MODE CONTROL SEISMIC DESIGN WITH DYNAMIC MASS

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1 DE NR SEISI DESIGN WIH DYNAI ASS ABSRA : aeh Frhah ad Sh Ihar Aoate Profeor, ollege of See ad eholog, Nho Uvert, oo, Japa Profeor, ollege of See ad eholog, Nho Uvert, oo, Japa Eal: frhah@arh.t.ho-.a.p, har@arh.t.ho-.a.p h paper preet a ew repoe otrol ethod for bldg trtre agat earthqae b ag e of the erta eleet oeted betwee a pot. he deve aed a the da a whh geerate the fore to be proportoal to the aelerato dfferee betwee a pot. I th paper, two top are troded. e of the the ethod whh the atral perod of trtre a be elogated eepg t ode hape. Net top the ethod that a be ade all partpato fator of hgher ode to eept the t ode. It ver ple to ae the table dtrbto of da ae alog heght whh atfed to the above tato. A a relt, repoe hear oeffet of all tore beoe ae, beae the repoe for hgher ode doe ot or. EYWRDS: ode otrol, Repoe otrol, Da a, Se Deg. INRDUIN I geeral, e deg of bldg are perfored b adtg the tffe ad the tregth ad, reet ear, b artfall gvg the dapg. he repoe otrol b ag e of thee ter ea to deg the tffe fator ad the dapg fator the eqato of oto. the other had, there are tde to otrol the repoe b ag ppleetar ae behave aordg to the dplaeet dfferee betwee a pot ]-]. hee repoe otrol ethod g the ppleetar ae de haratert hage of the vbrato te le a dereae effet for grod oto pt et., whh a ot be obtaed b ol otrollg the tffe ad dapg. Rghtl, the dapg eleet ad the tffe eleet eah geerate the fore to be proportoal to the velot dfferee ad the dplaeet dfferee betwee a pot. After the above epreo, the athor ewl defe "the da a" that geerate the fore to be proportoal to the aelerato dfferee betwee a pot. he hgh perforae "da a" to be h greater tha t atal a a be realzed b g the dplaeet aplfato eha h a the rotato eha et. h, we a ga a qte ew repoe otrol ethod. hat, the three a fator of a, dapg ad tffe the eqato of oto a be adted order to atf the egeer target deg perforae. h paper trode two top. e the ethod whh the atral perod of trtre a be elogated eepg t ode hape. Net the ethod that a be ade all partpato fator of hgher ode eept the t ode.. DYNAI SSS Fg. how the oept of the da a whh opoed of the rotato bod wth obed the er wheel ad the oter wheel. Ad a oetrated at the oter wheel. Now, we defe the aplfato rato β whh the rato of the rad of the oter wheel to the er wheel. Whe the er wheel phed the dreto of the taget wth the aelerato, the erta fore of the a of the oter wheel β. Ad the reato fore to ph the er wheel beoe β. A a relt, the a of the oter wheel a dpla the agtde of β at the poto of er wheel whh ea the forato of a aplfato deve. If β large eogh, th eha a be aed a the da a that geerate the fore to be proportoal to the aelerato dfferee betwee a pot. Now, we epre the agtde of da a a (β ) dtto fro the real a of the trtre.

2 Ierta Fore: F β Reato Fore: RβF Aelerato: β a: Aelerato: r r Rotato Aplfato Rato: β r /r er lder bearg eal over lder vo bod grato dapg eal eha bearg ball rew ball aplfato eha bearg haft aal oveet Fgre Rotato Bod Fgre Rotar Dapg be (RD) he pratal deve of da a opoed b a lttle proveet for a vo dapg deve alled "Rotar Dapg be" (RD) whh overt a aal oveet to the grato of the er lder wth a ball rew, ad geerate the retae fore fro the vo bod flled betwee the rotatg er lder ad the fed over lder. he dplaeet of the dreto of the taget of the er lder aplfed to abot to te of aal dplaeet. he effet of the erta a of the rotatg er lder aplfed to the qare of the dplaeet aplfato rato. It beoe, te or ore the a of the er lder. he da a deve wth, to ha bee ade for tral prpoe, ad a eperet wa eeted efll ].. SINGE DEGREE F FREED SYSE WIH DYNAI ASS oder the gle degree of freedo vbrato te that the above-etoed rotato bod blt to how Fgre (a), or the gle degree of freedo vbrato te that ha the da a how Fgre (b). he eqato of oto gve b Eq..,. ad. below: ( ) γ γ : Rato of Da a Fgre (a) Sgle Degree of Freedo Vbrato Fgre (b) Sgle Degree of Freedo Vbrato Ste wth Rotato Bod Ste wth Da a (Hereafter, da a how b.) whh, ( ) (.) ( ) ( ) (.) h (.) h, ( ) Fro Eq.., t dertood that da a de the followg haratert hage to te. () Elogato of the atral perod, () Dereae of dapg effet () Dereae effet for aelerato of grod oto. oderg Eq.., ae of ad, the abolte aelerato A beoe Eq.. that ot. h ea that the grod oto aelerato tratted throgh the da a. A a relt, t appear aother vbrato ode that repreet "aelerato tratted dretl throgh the da a". However, th effet doet beoe vble at the left de of Eq... A ( ) (.)

