On the performance of gyro-mass devices for displacement

Transcription

1 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online On te perforane of yro-a devie for diplaeent itiation in bae iolation yte Maato Saito * Gradate Sool of Siene and Enineerin, Saitaa Univerity 55 Sio-Okbo, Sakra-K, Saitaa, Japan Tel.: E-ail addre: aity@ail.aitaa-.a.jp Abtrat Ti tdy preent te perforane of a o-alled "yro-a" provided for itiatin diplaeent of bae iolation yte. Te yro-a enerate a reation fore de to te relative aeleration of te node between wi it i plaed. Ti tdy aee tree type of yte inorporatin a yro-a, in te freqeny doain and in te tie doain. Nerial tdie wit vario type of eartqake wave ow tat, alto te yte tend to rede te lateral diplaeent, tey till enerate lare diplaeent wen bjeted to an oberved eartqake wave ontainin lon-period oponent, exept a yte propoed in ti tdy. Te yro-a devie in te propoed yte i opoed of two nit arraned in erie: one nit onit of a yro-a and daper arraned in parallel; and te oter nit onit of a prin and daper arraned in parallel. It i fond tat te daper arraned in parallel wit te yroa a a lare effet on dereain te lateral diplaeent of te yte wen bjeted to lon-period eartqake wave. Ti tdy preent loed-for forlae derived baed on idealized iple odel of te bae iolation yte inorporatin yro-ae. Moreover, atrix expreion of te odel are alo preented for etiatin te tie itory of repone in te yte. I

2 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online INTRODUCTION Bae iolation yte are ed to protet objet fro daae de to eii otion propaatin fro te rond or floor on wi tey are pported. S objet rane fro lare-ale trtre, a bildin and oe, to aller trtre, a fine-art exibit, ritial opter yte, and frnitre. In te lat few deade, a nber of idea for bae iolation yte ave been propoed and applied in pratie [ee, for exaple, Kelly 986]. Slidin bearin [Contantino et al. 99, Naarajaia et al. 99, 99, 993a, 993b, and 993], lainated rbber bearin [Kelly 987, Yoo and Ki ], i-dapin rbber bearin [Dera and Kelly 985, Tai et al. 3], or lead-filled rbber bearin [Robinon 98] are often ed in bae iolation yte, epeially for i- or iddle-rie bildin, werea roller and perial bearin are typially ed for oe and oter all-ale objet. It a been fond in previo analytial and field tdie tat tee bearin an inifiantly rede te repone aeleration of te objet. It a been reonized, owever, tat tee bearin enerate naeptably lare lateral diplaeent de to teir low tiffnee [Dileli 7, Janid and Kelly ]. Te lare diplaeent ay retrit te appliability of te bae iolation yte ine a lare learane t be provided arond te iolated objet, wi i an iportant onideration in liited pae. Moreover, te orrene of eartqake wave ontainin lon-period oponent a been foed on a an iportant eii loadin in te eartqake enineerin field reently [Aria et al. 6]. It wa reported tat, in te 3 Tokai-oki eartqake, oil torae tank loated at Toakoai ity, Japan, wi i abot k ditane fro te epienter, tronly oillated beae of loin of te liqid tey ontained de to te eartqake wave (te reonant period of te loin ode rane fro five eond to ten eond in eneral) [e.., Zaa 4]. It wa fond tat an oberved eartqake wave reorded at No. HKD9/K-NET tation loated in te ity ontained lon-period oponent. Te veloity repone petr of te eartqake wave owed it peak ranin fro for eond to ten eond; te axi appeared arond even eond. Ti iplie tat te bae iolation yte old reonate de to lon-period eartqake wave, ain extreely lare diplaeent of te yte to or. Aria et al. 6] predited tat bae iolation yte ay reonate in te ae were te rond otion a a lare intenity of veloity repone petra wit a broad band in te lon natral period rane. It i alo expeted tat bae iolation oponent a bearin wold be detroyed by naeptably lare diplaeent. Yan et al. 99 propoed an aeii ybrid ontrol yte tat obine rbber bearin and a paive/ative tned-a daper to rede te diplaeent. Tai 995 perfored advaned nerial analye of te effet of vario type of eartqake otion on II

