Liquid damper for suppressing horizontal and vertical motions

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1 Computational Methods and Experimental Measurements XII 569 Liquid damper for suppressing horizontal and vertical motions M. Pirner & S. Urushadze Institute of Theoretical and Applied Mechanics Academy of Sciences of the Czech Republic Abstract The new type of passive tuned liquid damper (TLD) relies on the motion of liquid inside a movable rectangular tank with two degrees of freedom (horizontal displacement and rotation). The authors study the influence of vessel horizontal motion and rotation on the damping of the vertical and horizontal vibrations of the footbridges. Keywords: liquid damper, damping, effectiveness of a liquid damper, vibration table, harmonic excitation. 1 Introduction The motion of liquids in containers has been studied in recent decades (see [1]) and simplified analysis been made on rectangular and cylindrical tanks [], [1]. Numerous papers have been written on the motion of liquids both theoretically and experimentally; the studies being based on linear or nonlinear potential flow theory with the authors usually neglecting the influence of fluid viscosity (for details see [5]). This paper expands the application of sloshing dampers, formerly used only for the damping of horizontal motions of structures, to include the damping of rotary motion. The principal objective of this research was the ascertainment of the effectiveness of slosher damper damping. The verification of the application of Abramson s computing model [11] and the possible application of slosher damper to the damping of the motions of bridges and footbridges was also investigated.

2 570 Computational Methods and Experimental Measurements XII Experiment Few researchers have reported a fair agreement between experiments and the theoretical solution with some of them confirming the effectiveness of TSD (tuned sloshing damper) and the comparability with TMD (tuned mass damper). Despite this, we carried out the extended program of experiments, especially the combination of translative and rotation motion of container..1 Experiments of other authors One of the oldest papers concerned with the experimental examination of fluid dynamics in a moving container is probably that by Housner [1]. The motion of fluids in two rectangular basins differing in dimensions was studied in detail by Lepelletier and Raichlen [], who defined six dimensionless parameters defining the motion of liquid surface. Modi et al. [] studied energy dissipation through the sloshing motion of liquid in a torus container and the influence of dimensionless parameters (Weber and Froude numbers) on the optimum liquid level height. Fujino et al. [1] studied experimentally the conformity of the linear wave theory (according to Lamb, 19) with reality in a rectangular container. Verhagen and Wijngarden [] verified theoretical results by means of a rectangular tank rotating around the axis situated in the plane of its bottom.. Apparatus enabling the excitation of two tank motions Our objective was to design apparatus that enables the study of translative and rotation motions. Fig. 1 shows the principal components of the apparatus, which enables the simultaneous excitation of the translative and rotary motions of a 500 x 500 x 500 mm tank (t). The tank is supported by two arms (R) connected by means of axis (o) to a lattice structure. This structure has four mobile supports (b) supported by runners (f), fastened to a vibration table (tb) driven by a MTS cylinder (concealed by the table in the picture). The table motion is picked-up by sensor S 1 (and controlled by sensor S ), with the force between the vibration table and the lattice structure measured by sensor S. The rotation moment is converted by a lever system (see Fig. ) into the force couple according to (1), I R M s = Fs R1 (1) R which is picked up by sensor S. The position of the tank can be altered vertically within the length of the arms (R 1, R ) so that it is possible to determine the influence of the position of the liquid centroid with reference to the centre of rotation around the axis (o). The mobile supports (b) can be turned together with the whole apparatus so that the translative motion of the tank in the required direction can be selected. The mass of the part of the apparatus that generates the forces of inertia during horizontal motion is 7 kg.

3 Computational Methods and Experimental Measurements XII 571 Figure 1: The principle components of the apparatus. Figure : Schematic representation of tank support, arms R 1 /R and force sensor F s 1 (axonometry). The lever system (Fig. ) can control the rotation frequency of the tank by means of two rulers, R 1 and R. The mounting of the tank (t) by means of bearings guarantees the logarithmic decrement of rotation (of the empty tank) in the amount of ϑ 0,0. The rotary motion or the translative motion of the tank and consequently, of the liquid can be monitored separately, because the tank rotation can be locked. The phases between the motion of the tank and that of the liquid were ascertained within the scope of the frequency range of 0,5 and Hz by means of floater sensors.