3 I order to learl pef the effet of da a, the eqato of oto for two-a te, whh a d a a be added to oe-a te a how Fgre, gve b Eq.. a follow: (.) whh, d a, a fro the grod, <<. <<, d prg otat, >>, dplaeet of d γ h << >> Fgre Addto of D a oderg the egevale proble of the left de of Eq.. der the odto wth dregard of the vo dapg ter, the egevale, the egevetor { }, the partpato fator β ad the partpato vetor β {} are the followg., (.), (.) β { } [ ]{ } { } [ ]{ }, { } [ ]{ } { } { } β (.) β { }, β { } (.9) Now, the bol defed a the dereae effet of pt. he t ode "the ode of the repoe to the dereaed pt" ad the d ode "the ode of the aelerato that at dretl throgh da a".. W DEGREE F FREED SYSE WIH DYNAI ASS Fgre -a Ste wth Da a he eqato of oto for two-a te wth the da a how Fgre epreed a two-a te of Eq.. ad a three-a te wth a d a of Eq... I the epreo of two-a te Eq.., a pt de vetor at the rght de of the eqato beoe {}. Eah eleet of {} a vale of or le. he t ode ad the d ode are the ode of the repoe to the dereaed pt. I the other epreo of three-a te Eq.., the vetor { }, ad t ha the rd ode of the rgd bod whh dretl trat the aelerato of grod oto the rato of the ode hape throgh the da a deve. [ ]{ } [ ]{} [ ]{ } [ ]{ } (.)

4 whh,,, {} { }, ordar a atr, da a atr, { } {} { } { } (.) whh, ordar a atr, da a atr,, <<, >>. RESPNSE NR F W DEGREE F FREED SYSE WIH DYNAI ASS here are oe effetve e of the da a for the repoe otrol of the trtre agat earthqae... Repoe otrol hagg Egevale wthot hagg Egevetor he atral perod a be elogated wthot hagg egevetor b addg the da a proportoal to the tffe of eah tor of the vbrato te. Ag the followg egevale proble fro Eq.., add { } to the both de of the eqato. { } { } { } { } { } { } ( ){ } ( ){ } ( ) ( ){ } { } ( ){ } { } (.) whh, da a atr hage egevale to ( ) Whe the da a added to the te, the egevale hage fro to wthot hagg egevetor... Repoe otrol Adtg Partpato Fator of d ode to he partpato fator of the d ode a be adted to b operatg egevetor b addg the da a. If the t egevetor of Eq.. { }, the d partpato fator how b Eq.. beoe beae of the orthogoalt betwee the egevetor. Ad the repoe of the d ode dappear. { } { } { } { } β (.) he reqred odto to eep th tato a be olved a how below.,,

5 (.) whh, the vale of arbtrar, ldg. I th odto, the egevetor of the t ode { }, ad the partpato fator of the d ode. he egevale proble of the t ode gve b Eq... { } { } (.) Fro Eq.., oderg {} { }, the followg relato are obtaed. (.) ( ) (.) hat, whe the d partpato fator b addg the proper obato of the da a, the t egevale Eq... Ad fro Eq.., repoe hear oeffet of t ad d tore are the ae vale.. UI DEGREE F FREED SYSE WIH DYNAI ASS Fgre -a Ste wth Da a he eqato of oto of -a te wth da a how Fgre gve b Eq... he dfferee betwee Eq.. ad a ovetoal eqato of oto, the vetor of the rght de ot { } bt {}. Eah eleet of {} a vale of or le. h date the dereae effet of the pt. { } { } { } { } (.) whh,, {} { } ordar a atr,

6 da a atr, he eqato of oto of -a te wth the da a alo epreed a ()-a te wth a d a. I th epreo of ()-a te, the vetor of the rght de {}, ad t ha the ()th ode of the rgd bod. {} {} {} { } (.) whh, <<, >> ordar a atr, da a atr.. RESPNSE NR F UI DEGREE F FREED SYSE WIH DYNAI ASS A well a the ae of two-a te, there are oe effetve e of the da a for the repoe otrol of the trtre to earthqae... Repoe otrol hagg Egevale wthot hagg Egevetor he atral perod a be elogated wthot hagg egevetor b addg the da a proportoal to the tffe of eah level of the vbrato te. he proof ae a the prevo ae... Repoe otrol Adtg Partpato Fator eept the t ode to he partpato fator of fro d to -th ode a be adted to b operatg egevetor b addg a erta obato of the da a. he obato of the da a a be evalated eal b the followg proedre. he detaled proedre a be fod the referee ]-]. ( ) (.),,,,