3 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online lti-tory bildin by ean of a ybrid ontrol yte. Te relt of tee nerial analye owed a ffiient dereae in te diplaeent of bae iolation yte inldin a paive/ative tned-a daper. Te relt alo indiated tat a redtion of te diplaeent enerally reqire a lare diplaeent of te a daper, probably larer tan te axi periible diplaeent aplitde of te bae iolation yte, ine te tned-a daper t deal wit bae-iolated bildin avin an extreely lon fndaental period. Fro te viewpoint of pratial appliation, terefore, te above aeii ybrid ontrol yte ee to be appliable only to lare-ale trtre tat allow lare diplaeent of te a daper, werea applyin ti yte to all-ale objet, a oe, fine-art exibit, and frnitre, ay be diffilt de to te liited pae available. In reent year, te nber of patent appliation for redin te lateral diplaeent of bae iolation yte by inorporatin a yro-a a been inreain. Te yro-a enerate a reation fore de to te relative aeleration of te node between wi it i plaed. Te priary effet of te yro-a i to inreae te inertia of te iolated objet o tat te lateral diplaeent i retrited. Fro a pratial point of view, te advantae of te e of te yro-a devie i tat it an be inorporated into te onventional bae iolation yte witot any of te ontrol yte deribed above. Moreover, a deribed later, te yro-a an be ontrted by a opat eanial yte tat i eay to inorporate into te onventional bae iolation yte. Vario type of yro-a devie ave been propoed, inldin a devie opoed of a yro-a arraned in parallel wit a prin and a daper [e.., Okra 997, Katara et al. ]; and a devie opoed of a yro-a arraned in erie wit a nit avin a prin and a daper, wi are arraned in parallel [e.., Katara et al. 999, Saito 7]. In addition, tere i a ertain type of vio daper in wi an intrini rotary a bidiary beave a a yro-a [Saito et al. 4]. S a daper i ateorized a te forer devie wit a i dapin fntion. However, tere ave been few invetiation into differene in te perforane of tee yte, epeially wen bjeted to atally oberved eartqake wave, inldin a lon-period eartqake wave. Aordinly, te objetive of ti tdy are: () to derive loed-for forlae of te bae iolation yte wit tree type of yro-a devie opoed of a yro-a and prin/daper eleent, inldin a propoed odel tat i odified to rede lateral diplaeent de to lon-period eartqake wave; () to ow te reonant arateriti of te bae iolation yte in te freqeny doain; and (3) to ow te tie-itory repone wen bjeted to ilated eartqake, baed on atally oberved eartqake reord. GYRO-MASS DEVICE III

4 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online A yro-a i a eanial yte tat enerate a reation fore de to te relative aeleration of te node between wi te yro-a i plaed, a own in Fi. (a). Te yro-a onit of a rotatin dik and a rod attaed to te dik wit tron frition, ear for intane. Te dik rotate wit rotational aeleration a an external fore F i iven to te rod. Te relative aeleration of te rod & & wit repet to te fixed node at te top of te fire i eoetrially related to te rotational aeleration & θ. Coneqently, te followin relation between te external fore F and te relative aeleration & & an be obtained: were F = & () J. () r Here, r i te ditane fro te enter of te dik to te point were te rod i attaed to te dik; J i te oent of inertia of te dik; and i te eqivalent a enerated by te rotation of te dik. T, te reation fore at te left and ide of te rod i idential to te prodt of te eqivalent a and te relative aeleration & &. Te eqivalent a an be eaily inreaed by ean of te followin onventional teniqe ed in eanial enineerin: () inreain te radi of yration of te dik by onentratin te a at te ede of te dik; or () inreain te rotational aeleration of te dik by a obination of dik ear, a own in Fi. (b). In te latter ae, te eqivalent a an be expreed a follow: n r n J n r n = = (3) r Here, r i te radi of te dik ear woe enter of rotation i opatible wit te dik a own in Fi. (b); n and n are te nber of teet in te dik ear denoted in Fi. (b), repetively; and i te a weit of te dik, were it i aed tat te dik i olid and a a irlar ape a J = r i ed in Eq. 3. Fi. () ow a prototype eanial yte of te yro-a onitin of a rotatin dik and dik ear, were r r = 5, n, = IV

