PASSIVE CONTROL OF BUILDING FRAMES BY MEANS OF LIQUID DAMPERS SEALED BY VISCOELASTIC MATERIAL

Transcription

1 ASSIVE CONTROL OF BUILDING FRAMES BY MEANS OF LIQUID DAMERS SEALED BY VISCOELASTIC MATERIAL 98 Shigeya KAWAMATA, Naoki FUNAKI And Yoshiro ITOH 3 SUMMARY In the purpose of installing in passive vibration ontrol system of building frames, a liquid damper of new type has been developed. In the liquid damper, narrow gaps between a ylinder and a pair of pistons is paked with visoelasti polymer to form soft rings whih, permitting relative movement of the pistons and the ylinder, serve to seal pressurized liquid. This devie enables very simple form of liquid damper and its easy prodution. In the present paper, resisting fore harateristis of the new damper is reported, where the resistane is of two omponents: visoelasti resistane of the sealing ring and inner pressure of the liquid flowing through a narrow orifie. An analytial model of the resisting fore onstruted based on theory of visoelastiity and turbulent flow rule of liquid is presented. The results of shaking table tests of portal frame speimen provided with the dampers and their numerial simulation are disussed. INTRODUCTION Rapid growth of base isolated building onstrution in Japan sine disastrous earthquake in Kobe in 995 has been remarkable: 65 planned base isolated buildings were approved by the government by July 998 []. In parallel with the development of base isolation, inreasing attention has been paid to R&D of vibration ontrol tehnique. Among variety of vibration ontrol systems, passive ontrol by the use of inter-storey dampers seems to have potential of wide appliation to seismi design of building frames inluding the one for retrofitting []. It is advantage of this tehnique that it an be pratised by only small extension of onventional onstrution tehnique. Examples of appliations of steel and visoelasti dampers to large buildings [3] indiate that these tehniques are beoming mature to be used in ommon pratie of seismi design of buildings. Typial devies of energy absorption for the use of inter-storey installation are hystereti dampers and visous or viso-elasti dampers. Among the visous dampers, whih enables more effetive vibration ontrol than the hystereti one, oil dampers seem to be attrative for design purpose as it provides very high resisting apaity within ompat form. However, the oil dampers are relatively expensive as they need preision mahining in order to inorporate shaft bearings and pressure sealings. Take, Kawamata and Funaki [4] proposed a new type of liquid damper to eliminate this diffiulty. In the liquid damper, small gap between a ylinder and a pair of pistons was paked with viso-elasti polymer to form soft rings whih, permitting relative movement of the pistons, serve as sealants of inner pressure. The sealing rings, being onsisted by energy absorbing material, gave rise to additional resisting fore to inner pressure resistane aused by liquid flow through an orifie. This sheme of inner pressure sealing enabled very simple and ompat omposition of liquid damper. With regard to the new damper, resisting fore harateristis were investigated by dynami exitation tests of damper speimens and an analytial model of the damper resisting fore was onstruted. Also, to demonstrate the appliability and effiieny of the damper, /3-saled steel portal frames having the dampers were subjeted to shaking table tests. Time integration program for response analysis was developed where the resisting fore rule 3 Department of Arhiteture, Tohoku Institute of Tehnology, Sendai, JAAN kawamata@titan.tohteh.a.jp High-teh Researh Center, Tohoku Institute of Tehnology, Sendai, JAAN funaki@titan.tohteh.a.jp Tehnial Researh Center, HAZAMA Corporation, Tsukuba, JAAN itogiken@hazama.o.jp

