Distributed
TLDs in RC floors and their vibration reduction efficiency Earthquake Engineering and Engineering Vibration, 2008, 7(1): 107112. ABSTRACT: A novel distributed tuned liquid damper (DTLD) to reduce the vibration of structures is proposed in this paper. Its basic working principle is filling of the empty space inside the pipes or boxes of the castinsitu hollow reinforced concrete (RC) floor slabs with water or other damping liquid. Hence these pipes or boxes will work as a series of small TLDs inside the structure. Thus, no additional spaces are needed for TLDs whilst the damping ratio of the whole structure is obviously increased. Numerical simulation with the fluidstructure coupled effect is carried out to evaluate its vibrationreduction effect. The results indicate that distributed TLD can considerably increase the damping of the building and thus reduce the vibration. Some parameters influencing the vibrationreduction are also studied. Keywords: distributed tuned liquid damper (DTLD), fluidstructure interaction (FSI), vibration reduction, hollow floor slab 
1 Introduction Tuned liquid damper or TLD has been widely used in structure vibration control (Li 2005). Currently common installation pattern of TLDs in structures is to concentrate one or several TLDs, which have a shape of cubic boxes, cylinders or Ushape tubes, in one or several specificallychosen floors. According to existing research and application, TLDs show good performance in vibrationcontrol with a relatively acceptable cost (Qian 1995, Jia 2000, Jia 2002). However, some disadvantages limit their further applications which are as follows: (1) Big TLDs occupy too much architectural space, which often obstructs the free space for normal services of the building. They largely increase the burden of the structure to support them, which results in obvious cost increase. However, smaller TLDs with less total mass can not successfully meet the demands of vibration reduction. (2) The natural frequency of TLD needs to be tuned close to that of the structure in order to make full use of its vibration control ability (Jia 2006). But the natural frequencies of structures are often difficult to estimate accurately and will also change during their service life. In the past few years, castinsitu hollow floor slab has become popular in construction practice for its advantages such as lowweight, noise insulation and good structural properties (Xu 2005). PVC or rubber tubes or boxes are often used as the hollow moulds while they themselves are also good liquid containers. Filling such spaces inside the hollow floor slabs with proper amount of water or other damping liquid will turn the floor to be a system of distributed TLD (Fig. 1), which is expected to considerably increase the damping of the structure. The following advantages of such distributed TLD can be expected. (1) Setup Flexibility. The hollow volume ratio of currently used hollow floor slabs can be up to 66~75% or more, which ensures enough potential space to setup distributed TLD, and with a relatively large total mass of TLDs, the damping of the structure will be increased obviously. Moreover, such TLD can be embedded into not only floor slabs but also huge girders or columns in some highrise structures and thus further increase the structure damping. 
(2) No extra architectural space will be occupied by such TLD and their distributing nature makes it easier for structures to carry their load as compared with the traditional concentrated TLD. (3) Wide frequency range. Besides focusing on providing kinematical reaction force while the structure shaking of traditional TLDs, the distributed TLD aims at increasing the damping of the whole structure and to decrease its response. As a result, the vibrationreduction effect of distributed TLD will not be as sensitive to the structure’s natural frequencies as the traditional TLDs. (4) It’s easy to construct since almost the same construction procedure as normal hollow floor can be used. Furthermore, no extra cost is needed. (5) Fire extinguishing ability of buildings will be also increased if the water inside the floor slabs for TLD can be properly used in case of fire.
This paper aims at verifying the concept of such distributed TLD and theoretically proving its feasibility by means of numerical simulation which considers the fluidstructure interaction (FSI). Further research is being conducted to evaluate the effect of such distributed TLD experimentally. 
2 Fluidstructure interaction (FSI) simulation In structures containing TLDs, the structural vibration causes the sloshing of TLDs liquid and the sloshing will consume energy and impose reaction force on the structure. Different structural vibration will cause different liquid sloshing and thus different influence over the structure. Over decades, many practical simplied models to implement TLDs in sturcutural analysis have been proposed. In such models, TLD was often modeled as concentrated equivalent mass with elastic springs and viscous dampers, which would provide control forces over the structure. (Housner 1957, Jia 1998, Cai 1998). In recent years, with the development of computational mechanics as well as the hardware and software environment, fluidstructure interaction (FSI) has become a practical method in numerical simulations of structures with TLDs. In an FSI simulation, the following three modules are often included (Wu 2003). (1) Liquid domain: liquid is often treated as incompressible. (2) Solid domain: Material and geometrical nonlinearity can be considered. (3) Fluidsolid interface: The fluidsolid interface is the key problem in FSI simulation because different formulations are commonly adopted for liquid and solid. Euler formulation is used for liquid while Lagrange formulation for solid. Arbitrary LagrangianEulerian (ALE) formulation is often practical in solving such problems (Yue 2000). 
The following analysis procedures are generally needed. (1) Obtain the liquid pressure imposed on the structure surface by taking the undeformed structure as the liquid boundary and calculating the liquid field. (2) Apply the force to deform the structure and modify the liquid boundary and mesh according to the structural deformation, and then recalculate the liquid pressure. (3) Repeat the above (1) and (2) until the difference of liquid pressure between the two calculations become smaller than the tolerance. Detailed discussion on conducting FSI simulation based on ANSYS has already been made in (Lu 2005) and its feasibility been proved. Similar simulating method will be used in this paper to evaluate the vibrationreduction effect of distributed TLD. 3 Vibrationreduction effect of a single TLD 3.1 Realistic model Fig. 2 demonstrates a simplified model of a hollow floor slab with a height of 250mm containing a TLD with a height of 150mm. The hollow volume ratio and the slab height fulfill the requirement of relevant Chinese specification (CECS 2004). The water depth is 2/3 of the hollow height (that is 100mm) and the overall water mass ratio is 31%. The structure stiffness is represented by a horizontal spring and the bottom of the slab can slide freely in the horizontal direction. In analysis, the slab is pulled out against the spring to a certain distance and suddenly released to make it vibrate naturally. The damping of this system and the vibrationeffect of the TLD can be obtained by examining the declination of the vibrating amplitude.