5 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online and n 8. In ti yte, terefore, te eqivalent a an be inreaed tie a = lare a te a weit of te dik. Terefore, an extreely lare eqivalent a an be proded wit a all dik a in a opat pae. FREQUENCY-DOMAIN CHARACTERISTICS OF BASE ISOLATION SYSTEM WITH GYRO-MASS DEVICE Bai Model Te priary effet of te yro-a i to inreae te inertia of te bae-iolated objet in a partilar diretion. A onventional bae iolation yte i repreented by te idealized odel own in Fi. (a). Te iolation yte a lateral tiffne k and dapin. In ti tdy, te bae-iolated objet i aed to be a lped a. Ti aption a freqently been ed in reent tdie [e.. Ryan and Copra 4, Frkawa et al. 5] for repreentin te fndaental riid body ode of a bae iolation yte in eartqake vibration. Te diplaeent of te lped a relative to te bae i denoted a. On te oter and, a bae iolation yte inorporatin a yro-a i own in Fi. (b). Te yro-a a te eqivalent a. Te repone of ti bae iolation yte wen exited by rond aeleration & & i overned by te followin eqation: ( & && ) & k & = &. (4) Eq. 4 an be rewritten a follow: & & = & (5) were te natral irlar freqeny of te bae iolation yte i = k ( ) V ; te

6 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online VI dapin ontant of te yte i ( ) k = ; and te a ratio i ( ) =. Wen a aroni exitation i aed, Eq. 5 an be rewritten a follow: i = (6) were te exitation irlar freqeny i ( ) f π =. An eqation orrepondin to Eq. 5 in te ae of te onventional bae iolation yte witot te yro-a an be expreed a follow: & & & & & = (7) were te natral irlar freqeny of te bae iolation yte i k = ; and te dapin ontant of te yte i k =. Wen a aroni exitation i aed, Eq. 7 an alo be rewritten a follow: i =. (8)

7 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online It i fond tat te natral freqeny of te bae iolation yte inorporatin te yroa i aller tan tat of te bae iolation yte witot te yro-a. Moreover, it old be noted tat te aplitde of te eii exitation aoiated wit te rit and ide of Eq. 5 dereae aordin to te dereae in te a ratio a te eqivalent a of te yroa inreae. Coneqently, te relative diplaeent beoe all, a own in Eq. 6, aordin to te inreae in te eqivalent a. Te above arateriti are te fndaental effet of te yro-a pon te bae iolation yte. Fi. 3(a) ow te anifiation ratio of te relative diplaeent wit repet to te rond diplaeent a fntion of te freqeny f and te paraeter. Fi. 3(b) alo ow te anifiation ratio of te repone aeleration ( & & ) wit repet to te rond aeleration & &. In tee analye, a dapin ontant =. and a natral freqeny ( = π ) =. 5 f Hz were aed. Te oter paraeter in Eq. 5 an be related to tee propertie a follow: = (9a) =. (9b) Fi. 3(a) and 3(b) ow te preene of a loal axi aoiated wit te reonane of te bae iolation yte. Fi. 3(a) ow tat te relative diplaeent inifiantly dereae a te a ratio dereae. In addition, te reonant freqeny ift toward lower freqenie a te a ratio dereae. It i oneivable, terefore, tat te yro-a i effetive not only for redin te relative diplaeent, bt alo for akin te fndaental period of te bae iolation yte loner tan te onventional one. Te latter an eaily be predited fro Eq. 9(a). On te oter and, Fi. 3(b) ow tat te repone aeleration ( & & ) dereae aordin to te dereae in te a ratio at te reonant freqeny. In ontrat, te aeleration radally inreae a te a ratio dereae beyond te reonant freqeny. In priniple, te inreae of te aeleration at i freqenie i onidered to be inappropriate for a bae iolation yte. Coneqently, it i fond tat, alto te bae iolation yte wit te VII

8 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online yro-a ay rede te relative diplaeent, e of te yro-a ay interfere wit te bae iolation fntion. Model I Baed on te above relt, it wa ten attepted to retrit te inreae of te repone aeleration at ier freqenie wile alo dereain te relative diplaeent by ean of te yro-a. Fi. () ow a bae iolation yte wit a yro-a devie opoed of a yroa arraned in erie wit a nit avin a prin and a daper, wi are arraned in parallel. Ti type of odified odel a alo been fond in pratie a well a te Bai Model. Ti prin/daper nit ay rede te effet of te yro-a at ier freqenie were te effet of te bae iolation old be enaned. Te reaon for ti i tat te dynai tiffne of te yro-a enerally beoe larer tan tat of te prin/daper nit at ier freqenie ine te dynai tiffne of te yro-a i proportional to te qare of te freqeny. At ier freqenie, terefore, te diplaeent of te yro-a devie i ainly enerated by te prin/daper nit, and t, te arateriti of ti nit tronly inflene te bae iolation yte. Wen a teady-tate exitation wit irlar freqeny i aed, te dynai tiffne of te yro-a devie, K, opoed of te yro-a and te prin/daper nit an be expreed by te followin eqation: K = ( i k ) i k () were and k are te dapin oeffiient and prin oeffiient of te prin/daper nit, repetively. Te eqilibri eqation of te yte wen bjeted to rond aeleration & & an be forlated a follow: ( & && ) & k K = &. () VIII