4 57 Computational Methods and Experimental Measurements XII The floater motion is transmitted by a lever arm to the core of a relative induction sensor fastened to the tank. The floater motions are mutually independent so that it is possible to ascertain the states when the liquid waves are three-dimensional. Presentation of results The apparatus described in Section. was used for experiments with a tank, the dimensions of which (500 x 500 x 500 mm) conform to the required dimensions of the dampers designed for the footbridge..1 Translative motion of a rectangular tank With locked rotation of the tank, the theoretical analysis of natural frequencies of the translative movement of the liquid was verified and an excellent agreement ascertained. The dependence of the excitation force (RMS [N]) on the overall mass of the liquid, i.e. on the sum m = m 0 + m 1 in the frequency range 0.5 to Hz for three magnitudes of the double amplitude of the excited motion was obtained.. Rotation motion of the tank The testing apparatus described in Section. makes it possible to monitor the motion of the liquid in the tank and to determine natural frequencies. Fig. shows the frequencies of the tank response. The variable parameters include: liquid quantity, tuning of the rotation motion of the tank and the position of the liquid centroid with regard to the centre of rotation. Fig. also shows the dependence of the natural frequency of the translative vibrations of the liquid on its quantity. The curves in Fig. are labeled as follows: 1 natural frequencies of the translation motion. lowest natural frequency of the rotation motion: the center of rotation,5 mm below the bottom of the container, R 1 /R = 0,9. higher natural frequency of the rotation motion; (the same conditions as ). lowest natural frequency of the rotation motion: the center of rotation 86,5 mm above the bottom of the container, R 1 /R = 0,69. 5 higher natural frequency of the rotation motion; (the same conditions as ). 6 lowest natural frequency of the rotation motion: the center of rotation 0 mm above the bottom of the container, R 1 /R = 0,05. 7 higher natural frequency of the rotation motion; (the same conditions as 6). 8 lowest natural frequency of the rotation motion: the center of rotation 111 mm below the bottom of the container, R 1 /R =,7. 9 higher natural frequency of the rotation motion; (the same conditions as 8). 10 lowest natural frequency of the rotation motion: the center of rotation,5 mm below the bottom of the container, R 1 /R =,7. 11 higher natural frequency of the rotation motion; (the same conditions as 10)

5 Computational Methods and Experimental Measurements XII 57 1 hydraulic jump, which travels between the walls of the container: the center of rotation is in the bottom of the container (after [] linear theory do not agree with our experiments)., (),5 9 1 () f [Hz] 1 5 1, (1) 6 0, ,1 0, 0, 0, 0,5 h [m] Figure : Dependence of frequency on the height of the water.. Translative and rotation motion of the rectangular tank The experiments with the tank excited by a horizontal force with the selected double-amplitude of horizontal displacement (8 1 mm) and the possibility of free (uncontrolled) rotation yielded the values of response: the spectra show distinctly two peaks, the first belonging to the motion of the liquid and the other to the frequency of tank rotation.