2 of the damper was implemented. The vibrational response of the damped frame speimen simulated by the analysis program was ompared with the test results. Funaki presented in his dotoral thesis [5] the onstruted model of the damper resistane and response analyses of the tested damped frame speimen. This paper presents outlines of the development of the vibration ontrol system by the use of the new damper. LIQUID DAMER SEALED BY VISCOELASTIC MATERIAL Fig. shows the sheme of the proposed liquid damper. The damper is omposed of a ylinder and a pair of pistons, the latter being linked together by outer framework so as the simultaneous same movement is fored. Inside of the ylinder is divided by a diaphragm to form upper and lower avities whih are to be filled with liquid suh as oil. Through diaphragm a bolt is installed in whih an axial hole of small diameter is bored to form an orifie for liquid flow. As a harateristi feature of the damper, the gap between the ylinder and the pistons are paked with soft visoelasti polymer, thus rings serving to seal pressurised liquid being formed. When relative displaement of the pistons is fored, the sealing ring is subjeted to dynami shearing deformation whih gives rise to visoelasti resisting fore. At the same time, the ontained liquid moves reiproally between the upper and the lower avities flowing through the narrow orifie, in whih strong turbulene ours. The turbulent liquid flow in the orifie brings high inner pressure whih inreases nonlinearly with inrease of piston veloity. In onsequene, the damper exerts resisting fore of two omponents against piston movement: visoelasti resistane aused by shearing deformation of the sealing material whih is almost linearly proportional to piston veloity and axial fore orresponding to the inner pressure of the liquid whih inreases nonlinearly with regard to piston veloity. Viso-Elasti olymer Figure Sheme of Liquid Damper Figure Damper Speimen (unit: mm) Fig. shows a speimen of the liquid damper used in harmoni exitation tests by the use of a numerially ontrolled dynami atuator, INSTRON 85. Inner diameter of the ylinder was 7mm. Viso-elasti material of aryli polymer, VEM of Sumitomo-3M Co., was used to form the sealing rings having setion of 5.mm mm. The pistons were subjeted to harmoni exitation of frequeny of.33hz-5.hz and displaement amplitude up to 5.mm. The followings are typial examples of the tests results in whih damper oil (ν =.m /se, at ºC) was used. Fig.3 shows hysteresis loops of resisting fore versus piston displaement for the ase of the damper without oil, where viso-elasti resistane of the sealing material is the only omponent of the resisting fore. The loops took the forms of ellipse, the inlination of its axis beoming steeper for the exitation of higher frequeny as is ommon to many kinds of visoelasti polymer. Fig.4 shows hysteresis loops of the differene of inner pressure between the upper and lower avities versus piston displaement for the ase of damper filled with oil having orifie of.5mm diameter and length of 4mm. The shape of the loops apparently differs from ellipse, indiating inner pressure nonlinearly inreasing with flow veloity. It takes the maximum pressure with some phase-lag from the point of zero displaement where the piston veloity takes the maximum value. This point is disussed in the next setion. 98

3 Resisting Fore [kg] 4 3 Damper Wituout Liquid - -.Hz.Hz -3 3.Hz Hz.33Hz Inner ressure Differene [kg/m ] 5 5 Orifie:.5ƒÓ,4mm -5.Hz -.Hz -5 3.Hz Hz.33Hz Resisting Fore Amplitude [kg] Figure 3 Hysteresis Loop of Viso-Elasti Resistane Figure 4 Hysteresis Loop of Inner ressure 4 3 Total Resistane Inner ressure Resistane Viso Elasti Resistane Orifie:.ƒ Ó,4mm 3 4 iston Veloity Amplitude [m/se] 3 4 (a).hz Exitation (b).hz Exitation Figure 5 Relation of Resisting Fore Amplitude to iston Veloity Amplitude Fig.5 shows the relation of total resisting fore amplitude aompanied by onstituent viso-elasti resisting fore and inner pressure fore amplitudes plotted against piston veloity amplitude. While the viso-elasti resistane inreases almost linearly with the piston veloity, inrease of inner pressure is nolinear. Therefor, inner pressure surpasses the visoelasti resistane in some point of piston veloity, the surpassing point of piston veloity beomes the smaller for the higher frequeny of exitation. Aording to this observations, it an be onluded that inner pressure of liquid produes strong resistane for the strutural response of large amplitude and high frequeny while visoelasti resistane dominates for the response of low frequeny and small amplitudes. The different harateristi of both the omponents of resistane fortifies eah other in the weak points of respetive property. The maximum inner pressure of the ontained liquid was about 3kg/m in the extent of the test series, no damage to the sealing material having been experiened. Resisting Fore Amplitude [kg] 4 3 Total Resistane Inner ressure Resistane Viso Elasti Resistane Orifie:.ƒ Ó,4mm iston Veloity Amplitude [m/se] Visoelasti Resistane THEORETICAL MODEL OF DAMER RESISTANCE The hysteresis loops of the sealing material of the damper represent visoelasti resistane whose property has strong dependene on frequeny of exitation. Though the simple visoelasti model of Maxwell liquid unit is able to represent the elliptial loops having inlination of the axises beoming steeper towards higher frequeny, its dependene on frequeny seems too strong. Therefor, to realise more moderate dependene on frequeny, a 4- parameter visoelasti model whih is omposed of parallel ombination of a Maxwell fluid and a Kelvin solid was adopted, as the latter, having onstant inlination of loops for any frequeny, might moderate the dependene. Fig.6 shows the 4-parameter model, and δ representing fore and total displaement. When the model is subjeted to harmoni exitation, δ relation an be written by the following omplex form: + i = ( K + ik )( δ + iδ ) () where K + ik is a omplex spring onstant. In the present ase of 4-parameter model, the onstant is given by 3 98