9 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online IX Wen a aroni exitation i aed, Eq. an be rewritten a follow: i i i i = () were k =, =, and k =. Hereinafter, te reonant arateriti of ti yte are evalated baed on Eq.. In ti analyi, dapin ontant =. and freqeny ratio =. were aed. Te oter propertie aed ere are te ae a toe in Fi. 3. Fi. 4 indiate te preene of two loal axi area, wi an be ore learly identified a te a ratio dereae: te loal axi area at lower freqenie (referred to a te firt axi area) i aoiated wit te reonane ainly de to te bae iolation yte and te yro-a, a illtrated in Fi. 5(a); and te loal axi area at ier freqenie (referred to a te eond axi area) i ainly de to te bae iolation yte and te prin/daper nit, a own in Fi. 5(b). Herein, te vibratin ode in Fi. 5 are illtrated baed on te abolte vale of te deforation of te yro-a Δ and te prin/daper nit Δ, ea noralized by te total deforation of te yro-a devie ( Δ Δ = ) own in Fi. 6. Tey are obtained by te followin forla:

10 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Δ = i i (3a) Δ = i (3b) Fi. 6 ow te abolte vale for te ae were te a ratio =. 5. Te anifiation ratio of te relative diplaeent wit repet to te rond diplaeent a a fntion of te freqeny f i alo own. Fi. 6 learly explain te illtration in Fi. 5: te deforation of te yro-a beoe reater tan tat of te prin/daper nit in te yte arond te firt axi area, werea te oppoite tendeny or arond te eond axi area. Fi. 4(a) alo indiate tat te relative diplaeent at ier freqenie i larer tan tat of te Bai Model own in Fi. 3(a). Fi. 4(b) ow tat te repone aeleration onvere to zero a te exitation freqeny inreae. Tee arateriti iply tat providin te prin/daper nit in erie wit te yro-a dereae te effet of te yroa at ier freqenie, a expeted fro te above. It i noted tat te freqeny above wi te effet of te yro-a i reded an be adjted baed on in ter of an appropriate property of te prin in te prin/daper nit. Fi. 4 alo ow inifiant dereae in te relative diplaeent and te repone aeleration at te firt axi area wen opared wit toe of te Bai Model at te loal axi area own in Fi. 3. Model II - Model Propoed for Lon-Period Eartqake Wave Te firt axi area ay appear witin te freqeny reion were lon-period eartqake wave tend to be doinant. Te firt axi area an be diinied to a lare extent by in te followin teniqe. Fi. (d) ow a bae iolation yte wit a yro-a devie tat i X

11 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online XI alot idential to Model I deribed above (Fi. ()), exept tat te yro-a i arraned in parallel wit te daper. Te daper a a lare effet pon te firt axi area ine te firt axi area i aoiated wit te oveent of te yro-a; tat i, te daper aborb te eii enery ainly enerated by te yro-a and te bae iolation yte. Wen a teady-tate exitation wit irlar freqeny i aed, te dynai tiffne of ti yro-a devie an be expreed by te followin eqation: ( )( ) ( ) p p k i k i i K = (4) were p i te dapin oeffiient of te daper arraned in parallel wit te yro-a. Te eqilibri eqation of te yte wen bjeted to rond aeleration & & an be expreed by te ae eqation a tat own in Eq.. Wen a aroni exitation i aed, te relative diplaeent an be written a follow: ( ) ( ) p i i f i f = (5) were, ( ) ( ) p i f =, and p p k =.

