Analytical Solution of the Closed-Form Equations Governing the Hybrid Performance of a Tuned Liquid Column Gas Damper Equipped With a Variable Orifice

Document Type : Regular Paper

Authors

Department of Civil Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Abstract

Structural vibrations are one of the main concerns of engineering in recent decades. The tendency towards a flexible structure such as tall structures or structures with long spans has caused in more intense movements of the structure under service loading. Limiting acceleration in tall and slender buildings, as well as controlling vibrations, is a complex design issue. In this research, the new hybrid damper; "tuned liquid column gas damper equipped with variable orifice (H-O-TLCGD)" is introduced. The dominant mechanism for confronting with vibration in this damper is based on liquid movement, and the vibration energy is dissipated by the effects of fluid turbulence and friction caused by the local pressure drop of the orifice opening. In order to achieve the actual performance behavior of the system, the equations governing the dynamic response of the structure equipped with this damper are obtained along with damping modification and removation of some uncertainties, which cause non-linear equations. Also, in this research, according to the advantages of low energy demand, permanent stability of the system and economic efficiency of using semi-active control systems, the combination of semi-active and passive dampers and the increase of stiffness in the systems equipped with them by gas springs, with the aim of improving the performance of system are considered so that the performance level of structures equipped with this new control system improve at an acceptable level. This research presents the differential equations governing the axial performance of the liquid column damper, accounting for energy dissipation due to changes in flow cross-section and gas spring stiffness, and demonstrates how to combine these effects using hydrodynamics and structural control principles. Also, the closed-form analytical solution of these nonlinear equations is presented so that researchers can achieve their research goals in a shorter time. To facilitate practical applications, this research provides a methodology for designing systems equipped with this damper and optimizing its performance using semi-active control effects, which will be useful for researchers and construction engineers.

Graphical Abstract

Analytical Solution of the Closed-Form Equations Governing the Hybrid Performance of a Tuned Liquid Column Gas Damper Equipped With a Variable Orifice

Highlights

  • In this research, the new hybrid damper; " tuned liquid column gas damper equipped with variable orifice (H-O-TLCGD)" is introduced.
  • By using the sciences of hydrodynamics and structure control and dynamics and energy methods, the non-linear differential equations governing the dynamic behavior of the structure equipped with this damper, by separating and combining the performance of the U-shaped liquid column, the variable orifice and the gas spring, are obtained.
  • The analytical solution of the closed-form of the mentioned equations is presented in order to better understand the real behavior of the system.
  • The sensitivity analysis for the parameters affecting the performance and behavior of the system and the methodology along with the optimization of the design of the systems equipped with this damper, considering the semi-active control effects of the variable orifice, are presented.

