Abstract
Passive control devices are often added to slender and flexible systems in order to increase their structural safety. Several types of devices have been proposed in order to reduce the dynamic responses of different kind of structural systems. Among them, the tuned liquid column damper (TLCD) proved to be very effective in reducing vibration of various type of structures by means of a combined action which involves the motion of the liquid mass within the tube. The restoring force, in particular, is produced by the force of gravity acting on the liquid and the damping effect is generated by the hydrodynamic head losses that arise during the motion of the liquid inside the TLCD. Since the increasing use of TLCD in practical realizations, an approximated simplified formulation, by means of a statistical linearization technique has been previously developed by the same authors. This direct and ready-to-use formulation is able to predict the effectiveness of TLCD on a structure subjected to random loads and has been numerically validated by means of a parametric analysis in a stochastic framework by comparison with the numerical Monte Carlo simulation based on the nonlinear complete system for a wide range of the system parameters. In this paper optimal TLCD parameters have been computed taking advantage of the proposed approximated formulation, by which a smooth function, defining the main system variance, can be formulated and easily minimized, resulting in a significant reduction of the computational time and a valuable tool for design purposes. Moreover, starting from the proposed formulation, optimal design charts have been created which enable for an easy and quick evaluation of the TLCD parameters design.
Similar content being viewed by others
References
Frahm H (1909) Device for damped vibration of bodies. U.S. Patent No. 989958, 30 Oct 1909
Ormondroyd J, Den Hartog JP (1928) The theory of the dynamic vibration absorber. Trans ASME J Appl Mech 50(7):9–22
Den Hartog JP (1956) Mechanical vibrations. McGraw-Hill, New York
Sakai F, Takeda S, Tamaki T (1989) Tuned liquid column damper- new type device for suppression of building vibrations. In: Proceedings of the international conference on highrise buildings, pp 926–931
Hitchcock PA, Kwok KCS, Watkins RD (1997) Characteristic of liquid column vibration absorber (LCVA)—I. Eng Struct 19(2):126–134
Hochrainer MJ (2005) Tuned liquid column damper for structural control. Acta Mech 175:57–76
Won AYJ, Pirest JA, Haroun MA (1996) Stochastic seismic performance evaluation of tuned liquid column dampers. Earthq Eng Struct Dyn 25:1259–1274
Won AYJ, Pirest JA, Haroun MA (1997) Performance assessment of tuned liquid column dampers under random seismic loading. Int J Non-Linear Mech 32(4):745–758
Sadek F, Mohraz B, Lew HS (1998) Single- and multiple-tuned-liquid-column-dampers for seismic applications. Earthq Eng Struct Dyn 27:439–463
Balendra T, Wang CM, Cheong HF (1995) Effectiveness of tuned liquid column dampers for vibration control of towers. Eng Struct 17(9):668–675
Chang CC, Hsu CT (1998) Control performance of liquid column vibration absorbers. Eng Struct 20(7):580–586
Chang CC (1999) Mass dampers and their optimal designs for building vibration control. Eng Struct 21:454–463
Yalla SK, Kareem A (2000) Optimum absorber parameters for tuned liquid column dampers. J Struct Eng 126(8):906–915
Xue SD, Ko JM, Xu YL (2000) Optimum parameters of tuned liquid column damper for suppressing pitching vibration of an undamped structure. J Sound Vib 235(4):639–653
Wu JC, Chang CH, (2006) Design table of optimal parameters for tuned liquid column damper responding to earthquake. In: Proceedings 4th International Conference on Earthquake Engineering, Taipei, 12–13 Oct
Wu JC, Shih MH, Lin YY, Shen YC (2005) Design guidelines for tuned liquid column damper for structures responding to wind. Eng Struct 27:1893–1905
Wu JC, Chang CH, Lin YY (2009) Optimal designs for non-uniform tuned liquid column dampers in horizontal motion. J Sound Vib 326:104–122
Gosh A, Basu B (2007) Alternative approach to optimal tuning parameter of liquid column damper for seismic applications. J Struct Eng 133(12):1848–1852
Shum KM (2009) Closed form optimal solution of a tuned liquid column damper for suppressing harmonic vibration of structures. Eng Struct 31:84–92