12 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Fi. 7 ow te reonant arateriti of ti yte iven by Eq. 5. Te dapin ontant i aed to be.. Te oter propertie of te yte are idential to toe p own in Fi. 4. Fi. 7 indiate tat inifiant dereae in te relative diplaeent and te repone aeleration arond te firt axi area an be aieved by providin te daper in parallel wit te yro-a, a expeted. Fi. 7 alo ow tat te daper a a lit effet pon te repone of te bae iolation yte beyond te firt axi area beae of te prin/daper nit deribed above. Te dereae in te repone of te bae iolation yte arond te firt axi area i terefore expeted to be effetive for lon-period eartqake wave tat relt in a lare relative diplaeent tat wold daae oponent a lainated rbber bearin, oil daper, et. TIME-DOMAIN CHARACTERISTICS OF BASE ISOLATION SYSTEM WITH GYRO- MASS DEVICE In ti etion, te tie-itory repone of te odel preented above are allated for tree ilated eartqake baed on oberved eartqake reord in order to verify te effet of te yro-a devie. Te eqation of otion for te Bai Model and te onventional bae iolation yte are iply deribed a a one-deree-of-freedo yte, a own in Eq. 5 and Eq. 7, repetively. On te oter and, Model I and Model II are deribed a two-deree-offreedo yte. Terefore, atrix repreentation of te eqation of otion are efl for etiatin te tie-itory repone. Te eqation of otion for Model I an be forlated a follow: && && & k & = && k (6) were and are te relative diplaeent of te objet wit repet to te rond and tat of te node loated between te yro-a and te prin/daper nit, repetively (own in Fi. XII

13 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online XIII ). Ti eqation an be rewritten a: ( ) ( ) ( ) ( ) && & & && && = (7) Likewie, te eqation of otion for Model II an be expreed a follow: p p p p k k && & & && && = (8) Ti eqation an alo be rewritten a: ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) p p p p && & & && && = (9) Tie-itory analyi i perfored by nerial interation in Newark etod (te linear aeleration etod i ed ere), wit a tie interval t Δ of.. Te oberved eartqake reord ed for applyin te rond aeleration & & to te odel were a follow: ) Kobe NS (995), ) El Centro NS (94), and 3) Toakoai EW (3). Te tie itorie of te eartqake reord are own in Fi. 8. Te elati aeleration repone petra of te eartqake for 5% dapin are alo own in Fi. 9. Tee fire exibit te followin arateriti: Kobe NS a te laret axi aplitde; Toakoai EW a te laret effet pon lon-period yte; and El Centro NS a interediate arateriti in ter of

14 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online aplitde and reonane. In te tie-itory analye, te propertie of te odel are idential to toe ed in te freqeny-doain analye deribed above. Te tie itorie of te relative diplaeent wit repet to te rond and te aeleration & & of te bae-iolated objet are plotted for Kobe NS (Fi. ), El Centro NS (Fi. ), and Toakoai EW (Fi. ), were te repone of te odel in te yro-a devie are opared wit te repone of te onventional bae iolation yte. Te axi aplitde are arized in Fi. 3. In addition, Fi. 4 ow te redtion ratio (expreed a a perentae) defined a te ratio of te axi aplitde of te relative diplaeent of te odel to tat of te onventional bae iolation yte, wi an be rearded a an index tat deontrate te effetivene of te yro-a devie in redin te relative diplaeent. Fi. 4 alo ow te redtion ratio defined a te ratio of te axi aplitde of te aeleration of te onventional bae iolation yte and te odel to tat of te eartqake reord. Tee fire ow tat providin te yro-a devie ffiiently rede te relative diplaeent (4% dereae on averae), exept for te ae of Toakoai EW, wi ontain tron lon-period oponent. In te ae of Toakoai EW, Fi. ow tat te relative diplaeent of Model I i alot te ae a tat of te onventional bae iolation yte, wi i attribted to te reonant arateriti of te odel at lower freqenie, a own in Fi. 4. In partilar, in te ae of te Bai Model, te relative diplaeent i 4% larer tan tat of te onventional bae iolation yte de to te preene of te lare loal axi at lower freqenie, a own in Fi. 3. In ontrat, Model II aieve a inifiant redtion (a redtion ratio of p to 5%) of te relative diplaeent ine Model II a no loal axi at lower freqenie, a own in Fi. 7, beae of te daper arraned in parallel wit te yro-a. Tee fire alo ow a ffiient redtion of te aeleration (le tan / on averae), exept for te ae of te Bai Model: an aeleration of abot 4 / appear in te ae of Kobe NS wen in te Bai Model de to te reonant arateriti at ier freqenie, a explained above (alo own in Fi. 3). It i noted, terefore, tat te proviion of te prin/daper nit i extreely effetive in retritin te inreae of te aeleration at ier freqenie wen te yro-a i eployed. XIV