Keywords

Main Subjects


[1]     Symans MD, Constantinou MC. Semi-active control systems for seismic protection of structures: a state-of-the-art review. Eng Struct 1999;21:469–87. https://doi.org/10.1016/S0141-0296(97)00225-3.
[2]     Mulligan KJ. Experimental and analytical studies of semi-active and passive structural control of buildings 2007.
[3]     Feng Q. Use of a variable damper for hybrid control of bridge response under earthquake. Proc. US Natl. Work. Struct. Control Res., USC Publication; 1990.
[4]     Shinozuka M, Constantinou MC, Ghanem R. Passive and active fluid dampers in structural applications. Proc. US/China/Japan Work. Struct. Control, 1992, p. 507–16.
[5]     Kurata N. Shaking table experiment of active variable damping system. Proc. First World Conf. Struct. Control. 1994, vol. 2, 1994, p. 108–17.
[6]     Patten WN, Sack RL. Semiactive control of civil engineering structures. Proc. 1994 Am. Control Conf., vol. 1, IEEE; 1994, p. 1078–82.
[7]     Nouri Y, Jouneghani HG, Haghollahi A, Hemati E, Hemati SA, Mortazavi M. Experimental and numerical investigation of a steel yielding arc and ring damper. Structures 2024;68:107140. https://doi.org/10.1016/j.istruc.2024.107140.
[8]     De Domenico D, Ricciardi G, Takewaki I. Design strategies of viscous dampers for seismic protection of building structures: A review. Soil Dyn Earthq Eng 2019;118:144–65. https://doi.org/10.1016/j.soildyn.2018.12.024.
[9]     Mualla IH, Belev B. Performance of steel frames with a new friction damper device under earthquake excitation. Eng Struct 2002;24:365–71. https://doi.org/10.1016/S0141-0296(01)00102-X.
[10]   Ghafouri-Nejad A, Alirezaei M, Mirhosseini SM, Zeighami E. Parametric study on seismic response of the knee braced frame with friction damper. Structures 2021;32:2073–87. https://doi.org/10.1016/j.istruc.2021.04.009.
[11]   Ghasemi Jouneghani H, Nouri Y, Mortazavi M, Haghollahi A, Memarzadeh P. Seismic Performance Factors of Elliptic-Braced Frames with Rotational Friction Dampers through IDA. Pract Period Struct Des Constr 2024;29:1–24. https://doi.org/10.1061/PPSCFX.SCENG-1540.
[12]   Ghasemi Jouneghani H, Nouri Y, Memarzadeh P, Haghollahi A, Hemati E. Seismic performance and failure mechanisms evaluation of multi-story elliptic and mega-elliptic bracing frames: Experimental and numerical investigation. Structures 2024;70:107658. https://doi.org/10.1016/j.istruc.2024.107658.
[13]   Frahm H. Means for damping the rolling motion of ships. 1911.
[14]   Sakai F. Tuned liquid column damper-new type device for suppression of building vibration. Proc. 1^< st> Int. Conf. High-rise Build., 1989, p. 926–31.
[15]   Nanda B, Biswal K. A Review on Applications of Tuned Liquid Dampers in Vibration Control. Adv Civ Eng 2014.
[16]   Connor J, Laflamme S. Structural Motion Engineering. Cham: Springer International Publishing; 2014. https://doi.org/10.1007/978-3-319-06281-5.
[17]   Wu JC, Chang CH, Lin YY. Optimal designs for non-uniform tuned liquid column dampers in horizontal motion. J Sound Vib 2009;326:104–22. https://doi.org/10.1016/j.jsv.2009.04.027.
[18]   Guntur HL, Daman AAA, Hendrowati W. The Vibration Reduction in Multilevel Structure Model with the addition of Tuned Liquid Column Damper (TLCD):Study of the Influence of variations in TLCD’s mass ratio &amp; orifice cross-sectional area. IOP Conf Ser Mater Sci Eng 2019;588:012029. https://doi.org/10.1088/1757-899X/588/1/012029.
[19]   Pandey DK, Mishra SK, Chakraborty S. A tuned liquid mass damper implemented in a deep liquid storage tank for seismic vibration control of short period structures. Struct Des Tall Spec Build 2022;31. https://doi.org/10.1002/tal.1928.
[20]   Hokmabady H, Mohammadyzadeh S, Mojtahedi A. Suppressing structural vibration of a jacket-type platform employing a novel Magneto-Rheological Tuned Liquid Column Gas Damper (MR-TLCGD). Ocean Eng 2019;180:60–70. https://doi.org/10.1016/j.oceaneng.2019.03.055.
[21]   Hokmabady H, Mojtahedi A, Mohammadyzadeh S, Ettefagh MM. Structural control of a fixed offshore structure using a new developed tuned liquid column ball gas damper (TLCBGD). Ocean Eng 2019;192. https://doi.org/10.1016/j.oceaneng.2019.106551.
[22]   Gao H, Kwok KCS, Samali B. Optimization of tuned liquid column dampers. Eng Struct 1997;19:476–86. https://doi.org/10.1016/S0141-0296(96)00099-5.
[23]   Reiterer M, Ziegler F. Bi-axial Seismic Activation of Civil Engineering Structures Equipped with Tuned Liquid Column Dampers. J Seismol Earthq Eng 2005;7:45–60.
[24]   Yalla SK, Kareem A. Optimum Absorber Parameters for Tuned Liquid Column Dampers. J Struct Eng 2000;126:906–15. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:8(906).
[25]   Mendes MV, Ghedini LB, Batista RN, Pedroso LJ. A study of TLCD parameters for structural vibration mitigation. Lat Am J Solids Struct 2023;20. https://doi.org/10.1590/1679-78257412.
[26]   Masnata C, Di Matteo A, Adam C, Pirrotta A. Efficient estimation of tuned liquid column damper inerter (TLCDI) parameters for seismic control of base-isolated structures. Comput Civ Infrastruct Eng 2023;38:1638–56. https://doi.org/10.1111/mice.12929.
[27]   Idelchik IE. Handbook of hydraulic resistance. J Press Vessel Technol 1987;109:260–1.
[28]   Wu JC, Shih MH, Lin YY, Shen YC. Design guidelines for tuned liquid column damper for structures responding to wind. Eng Struct 2005;27:1893–905. https://doi.org/10.1016/j.engstruct.2005.05.009.
[29]   Belanger PR. Control engineering: a modern approach. Oxford University Press, Inc.; 1995.
[30]   Ogata K. Modern control engineering. B Rev 1999;35:1184.
[31]   Mousavi SA, Bargi K, Zahrai SM. Optimum parameters of tuned liquid columngas damper for mitigation of seismic-induced vibrations of offshore jacket platforms. Struct Control Heal Monit 2013;20:422–44. https://doi.org/10.1002/stc.505.
[32]   Bhattacharyya S, Ghosh A (Dey), Basu B. Nonlinear modeling and validation of air spring effects in a sealed tuned liquid column damper for structural control. J Sound Vib 2017;410:269–86. https://doi.org/10.1016/j.jsv.2017.07.046.
[33]   Mallik AK, Chatterjee S. Principles of passive and active vibration control. East West Press 2014:8176710989.
[34]   Chatterjee T, Chakraborty S. Vibration mitigation of structures subjected to random wave forces by liquid column dampers. Ocean Eng 2014;87:151–61. https://doi.org/10.1016/j.oceaneng.2014.05.004.
[35]   Chen B, Zhang Z, Hua X. Closed-form optimal calibration of a tuned liquid column damper (TLCD) for flexible structures. Int J Mech Sci 2021;198. https://doi.org/10.1016/j.ijmecsci.2021.106364.
[36]   Di Matteo A, Masnata C, Adam C, Pirrotta A. Optimal design of tuned liquid column damper inerter for vibration control. Mech Syst Signal Process 2022;167. https://doi.org/10.1016/j.ymssp.2021.108553.
[37]   Mehrkian B, Altay O. Mathematical modeling and optimization scheme for omnidirectional tuned liquid column dampers. J Sound Vib 2020;484. https://doi.org/10.1016/j.jsv.2020.115523.