NUMERICAL MODELING ON THE DAMPING CONTROL OF TLD STRUCTURE

Transcription

1 4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 2006 Paper No. 183 NUMERICAL MODELING ON THE DAMPING CONTROL OF TLD STRUCTURE Han jun 1, Li Yingmin 2, Liu Liping 3, and Lv Hui 4 ABSTRACT TLD i an efficient control mode of paive diipative damping of vibration, of which the rule and analyi deign method have received much attention. Actually, mot previou reearch wa relied on tet and ha got fruitful achievement in the damping of vibration rule. Though the implified analyi method of damping of vibration effect ha alo been developed baed on thoe tet, it application ha been greatly limited due to the rough model. Recently, with the development of computer technology, it i likely to do reearch into TLD numerical modeling analyi of fluidtructure interaction, which would become a valuable upplement. The fluid- tructure interaction of general tructural analyi oftware ADINA i applied in thi article to conducting the eimic repone analyi of fluid- tructure interaction in the high-rie frame tructure controlled by TLD of roof tank intallation. Meanwhile, earlier tet rule and implified method are alo compared and checked in thi paper. Beide, the calculation and model building of fluid- tructure interaction are initially explored and examined whereby realizing the TLD numerical modeling of fluid- tructure interaction a well a ummarizing the TLD damping of vibration rule of high-rie frame tructure. Keyword: TLD, fluid- tructure interaction, Finite element, Damping of vibration, INTRODUCTION Tuned liquid damper (TLD for hort) i a tank device of paive diipative damping of vibration fixed on tructure floor or roof, the damping mechanic of which i TLD-tructure ytem vibrate upon the influence of earthquake or wind loading, leading to the movement of tank. Accordingly, the liquid in the tank would hake followed by urface wave, which could caue hydrodynamic preure difference on tank wall a well a the inertia force triggered by the movement of the liquid with the tructure. Thu, the damping force of the building could be attained if the tank and it parameter are reaonably deigned. On the one hand, ince TLD bear the merit of imple tructure, eay intallation, brilliant automatic activation performance without actuation device and upply tank a well, it ha been widely applied in wind induced vibration control. On the other hand, the TLD damping of vibration rule and it analyi deign method remain to be further explored due to the immature reearch and application of eimic hock control at preent. Beide, owing to the complexity of the interaction between the force of the tructure and liquid in the tank, mot previou reearch wa relied on tet and ha got fruitful achievement in the damping of vibration rule. Though the implified analyi method of damping of vibration effect ha alo been developed baed on thoe 1 Ph. D Candidate, College of Civil Engineering, Chongqing Univerity, Chongqing, P. R. China, hanjun009@126.com 2 Profeor, College of Civil Engineering, Chongqing Univerity, Chongqing, P. R. China, liyingmin@cta.cq.cn 3 Aociate Profeor, College of Civil Engineering, Chongqing Univerity, Chongqing, P. R. China 4 Graduate Student, College of Civil Engineering, Chongqing Univerity, Chongqing, P. R. China