4 km M ω + km M ω K + = + + ω ik k K i K () km + M ω km + M ω where ω is frequeny of exitation. Constants K and K in Eq.() an be found in observed hysteresis loops as shown in Fig.7. As it is diffiult to determine the four parameters simultaneously from observed data, an alternative method was proposed [6], in whih the unknown parameters were identified suessively in the following steps: ) k K for the Kelvin spring is determined using hysteresis data orresponding to effetively stati loading, ) k M and M for the Maxwell unit are obtained from a set of hysteresis data for exitations in two different frequenies, and 3) finally K is alulated by introduing the obtained K data and k M and M determined already into the relation of K and the parameters. The parameters atually identified with regard to the test speimen shown in Fig. is given in Table. In Fig.8 hysteresis loop of the damper fore theoretially predited using parameters in Table are ompared to the test results. Table Visoelasti arameters for Speimen k M M k K K 84 kg/m 6 kg se/m 5 kg/m 3.8 kg se/m ƒâ k M K k K M ƒâ K = /ƒâ K = /ƒâ Figure 6 4-parameter Model Figure 7 Fore-Displaement hysteresis Loop Damper Fore [kg] Theory Damper Fore [kg] Theory Inner ressure Resistane (a).33hz Exitation (b) 3.Hz Exitation Figure 8 Comparison of redited Visoelasti Resistane with Results As seen in the test results, hysteresis loops of inner pressure differene between the upper and lower avities show phase-lag in the point of the maximum value. Fig.9 shows a shemati representation of the loop. As is well known, Maxwell fluid model of visoelastiity provides hysteresis ellipse in whih the maximum fore ours with some phase-lag from the point of zero displaement. This is aused by the deformation of the spring element whih is linked with dashpot in series and subjeted to the same fore as the dashpot. In the ase of the present damper, the visoelasti sealing rings are supposed to be subjet to outward defletion by inner pressure as shown in Fig.. Therefor, it was presumed that the phase-lag of inner pressure resistane ould be simulated 4 98

5 by idealizing the mehanism of pressurization by a Maxwell fluid model shown in Fig., where the spring element ( k ) orresponds to the elasti deformation of the sealing rings and the dashpot ( ), to flow resistane in the orifie. Inner ressure p max Q iston Displaement ƒâ ƒâ Figure 9 Shemati Diagram of Hysteresis Loop of Inner ressure Resistane Figure Elasti Deformation of Sealing Ring by Inner ressure In the following, the methodology of parameter identifiation for the Maxwell fluid model is briefly outlined. Referring to Fig.9, at the point Q, where the maximum inner pressure ours, displaement of the dashpot, δ is zero. Therefor, the piston displaement δ represents solely the deformation of the spring element, δ and p max δ relations plotted for the hysteresis loops Figure Maxwell Fluid Model of various piston displaement amplitude orrespond to for ressure Resistane p δ urve of the spring element. Fig. shows pmax δ relations obtained from the results of a test ase. The diagram shows almost linear relations and the spring onstant k an be determined for the respetive ases of exitation frequeny. Inner ressure p max [ kg/m ] Orifie:.ƒ Ó,4mm.33Hz.5Hz.Hz.Hz 3.Hz 5.Hz iston Displaement ƒ  [mm] Figure p max δ Relations Figure 3 Relation of ipe Frition to Reynolds Number In the next step, visous parameter of the dashpot, K, has to be searhed for. As the dashpot orresponds to resistane of turbulent liquid flow in the orifie, K is not a onstant parameter, the pressure differene being non-linear with regard to veloity of the liquid flow. As the spring element takes the maximum stress p max at the point Q in Fig.9, its veloity is zero. Hene, veloity at the point Q is equal to the maximum veloity of the dashpot, δ max, orresponding to p max. Deriving orrelation of the maximum dashpot veloity to the maximum pressure differene from the exitation test data and following the methodology presented by Kawamata et al. [7], flow rule of liquid through the orifie an be onstruted. In the flow rule, the pressure differene is given by ρl p = um f (3) D where ρ : density of liquid, L : length of orifie, D : diameter of orifie, u m : mean veloity of orifie flow, f : pipe frition oeffiient. The frition oeffiient is to be orrelated to Reynolds number defined by Re = u m D ν (4) ipe Frition Coeffiient f...33hz.5hz.hz.hz 3.Hz 5.Hz k ƒâ' ƒâ" Total Displaement ƒâ Reynolds Number Re Orifie:.ƒ Ó,4mm 5 98

