i concluded ha uing MTMD conidering variaion in parameer like change in ma raio, change in ine coeicien o, boh damper and main rucure, we ind ha MTMD i more eecive han STMD. 6 I we increae no o damper more han, he projec co o ESR will increae, o opimum no o damper o be ued. REFERENCES [] Dynamic o rucure by Anil K Chopra. [] Srucural Dynamic by Shrikhande. [3] Dynamic o rucure by Mario Paz I.S [4] Keu Liu, Gianmarc Coppola 8 (February 00) Opimal deign o damped dynamic vibraion aborber or damped primary yem FOR No. 09-CSME-38, E.I.C. Acceion 34. [5] Kangming Xu, Takeru Igua 4 ( JAN 007) Dynamic characeriic o muliple ubrucure wih cloely paced requencie, Earhquake Engineering & Srucural Dynamic Volume, Iue, page , 99. [7] M. Abé e.al 7 (9 DEC 006) Tuned ma damper or rucure wih cloely paced naural requencie Earhquake Engineering & Srucural Dynamic Volume page [8] G. B. Warburon 0 (3 DEC 006) Opimum aborber parameer or variou combinaion repone exciaion parameer or yem Earhquake Engineering & Srucural Dynamic, Volume 8, Iue 3, page 9 36, 980. [9] R. S. Jangid 6 (5 AUG 999) Opimum Muliple Tuned Ma Damper or bae-excied undamped yem Earhquake Engineering & Srucural Dynamic Volume 8, Iue 9, page [0] V.A. Bapa e al 9 (4 July 003) Eec o primary yem damping on he opimum deign o an ununed vicou dynamic vibraion aborber Journal o Sound and Vibraion Volume 63, Iue 4, April 979, Page

6 ISSN: ISO 900:008 Ceriied Inernaional Journal o Engineering and Innovaive Technology (IJEIT) Volume, Iue 6, June0 AUTHOR BIOGRAPHY Pro. S. S. Pail, M.E. (Civil-Srucure), Puruing Ph.D. Head, Civil Engineering Deparmen W.I.T, Solapur (Maharahra) Chairman o ISSE, Solapur cener Reearch wok: Guided more han 0 P.G. uden Involved in variou Teing & conulancy work. Mr. S. B. Javheri, M.E. (Civil-Srucure) A. Proeor in Civil Engineering Deparmen. W.I.T, Solapur (Maharahra) Member ISSE, Solapur Cener. Pro C. G. Konapure, M.E. (Civil-Srucure) P.G. Coordinaor (Civil-Srucure) W.I.T, Solapur (Maharahra) Reearch work: Guiding 4 P.G. uden Member ISSE & IEI Solapur, ACCE Solapur Involved in proo conulancy or ESR & R.C.C. rucure, 83