Abstract
Tuned mass damper (TMD) is an effective passive device in reducing harmful vibrations as long as they are designed correctly. An optimal TMD design method is proposed based on transfer functions and also differential evolution (DE) algorithm is used. The method includes optimization of all parameters which are the mass, stiffness and damping coefficients of a TMD. By using random vibration theory, the mean-square of top floor absolute acceleration, top floor displacement and the sum of mean-squares of interstorey drifts have been chosen as objective functions to be minimized with respect to upper and lower limits of TMD parameters. In the classical design, the mass is usually chosen by the designer to find the optimum values of the stiffness and damping coefficient. In addition to optimizing stiffness and damping coefficients, in this study TMD mass quantity is also optimized by using DE algorithm to minimize objective functions for TMD design. After that, structure system with TMD is tested under six near fault and three far fault ground motions by evaluating responses of the structure. The results obtained here are compared with the methods available in the literature for verification. Numerical results show that the proposed method is effective for optimal TMD design.
Similar content being viewed by others
References
Almazan, J. L., Espinoza, G, and Aguirre. J. J. (2012). “Torsional balance of asymmetric structures by means of tuned mass dampers.” Engineering Structures, Elsevier, Vol. 42, pp. 308–328, DOI: https://doi.org/10.1016/j.engstruct.2012.04.034.
Arfiadi, Y. and Hadi, M. N. S. (2011). “Optimum placement and properties of properties of tuned mass dampers using hybrid genetic algorithms.” International Journal of Optimization in Civil Engineering; Iran University of Science and Technology, Vol. 1, No. 1, pp. 167–187.
Bekdas, G. and Nigdeli, S. M. (2011). “Estimating optimum parameters of tuned mass dampers using harmony search.” Engineering Structures, Elsevier, Vol. 33, No. 9, pp. 2716–2723, DOI: https://doi.org/10.1016/j.engstruct.2011.05.024.
Bekdas, G. and Nigdeli, S. M. (2013) “Mass ratio factor for optimum tuned mass damper strategies.” International Journal of Mechanical Sciences, Elsevier, Vol. 71, pp. 68–84, DOI: https://doi.org/10.1016/j.ijmecsci.2013.03.014.
Bernal, A. G, Lecea, M. A, and Garcia, H. J. (2012). “Empirical attenuation relationship for Arias Intensity in Mexico and their relation with the damage potential.” XVWCEE, Lisboa, Portugal, pp. 2012-3826.
Biswas, P. P., Suganthan, P. N, Wu, G, and Amaratunga, G. A. J. (2019). “Parameter estimation of solar cells using datasheet information with the application of an adaptive differential evolution algorithm.” Renewable Energy, Elsevier, Vol. 132, pp. 425–438, DOI: https://doi.org/10.1016/j.renene.2018.07.152.
Cetin, H., Aydin, E., and Ozturk, B. (2017). “Optimal damper allocation in shear buildings with tuned mass dampers and viscous dampers.” International Journal of Earthquake and Impact Engineering, Inderscience, Vol. 2, No. 2, pp. 89–120, DOI: https://doi.org/10.1504/IJEIE.2017.089038.
Cetin, H., Aydin, E., and Ozturk, B. (2019). “Optimal design and distribution of viscous dampers for shear building structures under seismic excitations.” Frontiers in Built Environment, Frontiers, Vol 5, No. 90, pp. 1–13, DOI: https://doi.org/10.3389/fbuil.2019.00090.
Champion, B. and Strzebonski, A. (2008). Constrained optimization, Wolfram Mathematica Tutorial Collection, Champaign, IL, USA, pp. 41–54.
Cheung, Y. L. and Wong, W. O. (2011). “H2 optimization of a non-traditional dynamic vibration absorber for vibration control of structures under random force excitation.” Journal of Sound and Vibration, Elsevier, Vol. 330, No. 6, pp.1039–1044, DOI:10.1016/j.jsv.2010.10.031.
Cheung, Y. L., Wong, W. O., and Cheng, L. (2013). “Optimization of a hybrid vibration absorber for vibration control of structures under random force excitation.” Journal of Sound and Vibration, Elsevier, Vol. 332, No. 3, pp. 494–509, DOI: 10.1016/j.jsv.2012.09.014.
Connor, J. J. and Klink, B. S. A. (1996). Introduction to motion based design, Computational Mechanics Publication, Boston, USA, pp. 145–196.
Den Hartog, J. P. (1956). Mechanical vibrations (4th Ed.), McGraw-Hill, New York, NY, USA, pp. 87-117.