6 where ν : kinemati visosity of liquid. Fig.3 shows an example of f -Re relation obtained from the results of exitation test. For this ase, the pipe frition oeffiients an be represented as.75.5 > f =. Re for Re 7 : f =.765 Re for Re 7 : ( Transition region) ( Turbulent region), (5). (6) Eq.(6) means that pressure differene in turbulent region is proportional to.75th power of the flow veloity as in the ase of steady liquid flow in a smooth pipe. In Fig.4, hysteresis loops of pressure differene obtained by the test are ompared with those simulated by time step analysis based on the derived flow rule and the spring onstant. ressuer Differene p [kg/m ] Orifie:.ƒ Ó, 4mm ressure Differene p [kg/m ] 8 Orifie:.ƒ Ó, 4mm k =5kg/m 3 and f s in Eq.(5) and (6) were applied (a).33hz Exitation (b) 3.Hz Exitation Figure 4 Comparison of ressure Differene: and EXCITATION TESTS OF A STEEL FRAME MODELWITH ASSIVE VIBRATION CONTROL SYSTEM Speimen To demonstrate the effet of passive ontrol of vibration by the use of the proposed liquid damper, a /3-saled steel frame was subjeted to exitation tests. A pair of portal frames were linked together by transverse beams to form a table shape on whih steel weight of 4. ton was plaed as shown in Fig.5. In a vibration ontrolled speimen, a liquid damper was installed between V-shaped braing and a basement beam in eah frame as shown in Fig.6. The used dampers were the same as shown in Fig. and the damper oil (ν =.m /se, at ºC) was filled. Orifie of.mmφ and 4mm long was inorporated. In this damped speimen, the web of main beams was perforated to form an opening in order to make it more flexible. For the purpose of omparison, a speimen without dampers and braings was also tested, where the main beams were replaed by full web one without opening. Stati loading tests of horizontal fore and free vibration tests were onduted. The obtained fundamental parameters of the speimens are listed in Table. H ~9 9 ~4. 5 ~7 O p e n i n g 4 5 D a m p e r B a s e m e n t B e a m Figure 5 Frame with Damper Figure 6 Frame with Damper (unit: mm) 6 98