15 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online CONCLUSIONS In te preent tdy, te followin ay be onlded:. Ti tdy invetiate into te dynai repone of bae iolation yte inorporatin a o alled "yro-a" devie for redin lare lateral diplaeent. Te yro-a i defined a a eanial yte tat enerate a reation fore de to te relative aeleration of te node between wi it i plaed.. Tree type of bae iolation yte inorporatin yro-ae are foed on in ti tdy. Eqation repreentin teir aroni repone are preented, and te freqeny-doain reonant arateriti are tdied. A odel propoed in ti tdy, alled "Model II", exibit a inifiant dereae in te relative diplaeent of te objet wit repet to te bae at low freqenie a well a alot te ae dereae in te repone aeleration at i freqenie a a onventional bae iolation yte. 3. Te tie-itory repone are allated for tree oberved eartqake reord in order to verify te effet of te yro-a devie. Matrix repreentation of te eqation of otion are preented. Model II ow tat te relative diplaeent i arkedly reded even for lonperiod eartqake wave. Moreover, te odel ow a ffiient redtion of te repone aeleration, wi i oparable to te onventional bae iolation yte. 4. A odel, alled "Model I", i onidered to be effetive for ordinary eartqake wave, werea te odel annot ffiiently rede te relative diplaeent for lon-period eartqake wave. Terefore, deiner need to take are of te e of ti odel wen a ertain probability of orrene in lon-period eartqake wave i expeted at a ite were te odel i applied. 5. A odel, alled "Bai Model", tend to enerate lare repone aeleration wen bjeted to tron rond otion de to te deradation of bae iolation fntion. Moreover, ti odel alo inreae lare diplaeent of bae iolation yte for lon-period eartqake wave. Terefore, te perforane of Bae Model tronly depend on te type of eartqake wave o tat deiner ave to pay attention to te above arateriti wen ti odel i applied. Referene. Kelly J M, Aeii bae iolation: Review and bibliorapy, Jornal of Soil Dynai and Eartqake Enineerin 986; 5(3); -6.. Contantino M C, Moka A, Reinorn A M, Teflon bearin in bae iolation II: Modelin, XV

16 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Jornal of Strtral Enineerin, ASCE 99; 6(); Naarajaia S, Reinorn A M, Contantino M C, Nonlinear dynai analyi of 3D-bae iolated trtre, Jornal of Strtral Enineerin, ASCE 99; 7(7); Naarajaia S, Reinorn A M, Contantino M C, Experiental tdy of lidin iolated trtre wit plift retraint, Jornal of Strtral Enineerin, ASCE 99; 8(6); Naarajaia S, Reinorn A M, Contantino M C, Torional oplin in lidin bae iolated trtre, Jornal of Strtral Enineerin, ASCE 993; 9(); Naarajaia S, Fen M Q, Sinozka M, Control of trtre wit frition ontrollable lidin bearin, Jornal of Soil Dynai and Eartqake Enineerin 993; (); Naarajaia S, Riley M A, Reinorn A M, Control of lidin iolated bride wit abolte aeleration feedbak, Jornal of Enineerin Meani, ASCE 993; 9(); Kelly J M, Reent developent in eii iolation, 987 ASME Prere Veel and Pipin Conferene, San Dieo, California 987; PVP-7; Yoo B, Ki Y-H, Stdy on effet of dapin in lainated rbber bearin on eii repone for a /8 ale iolated tet trtre, Eartqake Enineerin and Strtral Dynai ; 3; Dera C J, Kelly J M, Cobined eartqake protetion and vibration iolation, Natral Rbber Tenoloy 985; 6; 3-.. Tai C S, Cian T-C, Cen B-J, Lin S-B, An advaned analytial odel for i dapin rbber bearin, Eartqake Enineerin and Strtral Dynai 3; 3; Robinon W H, Lead-rbber ytereti bearin itable for protetin trtre drin eartqake, Eartqake Enineerin and Strtral Dynai 98; ; Dileli M, Sppleental elati tiffne to rede iolator diplaeent for eii-iolated bride in near-falt zone, Enineerin Strtre 7; 9; Janid R S, Kelly J M, Bae iolation for near-falt otion, Eartqake Enineerin and Strtral Dynai ; 3; Aria T, Kanno Y, Takewaki I, Reonant beavior of bae-iolated i-rie bildin nder lon-period rond otion, Strt. Dein Tall Spe. Bild 6; 5; Zaa S, Seii azard aeent for liqid loin of oil torae tank de to lonperiod tron rond otion in Japan, 3 t World Conferene on Eartqake Enineerin 4; No3. XVI

