Fig 1: Applications of Liquid Dampers

Researchers are studying new types of cost-efficient dampers for mitigating wind and earthquake induced vibrations in tall buildings and other structures like long span bridges and offshore structures. The most commonly used auxiliary damping device is the Tuned Mass Damper (TMD), which is based on the inertial secondary system principle, and consists of a mass attached to the building through a spring and a dashpot. Such systems have been implemented, for example, in the John Hancock tower in Boston and the Citicorp Building in New York City. A Tuned Liquid Damper (TLD) is a type of TMD where the mass is replaced by a liquid (usually water). Tuned Liquid Column Dampers (TLCDs) are a special type of TLDs relying on the motion of a column of liquid in a U-tube like container to counteract the forces acting on the structure. Damping is introduced in the oscillating liquid column through an orifice in the liquid passage. The damping, however unlike TMDs, is amplitude dependent, and thus the TLCD dynamics are non-linear. The advantages of TLCD systems include low cost and maintenance and most importantly, such containers can be utilized for building water supply, unlike a TMD where the dead weight of the mass has no other functional use. Some of the innovative applications for liquid dampers studied in the past were in ship stabilization, satellite stabilization and recently in building applications (Fig. 1).

At the NatHaz Modeling Laboratory at the University of Notre Dame, researchers are studying the design and development of the next generation of these liquid dampers for structural applications. Although, some applications have been made in Japan for these passive dampers, there are certain limitations, such as their inability to respond quickly to sudden loads and their inability to maintain the optimal level of damping at all levels of excitation. A controllable passive (or semi-active) system may be utilized to overcome the shortcomings of a passive system like a TLCD in which the damping is dependent on the level of excitation. Basically the controllable passive TLCD strives to maintain the optimal damping at all levels of excitation. Semi-active liquid column dampers are being studied which actively control the orifice induced forces. This short report highlights some of the key features of these dampers. The semi-active TLCD can boost the performance of the passive TLCD with fixed orifice by 15-25%. TLCDs require low or no maintenance as compared to traditional TMDs. A conventional TMD requires frictionless rubber bearings, special floor for installation, activation mechanism, springs, dashpots and other mechanical elements which drive up the cost of the vibration absorber. TLCDs, by the nature of their design, are low cost inertial devices with performances comparable to TMDs.

In the area of modeling of these dampers and determination of their optimal values, a considerable work has been done by the laboratory^1,2. Yalla and Kareem (1999) have presented a Sloshing-Slamming damper analogy for the tuned liquid sloshing dampers (Fig. 2). Tuned sloshing dampers are very easy to implement and do not require any sophisticated components. However, it is very difficult to tune them to their optimal parameters as the frequency of the damper increases nonlinearly with the amplitude of excitation. Similarly, the damping ratio of sloshing dampers also increases with the amplitude of excitation. Therefore, the optimal performance of these dampers under all excitations is not always guaranteed. One can still find optimal damping for the serviceability loading conditions, for e.g., in case of a 10-year recurrence interval wind speed. The damper performance will remain satisfactory around the design winds, however for winds exceeding or below the design conditions, the damper would be non-optimal. Experimental results indicate that at higher amplitudes, the TLD performance becomes more robust and less sensitive to proper frequency tuning.

Tuned Liquid Column Dampers, on the other hand, are described by a simpler mathematical model which makes them amenable for semi-active and active control. Moreover, it is feasible to induce oscillations in a liquid column rather than active sloshing in tanks. The damping in the TLCD can be controlled through the orifice. The orifice opening ratio affects the headloss coefficient which in turn affects the effective damping of the liquid damper. Proportional valves can be actuated by a voltage signal to obtain the required damping. The TLCD can be tuned by changing its frequency by way of adjusting the liquid column length in the tube. This is an attractive feature should the tuning become desirable in case of a change in the primary system frequency. Yalla and Kareem (2000a) have given design charts for the optimal absorber parameters under various excitation cases.

In order to adjust damping in the TLCD, two different types of valves are being investigated, namely, the ball valve and the butterfly valve shown below attached to the TLCD (Fig. 3). The valve supplier have provided the characteristic curves for orifice opening and the head-loss coefficient. A unique feature of the design is that these are true union valves, so one can take these off and fit a separate valve without disassembling the whole damper.