7 Table Fundamental arameters of Frames *ase of dampers inorporated Speimen Horizontal Stiffness Natural Frequeny Effetive Mass Damping Ratio [ 3 kg/m] [ Hz ] [ kg se /m ] [ % ] Undamped (Full Web Beam) Damped (Open Web Beam) (4.8*) (.*) Response of Frames with Dampers The test frame speimen with the dampers an be idealised by a single mass system shown in Fig.7 (a). Ation of the damper is represented by a parallel ombination of a 4-parameter model for visoelasti resistane and a Maxwell fluid model for pressure resistane. In this ase, the inner pressure whih is evaluated in a manner desribed in the previous setion has to be transformed into resultant fore being multiplied by effetive setional area of the pistons. As the spring and dashpot of the Kelvin solid ( k K and K ) are subjeted to idential displaement to the mass, these parameters an be inluded in those of the struture as shown in Fig.7 (b), the pair of Maxwell fluid models remaining for evaluating the additional resisting fore to the vibration system. A time integration program for the response analysis of the single mass system was developed using Runge-Kutta method. In the disretized time step equation of motion, the additional terms of resisting fore by the two Maxwell fluid models were inluded for whih evaluation proedure proposed by Hatada, Kobori et al. [8] was adopted. m k k K M k M K Vi so- El ast i Resi stane k r essur e Resi stane : Damping Coeffiient of Frame k: Spri ng Constant of Frame m +K k+ kk k M k M Results of and (a) (b) Figure 7 Single Mass System for Damped Frame Fig.8 shows resonane urves obtained both from harmoni exitation test of the damped speimen and the orresponding analysis. In Fig.9 results of the test and the analysis are ompared with respet to hysteresis loop of resisting fore of the damper. Fairly good agreement an be seen between tests and analysis. Fig. shows input and response of the damped speimen to an earthquake input, Hahinohe EW with time axis ompressed into /. While the maximum response aeleration of the undamped frame to the same input was gal, the one of the damped ase was redued to 454gal. Also, maximum relative displaement of 8.9mm of the undamped speimen was redued to 3.7mm for the damped one. The results of numerial simulation of the responding aeleration and the hysteresis of damper resistane are shown in Fig. (b) and () providing good oinidene with the test results. Amplifiation Fator of Aereration.5 Aeleration Amplitude: 4gal Frequeny of Exitation [Hz] Figure 8 Resonane Curve to Harmoni Exitation Resisting Fore [kg] Figure 9 Hysteresis Loop of Damper Resistane for 4.Hz Exitation 7 98

8 Aerelation [gal] Mª ax=36gal Tim e [se] (a) Aeleration of Shaking Table Aeleration [gal] , Time [se] (b) Aeleration of Frame M ax=454gal A nalysis, M ax=356gal Resisting Fore [kg] 5-5 Resisting Fore [kg] ( ) Hysteresis Loop of Damper Figure Response of Damped Frame to Exitation of Earthquake, Hahinohe EW, / Time Axis CONCLUSION In order to apply as inter-storey dampers in passive vibration ontrol system for building frames, a liquid damper of the simplest form was developed. In the new damper, soft rings of visoelasti polymer paked in the gap between a ylinder and pistons took the role of sealing the liquid under high inner pressure. Dynami exitation tests of the damper revealed the harateristis of resisting fore of the damper whih was onsisted of two omponents: viso-elasti resistane of the sealing rings and inner pressure resistane of the liquid flowing in narrow onduit of orifie. It was verified that the analytial model for the resisting fore onstruted on the basis of theory of visoelastiity and turbulent flow rule represented hysteresis of the damper resisting fore with enough auray. Shaking table tests onduted on /3 saled portal frames provided with the new dampers demonstrated remarkable redution of vibration response and proved the appliability and the validity of response analysis program developed for the passive ontrol system. REFERENCES All referenes but [7] are written in Japanese. Menshin, Quartery journal of Japan Soiety of Seismi Isolation, No.4 (999) pp Steel Struture Researh Committee (998) resent status and subjets of steel buildings having vibration ontrol devies, anel Disussion, Annual Convention of Arhitetural Institute of Japan 3. Inada.Y, Saruta.M, et al. (999), Introdution to aseismi, seismially isolated and vibration ontrolled building strutures, Shokokusha, Tokyo, pp Take.Y, Kawamata.S and Funaki.N, Resisting fore harateristis of turbulent flow dampers sealed by visoelasti material, reprints of Annual Meeting of Arhitetural Institute of Japan 997, 48, Funaki.N, Vibration response harateristis of building frames vibrationally ontrolled by turbulent flow dampers sealed by viso-elasti material, Dotoral thesis, Tohoku Institute of Tehnology, Funaki.N, Kawamata.S and Take.Y, Resisting fore model of viso-elasti dampers for vibration ontrol of frameworks, Bulletin of Informatis Laboratory of Tohoku Institute of Tehnology EOS, Vol., No., pp.33-46, Kawamata.S, Ohnuma.M, et al. Appliation of aelerated liquid flow dampers to base isolation of reator buildings, Transations of -SMiRT Conf., 993, Vol.K, pp Hatada.T, Kobori.T, et al. Method of response analysis for vibration systems inluding Maxwell models, reprints of Annual Meeting of Arhitetural Institute of Japan 994,