6 57 Computational Methods and Experimental Measurements XII Effectiveness of a liquid damper The effectiveness of a liquid damper installed on a real structure is usually expressed by the ratio of the displacements of the selected part of the structure in two states: 1 damper excluded, damper active. Note: If the response is of random character, the derived damping is expressed by the square root of the logarithmic decrement; if the response is of harmonic character, the derived damping is expressed by the first power of the logarithmic decrement. In our case the water damper was tested in the apparatus described in Section., the mobile (excited) part of which weighs 7 kg and the tank of which was designed on 1:1 scale to the damper intended for the actual structure. The effectiveness of our damper is expressed by the relation, RMS FHO ε = () RMS F0 where: F is the harmonic excitation force needed for the excitation of the HO required amplitude of the horizontal motion of the appliance with water. F 0 is the harmonic excitation force needed for the excitation of the required amplitude of horizontal motion of the appliance without water. The effect of friction in runners (f) is not included. The effectiveness is calculated from relation of exciting forces only..1 Liquid damper effectiveness during translation movement of the tank in direction α 0 As stated in Section., the mobile support (b) in Fig. 1 can be turned together with the whole support so that the required direction can be selected. During simple translation movement of the tank in the directions α=0,.5 and 5, the RMS values of the excitation forces were ascertained. The tank was filled with water in the steps of 5 l, 50 l, 75 l. Fig. shows the RMS of excitation force with double amplitude of the base deviation of 1 mm plotted against water quantity and the angle α. Fig. 5 shows the effectiveness of the damper filled with water under resonance plotted against the angle α during translation movement.. Damper effectiveness plotted against the dynamic viscosity of the liquid In standard conditions water cannot be used for the application of liquid dampers to bridge structures. Therefore, we have tested various non-freezing liquids such as methanol, glycerol and water (M, G, H). It was verified that the damper effectiveness decreases with increasing dynamic viscosity η when η = ν ρ [Pa s] () where ν is the kinematic viscosity [m s -1 ] ρ is the density [kgm - ].

7 Computational Methods and Experimental Measurements XII α =,5 0 l 5 l 50 l 75 l RMS F exc [N] ,5 0,6 0,7 0,8 0,9 1 1,1 1, 1, 1, 1,5 1,6 1,7 1,8 1,9,1,,,,5,6,7,8,9 frequency [Hz] Figure : Dependence of excitation force on total liquid mass, α=,5. ε l 50 l 75 l 0 0,5 5,5 0 α [ ] Figure 5: Effectiveness of the direction α. Fig. 6 shows the effectiveness of the damper filled with liquid plotted against liquid quantity (in terms of the weight of the liquid) and against the method of tank support (R 1, R ). It can be observed that the use of methanol (η=0.58) is more effective than the use of glycerol (η=180). Fig. 7 demonstrates the ratio RMS FHO RMS F 0 plotted against water quantity in the tank for a simple motion with a horizontal amplitude of 1 mm I I and 8 mm. The ratio of RMS FS / RMS F HO S in the same figure represents the force in sensor S (see Fig. 1).

8 576 Computational Methods and Experimental Measurements XII ε Effectiveness R 1 =, R =1,7 p p =15,5 mm R 1 =1, R =,75 p p =15,5 mm R 1 =1, m =5 kg R R =,75 1 =, R p z =9,5 mm =1,7 p p =79 mm m =5 kg R 1 =1, R =,75 p z =15 mm R 1 =17,5 R =7,5 p z =9,5 mm m =5 kg R 1 =, R =1,7 p p =79 mm R 1 =1, R =,75 p p =15,5 mm R 1 =17,5 R =7,5 p z =9,5 mm m =5 kg R 1 =1, R =,75 p p =79 mm m =5 kg R 1 =1, R =,75 p z =15 mm m m methanol water glycerol p p p z 0 0,58 1,0 180 Dynamic viscosity η Figure 6: Effectiveness of the direction α. (for curve ) RMS F s I H O / RMS F s I RMS FH O / RMS F (for curves 1,,, 5, 6, 7, 8) l 1. Horizontal motion, Vo=1 mm, - S, α =0.. Horizontal motion and rotation (gravity center upon the point of rotation), Vo=1 mm, - S, α =0. Horizontal motion and rotation (gravity center under the point of rotation), Vo=1 mm, - S, α =0. Horizontal motion and rotation (gravity center under the point of rotation), Vo=8 mm, - S, α =0 5. Horizontal motion, Vo=1 mm, - S, α =5 6. Horizontal motion, Vo=1 mm, - S, α =,5 7. Horizontal motion, hole 100%, Vo=1 mm, - S, α=0 8. Horizontal motion, hole 50%, Vo=1 mm, - S, α=0 Figure 7: Ratio RMS F / RMS F of a liquid damper. HO 0 5 Application to footbridges and bridges Footbridges, having very simple structural behaviour, are highly sensitive to dynamic loads because of their low bending rigidity mass, natural frequencies and damping [9], [10]. The vibrations of footbridges in the vertical and