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The controllable passive strategy ensures that the damping is kept optimal at all levels of excitation for the TLCD. This strategy utilizes a semi-active gain scheduling type lookup table which can estimate the optimal coefficient of head-loss for a given level of loading. This can then be changed in the valve based on feedback from the sensors (Fig. 4(a)). The Semi-active control valve is shown in the Fig. 4(b). This control valve is a pneumatically actuated ball/butterfly valve with an additional solenoid valve for modulating the valve opening. The electro-pneumatic positioner uses a 4-20mA signal to change the valve position. The positioner modulates the flow of supply air and converts the input signal to a 3-15 psi air signal for proportional modulation of the valve. One of the advantages of these smart dampers is that even if the electric valve fails for any reason, the system still functions at some level of damping available for that valve setting.

Most applications are described in a detailed paper by Kareem et al (1999)³. Structural implementation of TLDs on structures was first done in Japan. Examples of TLD-controlled structures include Nagasaki Airport tower, Yokohoma Marine Tower, Shin Yokohoma Prince Hotel and Tokyo international airport tower. (Fig. 5(b)). TLCDs have been implemented for Higashi-Kobe cable-stayed bridge to reduce wind-induced vibrations of the bridge towers (Fig 5(c)). A LCD-PA (liquid column damper with pressure adjustment) has been installed in the Hyatt Hotel, Osaka. Recently, tuned liquid dampers have been proposed in passive and active forms for the planned Millennium Tower in Tokyo Bay, Japan (Fig. 5(a)). A TLD is also planned to limit the wind induced motion of the proposed Shanghai Financial Trade Center, in China. Liquid vibration absorbers are also used in tall chimneys. These have been proven to be economical, can be easily adjusted to the physical and architectural requirements, and are extremely fail-safe.

3. Kareem, A., Kijewski, T. and Tamura, Y., (1999), "Mitigation of Motions of Tall Buildings with Specific Examples of Recent Applications," Wind and Structures: An international Journal, Vol. 2, No.3, pp. 201-251.

The various TLCD configurations discussed earlier are being tested in the laboratory. Coupled structure-liquid damper experiments are useful in understanding the merits and disadvantages of each damper. Figure 6 (b) shows the testing of TLCDs and TLDs. Innovative testing schemes such as Hardware-in-the-loop strategy is also being studied with regard to liquid dampers. In this method, a virtual structure is simulated on the computer and a real-time dynamic coupled structure-damper analysis can be conducted without the use of an actual structure or heavy actuators to load the structure.

Yalla and Kareem (2000b)⁴ have also looked into the beat phenomenon associated with a coupled structure-damper system (Fig. 7(a)). Beat phenomenon is an undesirable effect due to which energy can be transferred from the secondary system (i.e., damper) back to the primary system (i.e., the structure). Laboratory experiments have shown that the semi-active TLCD can boost the performance of the passive TLCD with fixed orifice by 15-25% (Fig. 7(b)). This justifies the additional costs of using sensors and controllable valves into the system2.

Fig. 7 Structure-TLD response to free vibration (b) -TLCD response to random loading

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**Table 1: Comparison of different systems for a wind excited buildng**
	RMS disp. U10 = 15 m/s (cm)	RMS disp. U10 = 20 m/s (cm)	RMS disp. U10 = 25 m/s (cm)	RMS accl U10 = 15 m/s (mg)	RMS accl U10 = 20 m/s (mg)	RMS accel U10 = 25 m/s (mg)
Uncontrolled	2.37	5.97	12.19	3.79	9.57	19.56
Stiffened Structure	1.54 (30.4 %)	3.87 (35.1 %)	7.92 (35 %)	2.95 (22.1 %)	7.44 (22.2 %)	15.23 (22.1 %)
Passive system	1.73 (23.4 %)	3.93 (34.1 %)	7.17 (41.2 %)	2.69 (29 %)	6.20 (35.2 %)	11.56 (40.9 %)
Semi-Active System	1.26 (40.6 %)	3.18 (46.7 %)	6.49 (46.7 %)	2.07 (45.4 %)	5.22 (45.4 %)	10.69 (45.3 %)

Table 1 shows some typical results for a wind excited building. The passive system has been designed for design speed of 30 m/s and therefore, at lower speeds, the semi-active system does better than the passive system (which is at non-optimal danping).

Some of the commonly used terms/parameters for liquid dampers are discussed briefly:

Mass ratio: is an important parameter, defined as the ratio of mass of the damper to the first modal mass of the structure. For civil engineering applications, this is typically of the order of 1-2%. Space requirements dictate the actual mass ratio of the dampers. Typically 1% mass ratio for a well designed damper can provide upto 50% reduction in response.