3.2 Numerical model 
One meter width of the hollow floor shown in Fig. 2 is simulated as a 2D numerical model in ANSYS. The liquid is modeled by the volume of fluid (VOF) technique implemented in ANSYS, which is capable of modeling the liquid surface vibration and the change of liquid height, and can also transfer the liquid pressure to the structure. Water is used for the TLD liquid here with a density of 1000kg/m^{3} and a kinematical viscosity of 1×10^{6}m^{2}/s. The container walls are modeled by beam elements. Fluidsolid interface is arranged between the container walls and liquid elements. The structure natural frequency can be adjusted by changing the spring stiffness. Initial displacements of 0.01m and 0.05m are imposed on the floor slab in two different cases respectively. To improve the numerical convergence, a 1% initial damping is assigned to the structure. 3.3 Simulation results The declining phenomena of the natural vibrations in cases with different TLD arrangement are demonstrated in Fig. 3. Compared with empty hollow space, the vibration amplitudes decline much faster when some water is in the hollow space. The floor equivalent damping ratios of different cases are calculated according to such declining phenomena and listed in Table 1. The equivalent damping ratio has been increased from the initial value of 1% to 2.4~2.8%. The mechanism of such an increase in the equivalent damping ratio lies on the energydissipating ability of sloshing water (Fig. 4) since water has some viscosity itself.

4 Vibrationreduction effect of DISTRIbUTED TLD 4.1 Numerical model Fig. 5 demonstrates a 4story steel frame with castinsitu hollow floor. Its first natural frequency is 1.78Hz and the initial structure damping is taken to be 1%. The height of the overall RC slab and the hollow space are 250mm and 150mm, respectively. The ElCentro earthquake record is input at the bottom of the structure. The following parameters are discussed in the simulation.
(1) Mesh density. It’s wellknown that the results of finite element analysis rely on the mesh density. To verify the mesh convergence, different element sizes (3mm and 5mm) are adopted to model the liquid. (2) Liquid depth. Three cases with different liquid depths (Empty; 75mm and 100mm) are carried out. (3) Length of hollow space. The length of a single liquid container changes from 2m to 4m. The weight of RC floor slabs is also adjusted in different cases to keep the overall weight of the controlled structure to be constant. 4.2 Results and discussions Fig. 6 shows the influence of element density on the simulation results. Since little effect can be seen of element density, the following simulations are all based on 5mm liquid element to save computational cost. The top floor displacement histories for models with different TLD arrangements are demonstrated in Fig. 6 and 7. Major statistic results are shown and compared in Fig. 8, where the depth in yaxis labels indicates the depth of liquid. It can be seen that the structure displacement response is decreased by 30% no matter in term of maximal displacement or displacement variance, which is equivalent to increase the structure damping ratio from 1% to 3~5%.

5 Conclusions The distributed tuned liquid damper (DTLD), which is developed by filling the castinsitu hollow floor slab with proper amount of liquid, is proposed in this paper to reduce the structure vibration. FSI simulation based on ANSYS is carried out to prove its effectiveness as well as feasibility. Results show that DTLD can considerably increase the structure damping. Thus it reduces the structure vibration without costing too much. Besides it does not occupy any architectural space. Further research on more detailed parameters, such as the optimal amount of liquid, the positions and arrangement of DTLD in the structural system and the inner configuration of the liquid container, is being conducted. References Cai, D.Y., Li, A.Q., Cheng, W.R. (1998) Study on equivalent mechanical model of tuned liquid damper. Earthquake Engineering and Engineering Vibration, vol. 18, no. 1: 8087. CECS 175 (2004) Technical specification for castinsitu concrete hollow floor system. Beijing. Housner, G.W. (1957) Dynamic pressure on accelerated fluid containers. Bulletin of Seismic Society of America, vol. 47, no. 1:1535. Jia, Y., Li H.N. (1998) Simulation of dynamic liquid pressure for tuned liquid damper. Earthquake Engineering and Engineering Vibration, vol. 18, no. 3: 8287. Jia, Y., Li, H.N., Li, Y.C. (2000) An actual computing example for a tall structure using TLD to reduce vibration. Earthquake Engineering and Engineering Vibration, vol. 20, no. 2: 135140 Jia, Y., Li, H.N., Song, Y.S. (2002) Simplied algorithm of tuned liquid damper for seismic response of fixed offshore platform. Earthquake Engineering and Engineering Vibration, vol. 23, no. 3: 160164 Jia, Y., Zhao, L., Yu, F. (2006) Effect of different parameters on TLD vibration control. Earthquake Engineering and Engineering Vibration, vol. 26, no. 4: 226230 Li, H.N., Jia, Y., Li, X.G. et al (2000) Study on vibration control using TLDs for multimode reponse of tall flexible structures. Earthquake Engineering and Engineering Vibration, vol. 20, no. 2: 122128. Li, H.N. et al. (2005) Structure vibration and control. China Architectural and Industrial Press, Beijing 
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