2 tet, it application ha been greatly limited becaue of the rough implified model. Recently, with the development of computer technology, it i likely to do reearch into TLD numerical modeling analyi of fluid- tructure interaction, which would become a valuable upplement to the current reearch on TLD deign method and damping of vibration rule. The fluid-tructure interaction of general tructural analyi oftware i applied in thi article to conducting the eimic repone analyi of fluid- tructure interaction in the high-rie frame tructure controlled by TLD of roof tank intallation. Meanwhile, current tet rule and implified method are alo compared and checked in thi paper. Beide, the calculation and model building of fluidtructure interaction are initially explored and examined whereby realizing the TLD numerical modeling of fluid- tructure interaction a well a ummarizing the TLD damping of vibration rule of high-rie frame tructure. FEM BUILDING AND PARAMETER SETTING The tructural analyi oftware ADINA i applied in thi article to conducting TLD damping of vibration effect analyi of fluid-tructure interaction (FSI). A brief introduction below will be given to the baic principle and model building of FSI analyi in ADINA(ADINA R&D. 2001). When the fluid-tructure model interaction analye arie, the fluid flow model ued here can be incompreible flow, lightly compreible flow, low and high peed compreible flow and flow through porou media. The olid model ued here can be all thoe available in ADINA. Heat and ma tranfer can alo be pecified in fluid-tructure interaction analye. Hence, the incompreible flow can be ued to ignify the water in tank here. In fluid-tructure interaction analye, fluid force are applied onto the olid and the olid deformation change the fluid domain. For mot interaction problem, the computational domain i divided into the fluid domain and olid domain, where a fluid model and a olid model are defined repectively, through their material data, boundary condition, etc. The interaction occur along the boundary of the two domain. The two model mut have alo been dicretized uing the element that are available in ADINA and ADINA-F, repectively. The typical tak of an analyi of a fluid-tructure model i to obtain the fluid and tructure repone through the coupled olution. The tructural model i baed on a Lagrangian coordinate ytem and the diplacement are the primary unknown. A pure fluid model i alway analyzed uing an Eulerian coordinate ytem. However, for fluid-tructure interaction problem, the fluid model mut be baed on an arbitrary-lagrangian-eulerian coordinate ytem ince the fluidtructure interface i deformable. Therefore, the olution variable of the fluid flow include the uual fluid variable (preure, velocity, etc.) a well a diplacement. KINEMATIC AND DYNAMIC CONDITIONS The fundamental condition applied to the fluid-tructure interface are the kinematic condition (or diplacement compatibility) d = d, and the dynamic condition (or traction equilibrium) n τ f = nτ, where f d and f d are, repectively, the fluid and olid diplacement andτ f and τ are, repectively, the fluid and olid tree. The underlining denote that the value are defined on the fluid-tructure interface only. The fluid velocity condition i reulted from the kinematic condition v= d, if a no-lip condition i applied, or nv g = nd g, if a lip condition i applied. The fluid and olid model are coupled a follow: The fluid nodal poition on the fluid-tructure interface are determined by the kinematic condition. The diplacement of the other fluid node are determined automatically by the program to preerve the initial meh quality. The governing equation of fluid flow in their ALE formulation are then

3 olved. In teady-tate analye, the meh velocitie are alway et to zero even the fluid nodal diplacement are updated. Accordingly, the fluid velocitie on the fluid-tructure interface are zero. SEPARATE MESHES OF FLUID AND SOLID MODELS Completely different element and mehe can be ued in fluid and olid model. The element are olely limited by the availability of olid and fluid model in the ADINA ytem. The nodal point poition of the two model are therefore generally not the ame on the fluid-tructure boundary. However, the nodal point poition hould be managed to be the ame when building model to avoid the problem of model calculation. Otherwie, the ditance of nodal point poition to the boundary hould be no more than 0.001~1 time of the unit length on the other ide. ELEMENTS ON FLUID AND SOLID INTERFACES Any fluid element that can be ued in a fluid model can alo be ued in fluid-tructure interaction model. Thee element are either two-dimenional element (including axiymmetric element) or three-dimenional element. The fluid-tructure interface are alway aigned to boundarie of element. In two dimenion and three dimenion, the interface are then formed by line element and urface element, repectively, which are generated automatically by the program. Any olid element, on the other hand, that can be ued in a eparate olid model can alo be ued in fluid-tructure interaction model. However, ome of the element cannot be directly connected with fluid element, which mean that no fluid-tructure interface can be aigned to thoe element. For example, the pring element cannot be directly connected with fluid element. MATERIAL MODELS Any fluid material that can be ued in eparate fluid model can alo be ued for fluid-tructure interaction model. Any olid material that can be ued in eparate olid model can alo be ued for fluid-tructure interaction model. ATTENTIONS IN MODEL BUILDING While carrying out FSI analye in ADINA, a mentioned above, firt there i a need to build tructural model in ADINA module and fluid model in ADINA-F followed by etting analyi parameter of the two model repectively. Then, after file being aved, SOLUTION/DATA FILE/RUN will be performed to generate the input file( *.dat) of tructural model and fluid model eparately. Finally, SOLUTION/LAUNCH ADINA-FSI will be alo performed along with the choice of generated input file of tructural model and fluid model. Only under thee condition doe FSI begin to calculate. Mot importantly, the following attention hould be paid to building tructural model and fluid model. ADINA STRUCTURAL MODELS 1TRANSIENT DYNAMICS i elected a the analyi type in ADINA, the integrate method in TRANSIENT DYNAMICS i et a impli cit and NEWMARK work a the implicit integrate method ; 2The automatic time-tepping i opened, the number of load tep and load ub-tep can be continuouly adjuted according to the convergence of model, and FSI i elected; 3 Geometric model building can be completed in light of tructural analyi a uual, the detail of which can be found in reference (ADINA R&D. 2001) and (ADINA R&D. 2001); 4MASS PROPORTIONAL i firt elected a the load type in on-load option; then the magnitude in load option i defined a the reference value to be filled with time function, i.e. the time load input from all direction become the direction coefficient of time value*magnitude value*; GROUND ACCELERATION i latly elected a the load owing to the dynamic analyi;

