Analysis model of structure-HDS

Journal of Harbin Institute of Technology( New Series ), Vol.7 , No.3 ,2000Article ID : 1005-9113( 2000 )03-0084-03Analysis model of structure-HDSQI Ail2, HE Zhong-yi3，LIU Ji|'，LI Hui祁皑，何钟怡,刘季，李惠( 1. Postdoctoral Station , Harbin Institute of Technology , Harbin 150001， China ;2. Shenyang Architectural and Givil Engineering Institute , Shenyang 10015 ,China ;3. Harbin University of Civil Engineering and Architecture , Harbin 150001 , China )Abstract : Presents the model established for Structure- HDS hydraulic damper system ) analysis on the basis of thetheoretical analysis model of non-compressed fluid in the round pipe will an uniform velocity used as the basic vari-able , and pressure losses resulting from cross section changes of fluid route taken into consideration. W hich providesnecessary basis for researches on earthquake responses of a structure with a spacious first story ，equipped with HDS atfirst floor.Key words : hydraulic damper system ; vibration ; earthquake responseCLC number :TU3Document code :A0 INTRODUCTIONmovement of fluid. So , the earthquake responses of theframework can be reduced .Text resultst 11 have shown that using the hydraulicdamper system to control the seismic responses of the2THEORETIC ANALYSIS MODEL OF NON-structure with spacious first story is very effective. In thisCOMPRESSED FLUIDpaper , an analysis model of Structure- HDS is established.It settles a foundation for more researches of this structureIn order to study the structural dynamic responsescontrol system.with HDS , the dynamic properties of the fluid in the pipeshould be investigated firstly . Therefore , from the Navier1 HYDRAULIC DAMPER SYSTEM HDS )Stokes equation of non-compressed fluid , the fluid motionequation in the round pipe has been established using theFig.1 is the schematic diagram of hydraulic damperuniform velocity as its variable in literature[ 2 ].system installed on a one- story framework .Jumoa,+cou=F( 1)where mo , Co are the equivalent mass and equivalentdamper coffcient respectively ; u is the uniform velocityand F is the applied force to the fluid.It is evident here that the inconsistency of the basic3variables in motion equations , caused by fluid and solidcoupling acts , is solved. The damper property and its af-fecting factors are also demonstrated clearly in this model.1- -Hydraulic Jar ;2- -Piston ;3- -Pipe3 THE ANALYSIS MODEL OF STRUCTURE-HDSFig.1 Schematic diagram of HDS installed on a one-storyframeworkIn this paper , the compression of fluid is demonstrat-ed by a non-mass spring with a siffness ko , similarly.From Fig. 1，we know that when the framework vi-The simplified model of one-story framework e-brates under earthquake , the framework pushes the fluidquipF中国煤化工from hydraulic jar into the pipe and invokes the vibrationn Fig.2 moves to right，of the fluid in it. Therefore parts of the structural vibratingits nYHCNMHG.energy is transferred to the fluid or dissipated away by them1x1 + c1x1 + k1x1 =- m1xg+ F2- F1 (2)Received 1999- 12- 08Sponsored by the National Natural Science Fundation of China and Science and Technology Foundation of Liaoning Province.Joural of Harbin Institue of Technology( New Series ), Vol.7 , No.3 ,2000C0。mF3 =7x10+-x10+ hid x10- x)- mHxgA( 10)sFrom Eq. (6)|划龙旧moC0.mun/2Cmo/2F4 =-2x1o--x10一koh x10一x0)+ mHxg( 11)ho 177ma/2mn/2kaSubtracting Eq.( 10 ) from Eq.( 11 ) givesF4- F3 = - mox1o- Cox10- 2k( x10- xo)+ig.2 Simplified model of HDS2mHxg. (12)Substituting Eq.( 12 ) into Eq. ( 9 ) giveswhere m| ,C1 and hi are the mass，damper coefficient andF2- F = a[- mox1o- Cox1o- 2kd x1o- xo)+stiffness of framework , respectively. x is the displace-oat'sment of the framework related to the ground ; xg is the .2muxg]-[1 +(a- 1}a.ground acceleration ; F2 and F1 are the control forces ap-( 13)plied to the framework by HDS.At point A , the cross-section of fluid route becomesConsidering the harmonic condition of displacementssmall suddenly , and causes a pressure loss , hencex10 = ax1 ,Eq. ( 13 ) becomespa'szFz- Fi= a[ - moai1- coaxi - 2kogax1 + 21koxo +F=2x行+ F3a(3)pa- swhere F3 represents the pressure of point A ,and a the in-2mμxg]-[21 +(a-1}a ]xtermal section ratio of hydraulic jar and pipe .( 14)The dfferential motion equation of fluid in A-B seg-Substituting Eq.( 14 ) into Eq.( 2) leads toment is(m +a2mo)i1+ {c1 + a2co+[(a- 191 +mo ;2x1o+ 2x10+ ke x1o一xo)= F3+ mHxg(4)a2os2]xi +(k] + 2a2ko)x- 2akoxo=(- m; +4c(2amH )i。