Farshidianfar A, Oliazadeh P (2009) Closed form optimal solution of a tuned liquid column damper responding to earthquake. World Acad Sci Eng Technol 59:1–6
Chakraborty S, Debbarma R, Marano GC (2012) Performance of tuned liquid column dampers considering maximum liquid motion in seismic vibration control of structures. J Sound Vib 331(7):1519–1531. doi:10.1016/j.jsv.2011.11.029
Debbarma R, Chakraborty S, Ghosh SK (2010) Optimum design of tuned liquid column dampers under stochastic earthquake load considering uncertain bounded system parameters. Int J Mech Sci 52(10):1385–1393. doi:10.1016/j.ijmecsci.2010.07.004
Di Matteo A, Lo Iacono F, Navarra G, Pirrotta A (2012) The control performance of TLCD and TMD: experimental investigation. In: Proceedings 5th European Conference on Structural Control, 18–20 June, Genoa, ISBN 978-889502313-7
Di Matteo A, Lo Iacono F, Navarra G, Pirrotta A (2012) The TLCD passive control: numerical investigations vs experimental results. In: Proceedings ASME 2012—international mechanical engineering congress & exposition IMECE2012, 9–15 November, 2012, Houston. doi:10.1115/IMECE2012-86568
Di Matteo A, Lo Iacono F, Navarra G, Pirrotta A (2013) Numerical and experimental validation of a simplified formulation for the design of TLCD. In: 11th international conference on structural safety & reliability ICOSSAR2013, 16–20 June 2013, New York City. ISBN: 978-113800086-5
Di Matteo A, Lo Iacono F, Navarra G, Pirrotta A (2014) Direct evaluation of the equivalent linear damping for TLCD systems in random vibration for pre-design purposes. Int J Non-Linear Mech 63:19–30. doi:10.1016/j.ijnonlinmec.2014.03.009
Di Matteo A, Lo Iacono F, Navarra G, Pirrotta A (2014) Experimental validation of a direct pre-design formula for TLCD. Eng Struct 75:528–538. doi:10.1016/j.engstruct.2014.05.045
Roberts JB, Spanos PD (1990) Random vibration and statistical linearization. Wiley, New York
Min KW, Kim J, Lee HR (2014) A design procedure of two-way liquid dampers for attenuation of wind-induced responses of tall buildings. J Wind Eng Ind Aerodyn 129:22–30. doi:10.1016/j.jweia.2014.03.003
Sarkar A, Gudmestad OT (2013) Pendulum type liquid column damper (PLCD) for controlling vibrations of a structure—theoretical and experimental study. Eng Struct 49:221–233. doi:10.1016/j.engstruct.2012.10.023
Al-Saif KA, Aldakkan KA, Foda MA (2011) Modified liquid column damper for vibration control of structures. Int J Mech Sci 53(7):505–512. doi:10.1016/j.ijmecsci.2011.04.007
Ziegler F (2008) Special design of tuned liquid column-gas dampers for the control of spatial structural vibrations. Acta Mech 201:249–267. doi:10.1007/s00707-008-0062-2
Gao H, Kwok KCS, Samali B (1997) Optimization of tuned liquid column dampers. Eng Struct 19(6):476–486
Spanos PD (1981) Stochastic linearization in structural dynamics. Appl Mech Rev 34(1):1–8
Di Paola M, Navarra G (2009) Stochastic seismic analysis of MDOF structures with nonlinear viscous dampers. Struct Control Health Monit 16:303–318. doi:10.1002/stc.254
Balendra T, Wang CM, Rakesh G (1999) Vibration Control of various types of buildings using TLCD. J Wind Eng Ind Aerodyn 83:197–208
Di Paola M, La Mendola L, Navarra G (2007) Stochastic seismic analysis of structures with nonlinear viscous dampers. J Struct Eng (ASCE) 133(10):1475–1478. doi:10.1061/(ASCE)0733-9445(2007)133:10(1475)
Di Paola M, Lo Iacono F, Navarra G (2008) Amplification of interstory drift and velocity for the passive control of structural vibrations. In: CIMTEC 2008—Proceedings of the 3rd International conference on smart materials, structures and systems—embodying intelligence in structures and integrated systems, vol 56. pp 363–373
Bryson AE, Ho YC (1969) Applied optimal control. Ginn e Co., Waltham
Di Paola M, Elishakoff I (1996) Non stationary response of linear systems under stochastic Gaussian and Non-Gaussian excitation: a brief overview of recent results. Chaos Soliton Fractals 7:961–971
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Di Matteo, A., Lo Iacono, F., Navarra, G. et al. Optimal tuning of tuned liquid column damper systems in random vibration by means of an approximate formulation. Meccanica 50, 795–808 (2015). https://doi.org/10.1007/s11012-014-0051-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-014-0051-6