4 5Since TIME FUNCTION mut be defined by the dynamic load in menu CONTROL, the extant data of eimic wave file can be directly tranmitted into TIME FUNCTION through IMPORT. Later, the time number of tep in menu TIME STEP i et a -1, and contant magnitude a time interval of eimic wave data; 6Conitent ma matrix or centralized ma matrix hould be determined in menu ANALYSIS ASSUMPTION; damp RAYLEIGH i et which can be attained according to the frequency calculation in the firt and econd order of model; 7 The option continue even when non-poitive definite tiffne matrix encountered i elected in menu SOLUTION PROCESS, and pare i et a the olution proce. The default et of option nonlinear analyi will be ued if the tructure i linear. Latly the eimic force i input; 8FSI boundary etting: Menu MODEL/BOUNDARY CONDITION/FSI CONDITION i opened and the tank wall contacting liquid i elected a the FSI boundary. In addition, FSI boundarie with different number will be et if there are many tank. ADINA-F FLUID MODEL 1TRANSIENT i elected a the analyi type in ADINA-F, automatic time-tepping i opened in option TRANSIENT DYNAMICS, and the number of load tep and load ub-tep can be continuouly adjuted according to the convergence of model. A the fluid in tank appear height nonlinear upon the impact of earthquake force, generally the ubdiviion will be et relatively larger; 2FSI SOLUTION i et a DIRECT in FSI OPTION, and convergence tolerance together with force and diplacement relaxation factor are determined. Conidering the accuracy of internal force calculation i not highly required in the civil engineering tructure, the convergence tolerance can be appropriately et a large a 0.05, which can trengthen the calculation convergence; 3Default et can be applied to TIME FUNCTION in menu CONTROL, and the et of TIME STEP and prior tructural model of ADINA hould be kept conitent; 4Solution proce i et a pare in menu SOLUTION PROCESS, and maximum memory for pare can be et relatively larger for the ake of calculation. NEWTON i choen a iteration method and default will be adopted in maximum iterate value and convergence tolerance that can be appropriately increaed if there i no convergence in calculation; 5Boundary etting (MODEL/SPECIAL BOUNDARY CONDITIONS menu): Two pecial boundarie mut be et in fluid model, of which one i free urface boundary, i.e. the water urface will be et a free urface boundary, while the other mean the water border line contacting the tank et a FSI boundary. Menu MODEL/BOUNDARY CONDITION/FSI CONDITION are opened and the tank wall contacting the liquid i elected a the FSI boundary. In addition, FSI boundarie with different number will be et if there are many tank. What mot important, FSI boundary numbering hould be correponding to that et in tructural model to avoid poible mitake. EXAMPLE ANALYSIS The numerical modeling analyi will be conducted to the damping of vibration effect of high-rie building tructure in which the TLD i et, whereby three model, i.e. FSI controlled model, noncontrol model and uncontrolled model, will be built for contrat. For the FSI controlled model, the aforeaid FSI function will be applied to perform the fluid-tructure interaction upon the influence of earthquake. In the FSI noncontrolled model the water in tank can be een a a rigid ma fixed on the tructure top only conidering the ma rather than the dynamic force of the water. The uncontrolled model mean there i no tank intallation on the roof, that i, the dynamic force a well a the ma of the water will not be taken into account. However, Story Range 1~10 11~20 Table 1. Parameter for tructural calculation model Structure Type Section Size (mm mm) Concrete Intenity Rank Elatic Modulu MPa Ratio of Reinforce -ment Beam C Column C Beam C Column C