( 15)where2and方are the equivalent mass and equivalentAssembling Eq.( 15 ) and Eq. (5 ) into the matrixdamping cofficients of fluid in A-B segment，respective-form , the differential equations of Structure-HDS are ob-ly iko is the stiffness cofficient of fluid ; x10 and dxo aretainedthe relative displacements of fluid in A-B segment and[ M k{i}+[ C]x}+[K k{x}=[ MgJc。B-C segment , respectively ; mH is the equivalent mass inwhere[ M ],[ C ]and[ K ]are the mass matrix , dampinghorizontal part of A- B segment .matrix and stiffness matrix of Structure-HDS , respective-The differential motion equation of B-C segment isly ,and are given bymoxo + coxo + 2kC x0一x1o) = moxg(5)[ M]=「 mo0The differential motion equation of C-D segment isl0 m1+ a2momo..2 xio+ 2*10+ ke x1o一xo)=- F4+ mHXg[c]=| C0l0. (6)where F4 represents the pressure of fluid in the pipe at Lwhere E =[(a-1}a5 +arps2]x;point.At D point , the cross -section of fluid route becomes[ K]=2hc- 2akolarge suddenly , and causes a pressure loss. Hence2ako hy + 2akoJ{x}=[xox|] ;F4=(a-1OSIx行+-F2(7){Mg}=[ mo,- m1 + 2amy].From the Eq. ( 7)Now ,the analysis model of Structure- HDS has beenF2= aF4-(a- 1)a号x行(8)obtained中国煤化工Subracting Eq. (3)from Eq. (8) givesDHCNMHGICIENTOFFLUDINF2-F=a(F4-F3)-THE ANALYSIS MODEL[ pa*s2+(a-1jaOS1 ](9)The sifness of fluid is given byFrom Eq.(4)ko = E。si/l85.Journal of Harbin Institute of Technology( New Series ), Vol.7 , No.3 , 2000where E。denotes the effective cubature modulus of elas-From Fig. 3 and Fig. 4 , we know that the calculat-ticity of the fluid ; S1 denotes the internal section of pipeing results are coincided with the test results. The waveand l the length of pipe.mode of the two time- histories is similar. The predominantE。can be given by534]:frequency and the peak value of the two frequency-spec-11.1Vg_1R)trum curves are also similar. Therefore , the analysis mod-el of structure-HDS established in this paper can describeE。Ethe characteristics of structure-HDS .whereVg is the initial volume of gas.the first foorV, is the total volume of the pipe.test frequency-spetrumE。is the volume modulus of elasticity of the pipe ,caleulating frequency-spectrum2:and can be obtained by20E。=TEd15where T is the thickness of the pipe wall ;d is the inner10diameter of the pipe ; E is the modulus of elasticity of ma-terials from which the pipe is made.E is the volume modulus of elasticity of fluid , which245is relative to the chemical components of fluid. Here Efrequency/ Hz= 1.55x 103 MPa ;Eg is the volume modulus of elasticity of gas , hereNote : The input is EI-Centro wave xg m. = 0.2g,a = 25 ,po= 0.5 MPaEg =1.4 Po po is the initial pressure of HDS.Fig.4 The comparison of calculating frequency-spectrum andtest frequency-spectrum5 THE TEST VERIFYING OF THE ANALYSIS6 BRIEF SUMMARIZATIONMODELThe analysis model of Structure- HDS establishedIn order to verify the correctness of the analysis mod-el established above , the seismic responses of the testabove is based on the exact motion equation of fluid. Fur-model in literature[ 1 ] are calculated. For the comparisonthermore，the pressure loss caused by cross-sectionchange of fluid route is considered , and the correctness ofconvenience , the same cases and earthquake inputs areused. The comparison of the calculating results and thethis model has been verified by model shaking table text.shaking table test results are shown in Fig. 3 and Fig.4.So , this mode can demonstrate the dynamic properties ofStructure-HDS , and make a necessary theoretical prepara-tion for the dynamic responses analysis of structure with athe first loorspacious first story , equipped with HDS at its first floor.------ test time-historycalculating time-historyReferences :[1] LI Hui ,QI Ai ,LIU Ji. Experimental rsearch on seismie re-sponse control by using hydraulic damper system( HDS I J].Earthquake Engineering and Engineering Vibration, 1997 ,17 ,( 4):94-98.-2[2] QI Ai HE Zhongyi LIU Ji ,et al. 'The theory model of hydraulice8damper system( HDS I A ] Inermational Workshop on SeismicT/sIsolation Energy Dissipation and Control of Structures[ C] Gu-anghou :Seismological Press , 1999.Note :The input is El-centro wave ,Xgmx = 0.2g,a = 25 ,Po= 0.5 MPa[3] CHEN Yanqing. Control System of Fluid M ] Beijing : Sci-Fig.3 The comparison of calculating time-history and testence Press , 1978.time-history[4] CAI Yigang. Dynamics of Fluid Transniting Pipeline[ M ]Hangzhou : Zhejiang University Press ,1988 .中国煤化工MYHCNMHG86 "