Investigating Performance of Tuned Liquid Damper Using Finite-Element Method Based on Lagrange and Hankel Functions with Nonlinear Boundary Conditions
Publication: Journal of Engineering Mechanics
Volume 147, Issue 11
Abstract
A numerical model was developed for studying the performance of a rectangular tuned liquid damper (TLD) and fluid–structure interaction. A TLD is a structure which dissipates excitation energy through the sloshing behavior of fluid inside a tank. To design this structure as an effective device, it should be investigated by considering different parameters such as frequency ratio, mass ratio, and structural damping ratio. For numerical modeling of the fluid, the finite-element method with nonlinear boundary conditions was developed. In this method, two types of shape functions are used: classic Lagrange shape functions, and new spherical Hankel shape functions. It was demonstrated that using the new functions with fewer elements than the classic method, the solution accuracy can be improved. After the numerical modeling of the fluid in the tank, the response of the structure, namely the displacement and acceleration, was calculated. The values of the parameters that produced the most effective TLD were obtained. To examine the accuracy and applicability of the algorithm, the numerical results were compared with available experimental data. The results indicated that the proposed model has the capability to study TLD performance with good accuracy.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request, including input data and numerical model output data.
References
Ashasi-Sorkhabi, A., H. Malekghasemi, A. Ghaemmaghami, and O. Mercan. 2017. “Experimental investigation of tuned liquid damper-structure interaction in resonance considering multiple parameters.” J. Sound Vib. 388 (Feb): 141–153. https://doi.org/10.1016/j.jsv.2016.10.036.
Ashasi-Sorkhabi, A., H. Malekghasemi, and O. Mercan. 2012. “Dynamic behaviour and performance evaluation of tuned liquid dampers (TLDs) using real-time hybrid simulation.” In Proc., Structures Congress 2012, 2153–2162. Reston, VA: ASCE.
Bauer, H. F. 1984. “Oscillations of immiscible liquids in a rectangular container: A new damper for excited structures.” J. Sound Vib. 93 (1): 117–133. https://doi.org/10.1016/0022-460X(84)90354-7.
Deng, X., and M. J. Tait. 2009. “Theoretical modeling of TLD with different tank geometries using linear long wave theory.” J. Vib. Acoust. 131 (4). 041014. https://doi.org/10.1115/1.3142873.
Di Matteo, A., F. Lo Iacono, G. Navarra, and A. Pirrotta. 2015. “Innovative modeling of tuned liquid column damper motion.” Commun. Nonlinear Sci. Numer. Simul. 23 (1–3): 229–244. https://doi.org/10.1016/j.cnsns.2014.11.005.
Dou, P., M. A. Xue, J. Zheng, C. Zhang, and L. Qian. 2020. “Numerical and experimental study of tuned liquid damper effects on suppressing nonlinear vibration of elastic supporting structural platform.” Nonlinear Dyn. 99 (4): 2675–2691. https://doi.org/10.1007/s11071-019-05447-y.
Farmani, S., M. Ghaeini-Hessaroeyeh, and S. Hamzehei Javaran. 2018. “The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions.” Int. J. Numer. Methods Fluids 87 (2): 70–89. https://doi.org/10.1002/fld.4482.
Farmani, S., M. Ghaeini-Hessaroeyeh, and S. Hamzehei-Javaran. 2019. “Developing new numerical modeling for sloshing behavior in two-dimensional tanks based on nonlinear finite-element method.” J. Eng. Mech. 145 (12): 04019107. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001686.
Frandsen, J. B. 2005. “Numerical predictions of tuned liquid tank structural systems.” J. Fluids Struct. 20 (3): 309–329. https://doi.org/10.1016/j.jfluidstructs.2004.10.003.
Gardarsson, S., H. Yeh, and D. Reed. 2001. “Behavior of sloped-bottom tuned liquid dampers.” J. Eng. Mech. 127 (3): 266–271. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:3(266).