5 it i the fact that the non-control model wa mot utilized in previou deign. What more, deigner till feel uncertain about whether the TLD in tank play the role of damping or aggravating in the coure of earthquake. Thu, the ecurity of calculating model adopted in deign can be attained through the contrat analye of FSI model and non-control model. Beide, the damping effect of TLD tank intallation on tructure roof can be informed via comparing FSI model and uncontrolled model, which can provide evidence for deciding whether to intall TLD tank. DESIGN OF CALCULATING EXAMPLES A high-rie regular frame tructure of 20 torie i targeted a the reearch object in calculating example, and the parameter for tructural calculation model are hown in Table 1. According to the modal analye, it can be found that the firt and econd mode frequencie of tructure uncontrolled model are 0.44 and 1.30 repectively, and by calculating the Rayleigh damp coefficientα = 0.206, β = Meanwhile, the calculating parameter of the water in tank can be diplayed a follow: kinematic vicoity 1.0e-3 N /m2, fluid bulk modulu 2.0e+9, denity 1000kg/m3. In order to explore the influence rule of different ma ratio, frequency ratio, etc. on damping of vibration effect, five group of calculating example a demontrated in Table 2 are deigned in thi paper, of which each calculating example include the aforementioned three model. The tank and water depth in example1-3 are the ame wherea with different number and the impact of different ma ratio on damping of vibration rule i invetigated. However, example 1, 4 and 5 examine the impact of frequency ratio on the damping of vibration rule. In addition, EL CENTRO work a the eimic wave input into example model 1-5. Still, wave TAFT i elected for calculating in example 1 to compare the impact of different eimic wave on damping of vibration effect. Alo, the built FSI FEM calculating model can be diplayed in Fig. 1, 2. The tructural model built in ADINA are hown in Fig. 1 while the fluid model in ADINA-F are given in Fig. 2. The non-control model ignifie tranforming the fluid unit into the plane olid unit and the rigidity value will be artificially et larger, whilt the uncontrolled model mean removing the tank and the model figure will be omitted due to the lack of pace. Example Numbering (Group) Water Height( H ) Table 2. Deign of calculating example Tank Length (L) Tank Number H/L Shaking f w Structure f 1 f w / f 1 Ma Ratio % % % % % CALCULATING RESULTS EL CENTRO wave i firt input into the five calculating example to analyze FSI dynamic interaction. Fig. 3 preent the haking diagrammatic ketch of the tructure-fluid ytem at a moment and from the time hitory repone animation of earthquake, it i dicovered that the haking direction of the water in tank i uually oppoite to that of tructure. Hence the damping force of the ytem mainly derive from the revere dynamic preure of the water in tank. Neverthele, TLD tank with varied ma ratio and frequency ratio will generate different hydrodynamic preure, o Table 3 illutrate the damping ratio reult of diplacement peak and acceleration peak on top floor of example1-5. And it can be een from Table 3 that after intalling TLD tank, compared with noncontrol and uncontrolled model, the tructural earthquake repone of model FSI will be reduced by 10-30%. In other word, the damping ratio of top-floor diplacement for non-control model i higher than that of uncontrolled model while the damping ratio of top-floor acceleration i lower than that of uncontrolled model. In accordance with example 1-3, when the frequency ratio i the ame, the

6 larger the ma ratio, the better the damping effect i. And in light of example 1, 4, 5, when the ma ratio i the ame, the cloer to 1 the frequency ratio, the better the damping effect i. Beide, the diplacement damping ratio in example 1 hould be larger than that in example 4, while it acceleration damping ratio hould be omewhat lower than that in example 4. Still, the reult from example1a and 1 reveal that the damping effect will be different with different eimic wave, and the damping ratio of top-floor diplacement of wave TAFT i higher than that of EL CENTRO, which can probably be attributed to the predominant period of TAFT i cloer than that of EL CENTRO to the firt natural vibration frequency 0.44 of tructure. (a)example1 (b) Example 2 (c) Example 3 (d) Example 4 (e) Example 5 Fig.1 Structural model of example 1-5( Module ADINA ) (a) Example 1 (b) Example 2 (c) Example 3 (d) Example 4 (e) Example 5 Fig.2 Fluid model of example 1-5( Module ADINA- F ) (a)example1 (b) Example 2 (c) Example 3 (d) Example 4 (e) Example 5 Fig. 3 Shaking of the fluid-tructure ytem at a moment in example 1-5( Wave EL CENTRO )