Frequency ratio: is defined as the ratio of the frequency of the damper to the frequency of the structure. Typically, auxiliary devices are tuned to the first modal frequency of the structure. A good rule of thumb is for mass ratios of 1% to have a tuning ratio of 0.99.

Damping ratio: This is the effective damping ratio of the damper. For a regular TMD, this represents the linear damping ratio. However, for liquid dampers this varies nonlinearly with amplitude. A good rule of thumb is to have about 4.5% damping ratio for mass ratios of 1%. In case the TLD is not able to provide that much damping at the design speed, one can add baffles, beads and other protrusions to artificially add damping. However, too much of damping again leads to non-optimal damping and reduces the damper performance.

Length ratio: is defined as the ratio of length of the horizontal part of the liquid in the U-tube to the total length of water in the U-tube. The total length of liquid column is determined by the frequency of the damper. To get an idea of the size of these tubes, a building of 0.16 Hz natural frequency (6.3 sec time period) requires 20 meters of liquid. Typical length ratios are between 0.6-0.7. This means the designer needs about 10 meters of vertical tube (5 m on each side and 5 meters for liquid oscillations to develop) and 12 meters of horizontal tube.

Area ratio: is the ratio of the cross-sectional area of the horizontal part of the U-tube to the cross-sectional area of the vertical part of the tube. In most cases it can be kept as unity. However, additional architectural benefits can be derived from the configuration with variable area ratio. The total cross sectional area can be calculated once the length of the liquid column and the mass ratio have been determined.

Coefficient of Head-loss: The damping introduced by the orifice/valve in the TLCD, by it very nature, is quadratic in nature. however, equivalent linearization can yield approximate linear damping at various amplitudes of excitation. The design process needs to calculate the variation of this head-loss coefficient for the particular valve used as a function of the valve angle opening. Figure 8 shows the variation of the dynamic magnification factor as a function of the coefficient of head-loss and the frequency ratio.

Multiple dampers: Multiple units of liquid dampers can be used to distribute the dampers spatially. In this regard one can have either multiple-tuned or multiple-slightly-detuned configurations. The proposed multiple-slightly- detuned damper configurations are known to have more robust dynamic characteristics, i.e., improved effectiveness under variations in frequency and damping of the primary system.

Thus the major focus of this research is the design and development of smart liquid dampers to maintain optimal damping levels under different loading conditions. On a more practical note, these next generation of liquid dampers would herald the new paradigm of vibration control in the design/construction industry. The NatHaz laboratory has been working on all aspects of these dampers, namely, the modeling, design, construction, algorithms, testing and cost and reliability analysis. The researchers would like to acknowledge the support given by the National Science Foundation under the NSF Structural Control Initiative.

1.Kareem, A., (1993), "Liquid Tuned Mass Dampers: Past, Present and Future," Proceedings of the Seventh U.S. National Conference on Wind Engineering, Vol. I, Los Angeles.

2.Kareem, A. and Kline, S., (1995), "Performance of Multiple Mass Dampers under Random loading," Journal of Structural Engineering, ASCE, Vol.121, No.2, 348-361.

3.Kareem, A. and Sun, W.J., (1987), "Stochastic Response of Structures with Fluid-containing Appendages," J. of Sound and Vibration, 119(3), 389-408.

4.McNamara, R. J., (1977), "Tuned Mass Dampers for Buildings," Journal of Structural Division, ASCE, 103, 9, pp. 1785-1789.

5.Sakai, F. and Takaeda, S. (1989), "Tuned Liquid Column Damper - New Type Device for Suppression of Building Vibrations," Proceedings International Conference on High Rise Buildings, Nanjing, China, March 25-27.

6.Yalla, S.K., Kareem, A., and Kantor, J.C. (2000), "Semi-Active Tuned Liquid Column dampers," submitted to Engineering Structures.

7.Yalla, S.K., Kareem, A., and Abdelrazaq, A. K. (2000), "Risk-based Decision Analysis for the Building Serviceability", Proceedings of the 8th ASCE Speciality Conference on Probabilistic Mechanics and Structural Reliability, University of Notre Dame, July 24-26.

8.Yalla, S.K., Kareem, A. and Kantor, J.C. (1998), "Semi-Active Control Strategies for Tuned Liquid Column Dampers to Reduce Wind and Seismic Response of Structures," 2nd World Conference on Structural Control, Kyoto, June 28-July 2nd.