Hamzehei Javaran, S., and S. Shojaee. 2017. “The solution of elastostatic and dynamic problems using the boundary element method based on spherical Hankel element framework.” Int. J. Numer. Methods Eng. 112 (13): 2067–2086. https://doi.org/10.1002/nme.5595.
Hamzehei Javaran, S. H., and N. Khaji. 2014. “Dynamic analysis of plane elasticity with new complex Fourier radial basis functions in the dual reciprocity boundary element method.” Appl. Math. Modell. 38 (14): 3641–3651. https://doi.org/10.1016/j.apm.2013.12.010.
Hamzehei-Javaran, S., and N. Khaji. 2012. “Inverse multiquadric (IMQ) function as radial basis function for plane dynamic analysis using dual reciprocity boundary element method.” In Proc., 15th World Conf. on Earthquake Engineering. Lisboa, Portugal: Sociedade Portuguesa de Engenharia Sismica.
Hamzehei-Javaran, S., and S. Shojaee. 2018. “Improvement of numerical modeling in the solution of static and transient dynamic problems using finite element method based on spherical Hankel shape functions.” Int. J. Numer. Methods Eng. 115 (10): 1241–1265. https://doi.org/10.1002/nme.5842.
Hamzeh Javaran, S. H., N. Khaji, and H. Moharrami. 2011a. “A dual reciprocity BEM approach using new Fourier radial basis functions applied to 2D elastodynamic transient analysis.” Eng. Anal. Bound. Elem. 35 (1): 85–95. https://doi.org/10.1016/j.enganabound.2010.05.014.
Hamzeh Javaran, S. H., N. Khaji, and A. Noorzad. 2011b. “First kind Bessel function (J-Bessel) as radial basis function for plane dynamic analysis using dual reciprocity boundary element method.” Acta Mech. 218 (3): 247–258. https://doi.org/10.1007/s00707-010-0421-7.
Kaneok, S., and M. Ishikawa. 1999. “Modeling of tuned liquid damper with submerged Nets.” J. Pressure Vessel Technol. 121 (3): 334–343. https://doi.org/10.1115/1.2883712.
Kanok-Nukulchai, W., and B. T. Tam. 1999. “Structure–fluid interaction model of tuned liquid dampers.” Int. J. Numer. Methods Eng. 46 (9): 1541–1558. https://doi.org/10.1002/(SICI)1097-0207(19991130)46:9%3C1541::AID-NME711%3E3.0.CO;2-Y.
Khaji, N., and S. Hamzehei Javaran. 2013. “New complex Fourier shape functions for the analysis of two-dimensional potential problems using boundary element method.” Eng. Anal. Bound. Elem. 37 (2): 260–272. https://doi.org/10.1016/j.enganabound.2012.11.001.
Kolukula, S. S., and P. Chellapandi. 2013a. “Finite element simulation of dynamic stability of plane free-surface of a liquid under vertical excitation.” Modell. Simul. Eng. 2013: 252760. https://doi.org/10.1155/2013/252760.
Kolukula, S. S., and P. Chellapandi. 2013b. “Nonlinear finite element analysis of sloshing.” Adv. Numer. Anal. 2013: 571528. https://doi.org/10.1155/2013/571528.
Longuet-Higgins, M. S., and E. D. Cokelet. 1976. “The deformation of steep surface waves on water - I. A numerical method of computation.” Proc. Royal Soc. London A. Math. Phys. Sci. 350 (1660): 1–26. https://doi.org/10.1098/rspa.1976.0092.
Love, J. S., and M. J. Tait. 2013. “Parametric depth ratio study on tuned liquid dampers: Fluid modelling and experimental work.” Comput. Fluids 79 (Jun): 13–26. https://doi.org/10.1016/j.compfluid.2013.03.004.
Marivani, M., and M. S. Hamed. 2017. “Evaluate pressure drop of slat screen in an oscillating fluid in a tuned liquid damper.” Comput. Fluids 156 (Oct): 384–401. https://doi.org/10.1016/j.compfluid.2017.08.008.