9 Computational Methods and Experimental Measurements XII 577 horizontal planes arouse a feeling of discomfort in pedestrians; in the case of major amplitudes they may result in the damage to footbridge pavement. Such vibrations may be generated by pedestrians, by wind or vandalism; for this reason the footbridges were subjected to the research of these loads [6]. Experiments on the apparatus described in Section. have proved the possibility of damping the translative and rotation motions. 6 Conclusion This paper has shown that the sloshing damper is a device that will restrict effectively undesirable horizontal vibrations and, in case of adequately selected conditions of tank support, undesirable torsional vibrations also. The apparatus used for our experiments has made it possible to test the tank phenomena on an actual scale, which has made it possible to dispense with some model laws. In comparison with spherical or pendulum vibration absorbers [1, 1] the effectiveness of liquid dampers is lower, if the moving mass serves as a means of comparison. Due to its compactness, the concentrated mass of the pendulum or spherical dampers is more effective than the active mass of the liquid. Alternatively, the liquid vibration absorber is more advantageous. This is because it can be tuned easily to the actual frequency of the required vibration mode, which usually differs for the most varied reasons, from its theoretical value. The installation and execution of a number of tanks e.g. in the extreme box beams, is easier to design than the location of a number of ball dampers. The authors of the paper are well aware that the generalization of the sloshing damper theory requires further analytical and experimental studies covering further these so far uninvestigated parameters, and are continuing their research in this field. Acknowledgements The authors acknowledge the co-operation of Messrs M. Černý, O. Vála and L. Krbec. The supports of grants GA AS CR B0710 and GA CR 10/05/066 are gratefully acknowledged. The identification code of the research project of the Institute of Theoretical and Applied Mechanics is AVOZ References [1] Fujino, A., Sun, L. & Pacheco, B.M., Tuned liquid damper (TLD) for suppressing horizontal motion of structures. Journal of Engineering Mechanics, 118(10), Oct [] Modi, V.J., Welt, F. & Irani, M.B., On the suppression of vibrations using nutation dampers. JWE and IA,, [] Verhagen, J.H.G. & Wijngaarden, L.van, Non-linear oscillations of fluid a container. Journal of Fluid Mechanics, (), pp , 1965.

10 578 Computational Methods and Experimental Measurements XII [] Lepelletier, T.G. & Raichlen, F., Nonlinear oscillations in rectangular tanks. Journal of Engineering Mechanics, 11(1), Jan [5] Kareem, A. & Sun, W.J., Stochastic response of structures with fluidcontaining appendages. Journal of Sound and Vibration, 119(), pp , [6] Pirner, M. & Fischer, O., Wind-induced vibrations of concrete stressribbon footbridges. JWE and IA, 7-76, pp , [7] Stráský, J. & Pirner, M., Stress-ribbon footbridges (in Czech). Special issue of the establishment Dopravní stavby (Constructions for Transport), Olomouc, 198. [8] Redfield, Ch., Kompfner, T. & Stráský, J., Stressed ribbon pedestrian bridge across the Sacramento river in Redding, California, USA. FIP XIth Int. Congr. on Prestressed Concrete, Hamburg, pp. 6-66, June [9] Simiu, E. & Scanlan, R.H., Wind Effects on Structures, Willey: New York, [10] Klöppel, K. & Thiele, F., Modelversuche in Windkanal zur Bemessung von Brücken gegen Gefahr Wind-erregter Schwingungen. Der Stahlbau, 6(1), [11] Abramson, H.N., The dynamic behavior of liquid in moving containers. NASA, SP106, [1] Housner, G.W., The dynamic behavior of water tanks. Bull. of the Seismological Society of America, 5(), pp , 196. [1] Haroun, M.A., Vibration studies and tests of liquid storage tanks. Earthquake Engineering and Structural Dynamics, 11, pp , 198.

STRUCTURAL CONTROL USING MODIFIED TUNED LIQUID DAMPERS

STRUCTURAL CONTROL USING MODIFIED TUNED LIQUID DAMPERS A. Samanta 1 and P. Banerji 2 1 Research Scholar, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India, 2 Professor,