17 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online 7. Yan J N, Danielian A, Li S C, Aeii ybrid ontrol yte for bildin trtre, Jornal of Enineerin Meani 99, ASCE; 7(4); Tai H -C, Te effet of trned-a daper on te eii repone of bae-iolated trtre, International Jornal of Solid and Strtre 995; 3; Okra A, Japan Patent Kokai, H (, Jly, 997). Katara R, Matnaa Y, Midorikawa K, Japan Patent Kokai, P-8759A (8, Mar, ). Katara R, Matnaa Y, Iii K, Koika N, Niira I, Saaki K, Szki Y, Japan Patent Kokai, H-4338A(6, Febrary, 999). Saito M, Japan Patent Kokai, P7-A (8, Janary, 7) 3. Saito, K, Yoo, K, Sira, Y, Nakainai, S, Park, K, Appliation of rotary inertia to diplaeent redtion for vibration ontrol yte, 3 t World Conferene on Eartqake Enineerin 4; No Ryan K L, Copra K C, Etiation of eii deand on iolator baed on nonlinear analyi, Jornal of Strtral Enineerin 4, ASCE; 3(3); Frkawa T, Ito M, Noori M N, Syte identifiation of bae-iolated bildin in eii repone data, Jornal of Enineerin Meani 5, ASCE; 3(3); APPENDIX A. NOTATION Te followin ybol are ed in ti paper: = dapin oeffiient of prin/daper nit; = dapin oeffiient of daper arraned in parallel wit yro-a; p = dapin oeffiient of onventional iolation yte; f = exitation freqeny; i = = iainary nit; J = oent of inertia of dik; k = prin oeffiient of prin/daper nit; k = prin oeffiient of onventional iolation yte; K = dynai tiffne of yro-a devie; XVII

18 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online = a of bae-iolated objet; = yro-a oeffiient; & & = rond aeleration; = exitation irlar freqeny. XVIII

19 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online & & F (a) θ J r F J r n n (b) Rotatin Dik Dik Gear Rod () FIG. Meanial yte of yro-a: (a) fndaental yte; (b) exaple for inreain rotational aeleration of dik de to obination of dik ear; () proto-type eanial yte of yro-a wit dik ear. XIX

20 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online k k (a) (b) k k () k k p (d) FIG. Stdied odel of bae iolation yte: (a) onventional bae iolation yte; (b) Bai Model; () Model I; and (d) Model II. XX

21 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online lo ) Hz] (f[ er et ra pa er et ra pa.6 (.... ) / 4 6 / (a) (f lo ]) [Hz (b) FIG. 3 Manifiation ratio of (a) relative diplaeent and (b) repone aeleration wit repet to rond otion wit by ean of Bai Model: =. and f =.5 Hz. XXI

22 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online lo ) Hz] (f[ er et ra pa r ete ra pa..8 (.... ) / 4 6 / (a) (f lo.5 ]) [Hz (b) FIG. 4 Manifiation ratio of (a) relative diplaeent and (b) repone aeleration wit repet to rond otion wit by ean of Model I: =., =., =., and f =.5 Hz. XXII

23 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online k k k k k k k k (a) (b) FIG. 5 Vibratin ode at loal axi area in freqeny doain: (a) firt axi area aoiated wit reonane de to bae iolation yte and yro-a; (b) eond axi area aoiated wit reonane de to bae iolation yte and nit opoed of prin and daper. XXIII

24 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Abolte Vale of Ratio 3 yro-a Δ / prin/daper nit Δ / total dip. / lo( f [Hz] ) FIG. 6 Abolte vale of te deforation of te yro-a and te prin/daper nit noralized by te total deforation of te yro-a devie wit anifiation ratio of diplaeent of yro-a yte wit repet to rond otion: =., =., =., =. 5 and f =. 5 Hz. XXIV