Marsh, A., M. Prakash, E. Semercigil, and Ö. F. Turan. 2011. “A study of sloshing absorber geometry for structural control with SPH.” J. Fluids Struct. 27 (8): 1165–1181. https://doi.org/10.1016/j.jfluidstructs.2011.02.010.
Modi, V. J., and M. L. Seto. 1997. “Suppression of flow-induced oscillations using sloshing liquid dampers: Analysis and experiments.” J. Wind Eng. Ind. Aerod. 67–68 (Apr–Jun): 611–625. https://doi.org/10.1016/S0167-6105(97)00104-9.
Nia, M. M., S. Shojaee, and S. Hamzehei-Javaran. 2020a. “A mixed formulation of B-spline and a new class of spherical Hankel shape functions for modeling elastostatic problems.” Appl. Math. Model. 77 (Part 1): 602–616. https://doi.org/10.1016/j.apm.2019.07.057.
Nia, M. M., S. Shojaee, and S. Hamzehei-Javaran. 2020b. “Utilizing new spherical Hankel shape functions to reformulate the deflection, free vibration, and buckling analysis of Mindlin plates based on the finite element method.” Scientia Iranica 27 (5): 2209–2229. https://doi.org/10.24200/SCI.2018.5113.1103.
Olson, D. E., and D. A. Reed. 2001. “A nonlinear numerical model for sloped-bottom tuned liquid dampers.” Earthquake Eng. Struct. Dyn. 30 (5): 731–743. https://doi.org/10.1002/eqe.34.
Reed, D., J. Yu, H. Yeh, and S. Gardarsson. 1998. “Investigation of tuned liquid dampers under large amplitude excitation.” J. Eng. Mech. 124 (4): 405–413. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(405).
Reyhanoglu, M., and J. R. Hervas. 2013. “Nonlinear modeling and control of slosh in liquid container transfer via a PPR robot.” Commun. Nonlinear Sci. Numer. Simul. 18 (6): 1481–1490. https://doi.org/10.1016/j.cnsns.2012.10.006.
Sriram, V., S. A. Sannasasiraj, and V. Sundar. 2006a. “Numerical simulation of 2D sloshing waves due to horizontal and vertical random excitation.” Appl. Ocean Res. 28 (1): 19–32. https://doi.org/10.1016/j.apor.2006.01.002.
Sriram, V., S. A. Sannasiraj, and V. Sundar. 2006b. “Simulation of 2-D nonlinear waves using finite element method with cubic spline approximation.” J. Fluids Struct. 22 (5): 663–681. https://doi.org/10.1016/j.jfluidstructs.2006.02.007.
Sun, L. M., Y. Fujino, B. M. Pacheco, and M. Isobe. 1989. “Nonlinear waves and dynamic pressure in rectangular tuned liquid damper (TLD).” Struct. Eng. Earthquake Eng. 6 (2): 251–262.
Tavakkoli Avval, I., M. R. Kianoush, and A. R. Ghaemmaghami. 2012. “Effect of three-dimensional geometry on the sloshing behavior of rectangular concrete tanks.” In Proc., 15th WCEE Conf. Lisbon, Portugal: Sociedade Portuguesa de Engenharia Sismica.
Wu, C.-H., O. N. Faltinsen, and B.-F. Chen. 2012. “Numerical study of sloshing liquid in tanks with baffles by time-independent finite difference and fictitious cell method.” Comput. Fluids 63 (Jun): 9–26. https://doi.org/10.1016/j.compfluid.2012.02.018.
Wu, G. X., and R. E. Taylor. 1995. “Time stepping solutions of the two-dimensional nonlinear wave radiation problem.” Ocean Eng. 22 (8): 785–798. https://doi.org/10.1016/0029-8018(95)00014-C.
Xin, Y., G. Chen, and M. Lou. 2009. “Seismic response control with density-variable tuned liquid dampers.” Earthquake Eng. Eng. Vibr. 8 (4): 537–546. https://doi.org/10.1007/s11803-009-9111-7.
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Received: Aug 16, 2020
Accepted: Jun 2, 2021
Published online: Aug 18, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 18, 2022
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