7 Table 3. Diplacement and acceleration reult of top floor in example 1-5(Wave EL CENTRO) FSI Model Non-control Model Uncontrolled Model Example Diplacement Acceleration Diplacement of Acceleration of of Top Floor of Top Floor Top Floor Top Floor Number d(m a Damp Damp Damp Damp ) (m/ 2 ) -ing a -ing -ing a -ing d(m) Ratio (m/ 2 d(m) ) Ratio Ratio (m/ 2 ) Ratio (%) (%) (%) (%) a Note: Example 1-5 input with wave EL CENTRO while example 1a with wave TAFT EVALUATIONS OF THE RESULTS The calculating reult of FSI fluid-tructure interaction can be contrated with previou tet rule to check the reaonability. And the above finding demontrate: (1) when the frequency ratio i the ame, the larger the ma ratio, the better the damping effect i; (2) when the ma ratio i the ame, the cloer to 1 the frequency ratio, the better the damping effect i; (3) when the predominant frequency of the input eimic wave get cloer to the ground frequency of tructure, the better the damping effect become. And the firt and the third can be verified by prior tet reult in reference (Li, H.N., Liang, Q.Z., Qu, C.Z., Z.N., 1999.), while the econd proved in reference (Wei, C. M., Z.N., Jin, J.Y., Chen and J.H., Chen, 2002.). However, the Simplified Centralized Ma Method propoed by HOUSNER(Houner, G.W ) wa often employed in preceding TLD damping analye. In thi way, two haking effect of equivalent ma with different joining form i applied to imulating the hydraulic preure of tank wall caued by the fluid in tank---one of the ma i linked with rigid bar and rigid tank wall, whilt the other with pring. And the detailed choice of parameter can be een in reference (Houner, G.W ). For the condition in example 1, Simplified Centralized Ma Method i ued to achieve model of hydrodynamic preure, inducing the horizontal diplacement peak of top floor m. That mean there i no damping effect yet with the acceleration peak 5.19m/ 2 and damping ratio 5.5% revealing the larger repone than that of uncontrolled model. Alo, Fig. 4, 5 preent the contrat between FSI coupling calculation, centralized ma diplacement and acceleration time hitory repone. And compared with FSI, the trend of diplacement and acceleration time hitory repone reulting from Centralized Ma Method appear the ame, yet with quite different peak. Thereby, although the analyi model of Centralized Ma Method concluded from tet finding for few ingleor multiple-tory building ha been applied to analyzing the TLD damping effect of high-rie building, the accuracy i likely to be relatively low. Thu, it i more reaonable to apply FSI eimic repone analyi baed on fluid-tructure interaction to analyzing TLD damping of vibration effect.

8 d(m) T() FSI Method CM Method a(m/ 2 ) FSI Method CM Method Fig.4 Comparion of the diplacement time hitory of the top Fig.5 Comparion of the acceleration time hitory of the top point of tructure with of model with two different mothed point of tructure with of model with two different mothed CONCLUSIONS Grounded on calculating with fluid-tructure interaction and model building in oftware ADINA, ADINA i applied in thi article to conducting the eimic repone analyi of fluid-tructure interaction in the high-rie frame tructure controlled by TLD. Under thi circumtance, the damping rule of high-rie frame tructure i attained, i.e. when the frequency ratio i the ame, the larger the ma ratio, the better the damping effect i; when the ma ratio i the ame, the cloer to 1 the frequency ratio, the better the damping effect i; when the predominant frequency of the input eimic wave get cloer to the ground frequency of tructure, the better the damping effect become. In the meantime, thee reult are alo compared and checked with earlier tet rule and Simplified Centralized Ma Method. And it i found that it i a tendency to apply FSI Method of fluid-tructure interaction to analyzing TLD damping of vibration effect in a more definite ene phyically. REFERENCES ADINA R&D. (2001). ADINA Theory and Modeling Guide. ADINA-F, 235~262. ADINA R&D. (2001). ADINA Uer Interface Uer Guide, USA. ADINA R&D. (2001). Theory and Modeling Guide. ADINA, USA, 1. Houner, G.W. (1957). Dynamic Preure on Accelerated Fluid Container, Bull Seim Soc. Am. 47(1): Li, H.N., S. Yan and L.G., Jia. (1995). Control of reearch progre by the damping tructure of TLD, Earthquake Engineering and Engineering Vibration, 15(3), Liang, Q.Z., J.M., Xiong and Q.H., Huang. (2002). A review on dynamic repone control of tall building and high-rie tructure by tuned liquid damper(tld), World Earthquake Engineering, 18(1), Qu, C.Z., Z.N., Jin and Y.S., Zhao et al. (1999). Application tet of TLD ytem in tructural damping of vibration, Journal of Northeat China Intitute of Electric Power Engineering, 19(4),3-58. Wei, C. M., Z.N., Jin, J.Y., Chen and J.H., Chen. (2002). The parametric analyi and optimization of MTLD ytem, Journal of Northeat China Intitute of Electric Power Engineering, 22(3), Zhang, H., and Bathe, K.J., (2001). Direct and Iterative Computing of Fluid Flow fully Coupled with Structure, Computational Fluid and Solid Mechanic. Elevier Science. T()