25 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online lo ) Hz] (f[ er et ra pa r ete ra pa.6 (.... ) 4 6 / 6 / (a) (f lo ]) [Hz (b) FIG. 7 Manifiation ratio of (a) relative diplaeent and (b) repone aeleration wit repet to rond otion wit by ean of Model II: =., =., p =., =., and f =.5 Hz. XXV

26 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Aerelation (/ ) Aerelation (/ ) Aerelation (/ ) Maxi Aeleration (8.78/ ) (a) Maxi Aeleration (3.47/ ) Tie (e) Maxi Aeleration (.79/ ) Tie (e) Tie (e) (b) () FIG. 8 Tie itorie owin oberved eartqake reord ed for tie-itory analye: (a) Kobe NS 995; (b) El Centro NS 94; () Toakoai EW 3. XXVI

27 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Kobe NS 995 Spetral A.(/ ). El Centro NS 94 Toakoai EW 3.. Period (e.) FIG. 9 Repone petra for oberved eartqake reord. XXVII

28 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Diplaeent () Conventional Iolation Model (.76) Bai Model (.9) Tie (e) Aerelation (/ ) Conventional Iolation Model (.744/ ) 6. Bai Model (3.985/ ) Tie (e) Diplaeent () Conventional Iolation Model (.76) Expanded Model I (.67) Tie (e) Aerelation (/ ) Conventional Iolation Model (.744/ ) 6. Expanded Model I (.74/ ) Tie (e) Diplaeent () Conventional Iolation Model (.76) Expanded Model II (.84) Tie (e) Aerelation (/ ) Conventional Iolation Model (.744/ ) 6. Expanded Model II (.7/ ) Tie (e) FIG. Tie-itory repone of relative diplaeent (left) and repone aeleration (rit): Coparion between onventional bae iolation yte and preented odel exited by Kobe NS 995; te axi aplitde of te repone are own in parentee. XXVIII

29 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Diplaeent () Conventional Iolation Model (.55).3 Bai Model () Tie (e) Aerelation (/ ) Conventional Iolation Model (.53/ ) Bai Model (.785/ ) Tie (e) Diplaeent () Conventional Iolation Model (.55) Expanded Model I () Tie (e) Aerelation (/ ) Conventional Iolation Model (.53/ ) Expanded Model I (.77/ ) Tie (e) Diplaeent () Conventional Iolation Model (.55) Expanded Model II (84) Tie (e) Aerelation (/ ) Conventional Iolation Model (.53/ ) Expanded Model II (.75/ ) Tie (e) FIG. Tie-itory repone of relative diplaeent (left) and repone aeleration (rit): Coparion between onventional bae iolation yte and preented odel exited by El Centro 94; te axi aplitde of te repone are own in XXIX

30 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online parentee. Diplaeent () Conventional Iolation Model (.39).6 Bai Model (.475) Tie (e) Aerelation (/ ) Conventional Iolation Model (.884/ ) Bai Model (.8/ ) Tie (e) Diplaeent () Conventional Iolation Model (.39) Expanded Model I (.36) Tie (e) Aerelation (/ ) Conventional Iolation Model (.884/ ) Expanded Model I (.548/ ) Tie (e) Diplaeent () Conventional Iolation Model (.39) Expanded Model II (.6) Tie (e) Aerelation (/ ) Conventional Iolation Model (.884/ ) Expanded Model II (.533/ ) Tie (e) XXX

31 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online FIG. Tie-itory repone of relative diplaeent (left) and repone aeleration (rit): Coparion between onventional bae iolation yte and preented odel exited by Toakoai 3; te axi aplitde of te repone are own in parentee. XXXI

32 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Relative Dip. () Kobe El Centro Toakoai Aeleration ( / ) Kobe El Centro Toakoai Conv. Bai Model I Model II Conv. Bai Model I Model II (a) (b) FIG. 3 Maxi aplitde of repone of (a) relative diplaeent and (b) repone aeleration of onventional bae iolation yte and preented odel. XXXII

33 STRUCTURAL CONTROL AND HEALTH MONITORING Strt. Control Healt Monit. () Pblied online Redtion Ratio (%) Kobe El Centro Toakoai Redtion Ratio (%) Kobe El Centro Toakoai Conv. Bai Model I Model II Conv. Bai Model I Model II (a) (b) FIG. 4 Redtion ratio related to (a) relative diplaeent and (b) repone aeleration of onventional bae iolation yte and preented odel. XXXIII