7 { } { } { } D ( ) ( D ) ( ) D.. Eaple of Repoe otrol wth Da a able how the proe ad the relt of obtag the obato of the da a that adt the partpato fator of all hgher ode of the eaple vbrato te to. able how the relt of the egevale aal of the vbrato te wth the da a. he partpato fator of d to th ode are. he 9th ode of rgd bod (.e., ) appear, ad t ha the phal eag of trat of the aelerato related to the grod oto. Fgre how oparo of te htor repoe aal relt of the orgal te ad the otrolled te. he pt earthqae oto El etro 9 NS (A a. / ). he dapg aged h. for the frt ode proporto to the tffe of the orgal te. B addg the da a, the frt perod elogated fro. [e] to. [e]. he dapg fator of the t ode ha dereaed fro h. to h.. A a relt of ode otrol, the repoe of the hgher ode dappear. Repoe aelerato dereae. Repoe hear oeffet of all tore are the ae. It how the qe ad effetve repoe otrol. able... Evalato of Da a (to) (N/) Σ (to) Σ(/ Σ ) - D (to)., ,, ,, ,..,,..9...,. 9. 9,,..9...,.. 9,,.....,9.. 9,,....., ,, , able Egevale Aal of otrolled Ste t d rd th th th th th 9th β A.(/e ) Daa rgal Ste otrolled Ste (Stffe Fore) otrolled Ste (Stffe,Dapg ad Ierta Fore) Dp.()..... Shear(N) Shear oeffet Drft()...( N ) Fgre oparo of a Repoe

8 . DE VIBRAIN EXPERIEN A -tor odel vbrato eperet that ofr the effet of the ode otrol effet b the da a wa eeted. Fgre how the otle of the vbrato odel. Partpato fator of all hgher ode are adted to b addg the da a. A a relt of the e wave etato eperet, the reoae of hgher ode lot ad the repoe ol of the t ode reaed. Fgre 9 how the oparo of the abolte aelerato aplfato rato of eah a pot betwee the orgal te ad the otrolled te. he abolte aelerato aplfato rato of eah a pot of the otrolled te agree wth the allated vale ver well. a Pot Da a a Pot Da a a Pot Da a a Pot (g) (N/) (g).,9..,9. Aplfato Rato apot apot apot apot apot apot apot apot Da a.,9 9..,9. Freqe(Hz) rgal Ste Freqe(Hz) otrolled Ste Fgre tle of Vbrato odel Fgre 9 Aplfato Rato of Abolte Aelerato 9. NUSINS he da a defed a a eleet betwee a pot of vbrato te that geerate the fore to be proportoal to the aelerato dfferee betwee a pot. Sh a eleet a be pt to pratal e wth a erta a aplfato deve that e a dplaeet aplfato eha. Da a efl to otrol repoe of trtre. he haratert hage are ded to the vbrato te, h a the elogato of the atral perod, the dapg dereae, ad the pt dereae. B adtg the vale of the da a of the eah tor, the atral perod a be haged wthot hagg the egevetor of the lt degree vbrato te ad the partpato fator of a hgher ode a be adted to. Epeall, the obato of the da a a be evalated eal, that ae all partpato vetor of hgher ode zero eept the t ode. REFERENES ] awaata, S., et al. (9), "otrol of Strtral Vbrato b Ierta Pp Daper Part(), Part()", Sare of ehal Paper of Aal eetg, Arhtetral Ittte of Japa, Agt 9, - ] ra, A. (), "Vbrato Iterepto oeto eha", Waeda Uv. See eholog Seed, N. -, arh ] Ihar, S. (99), "tle of Repoe otrol of Strtre agat Earthqae, Deg eha ad otrol Da of Bldg Strtre", Arhtetral Ittte of Japa, Noveber 99, 99- ] Naaa, S., et al. (), "Developet of Vo Dapg Deve wth Ierta a Eleet", REPRS F EHNIA RESERH INSIUE F SUI ISUI NSRUIN., D. No., Septeber ] Frhah,. ad Ihar, S. (), "ode olato b ertal a, Std o repoe otrol b ertal a o.," Joral of Strtral ad otrto Egeerg, Arhtetral Ittte of Japa, Febrar, - ] Frhah,. ad Ihar, S. (), "Repoe otrol of lt-degree te b ertal a, Std o repoe otrol b ertal a o.," Joral of Strtral ad otrto Egeerg, Arhtetral Ittte of Japa, arh, -9 ] Sa,., taa, Y., Frhah,. ad Ihar, S. (), "Std o haratert of SDF te repoe wth Iter-tor Iertal a Part, Part ad Part ", Sare of ehal Paper of Aal eetg, Arhtetral Ittte of Japa, Agt, B-, -