Falcon, K. C., Stone, B. J., Simcock, W D., and Andrew, C. (1967). “Optimization of vibration absorbers: A graphical method for use on idealized systems with restricted damping.” Journal of Mechanical Engineering Science, Sage, Vol. 9, No. 5, pp. 374–381, DOI: 10.1243/JMES_JOUR_1967_009_058_02.
Fujino, Y. and Abe, M. (1993). “Design formulas for tuned mass dampers based on a perturbation technique.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 22, No. 10, pp. 833–854, DOI: https://doi.org/10.1002/eqe.4290221002.
Garrido, H., Curadelli, O., and Ambrosini, D. (2013). “Improvement of tuned mass damper by using rotational inertia through Tuned viscous mass damper.” Engineering Structures, Elsevier, Vol 56, 2149-2153, DOI:10.1016/j.engstruct.2013.08.044.
Goldberg, D. E. (1989). Genetic algorithm in search, optimization, and machine learning, Addison-Wesley Longman Publishing, Boston, USA, pp. 1–25.
Hadi, M. N. S. and Arfiadi Y (1998). “Optimum design of absorber for MDOF structures.” Journal of Structural Engineering, ASCE, Vol. 124, No. 11, pp. 1272–1280, DOI: 10.1061/(ASCE)0733-9445(1998)124: 11(1272).
Ikago, K., Saito, K., and Inoue, N. (2012). “Seismic control of single degree-of-freedom structure using tuned Viscous mass damper.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 41, No. 3, pp. 453–474, DOI: 10.1002/eqe.ll38.
Ioi, T and Ikeda, K. (1978). “On the dynamic vibration damped absorber of the vibration system.” Bulletin of the Japan Society Mechanical Engineering, The Japan Society of Mechanical Engineering, Vol. 21, No. 151, pp. 64–71, DOI: https://doi.org/10.1299/jsmel958.21.64.
Jacquot, R. G and Hoppe, D. L. (1973). “Optimal random vibration absorber.” Journal of Engineering Mechanics, ASCE, Vol. 99, No. 3, pp. 612–616.
Kitayama, S., Arakawa, M., and Yamazaki, K. (2011). “Different evolution as the global optimization technique and its application to structural optimization.” Applied Soft Computing, Elsevier, Vol. 11, No. 4, 3792-3803, DOI: https://doi.org/10.1016/j.asoc.2011.02.012.
Lee, C. L., Chen, Y T, Chung, L. L., and Wang, Y P. (2006). “Optimal design theories and applications of tuned mass dampers.” Engineering Structures, Elsevier, Vol. 28, No. 1, pp. 43–53, DOI: https://doi.org/10.1016/j.engstruct.2005.06.023.
Leung, A. Y. T., Zhang, H., Cheng, C. C. K., and Lee, Y. Y. (2008). “Particle swarm optimization of TMD by non-stationary base excitation during earthquake.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 37, No. 9, pp. 1223–1246, DOI: https://doi.org/10.1002/eqe.811.
Levy, A. V. and Montalvo, A. (1985). “The tunneling algorithm for the global minimization functions.” SIAM Journal on Scientific and Statistical Computing, SIAM, Vol. 6, No. 1, pp. 15–29, DOI: https://doi.org/10.1137/0906002.
Lin, J. L, Tsai, K. C., and Yu, Y. J. (2011). “Bi-directional coupled tuned mass dampers for the seismic response control of two-way asymmetric-plan buildings.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 40, No. 6, pp. 675–690, DOI: https://doi.org/10.1002/eqe.l054.
Lu, Z., Chen, X., Zhang, D., and Dai, K. (2017). “Experimental and analytical study on the performance of particle tuned mass dampers under seismic excitation.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 46, No. 5, pp. 697–714, DOI: https://doi.org/10.1002/eqe.2826.
Luft, R. W. (1979). “Optimal tuned mass dampers for building.” Journal of the Structural Division, ASCE, Vol. 105, No. 12, pp. 2766–2772.
Marano, G C., Greco, R, and Chiaia, B. (2010). “A comparison between different optimization criteria for tuned mass dampers design.” Journal of Sound and Vibration, Elsevier, Vol. 329, No. 23, pp. 4880–4890, DOI: https://doi.org/10.1016/j.jsv.2010.05.015.
Moustafa, A. and Takewaki, I. (2009). “Deterministic and probabilistic representation of near-field pulse-like ground motion.” Soil Dynamics and Earthquake Engineering, Elsevier, Vol. 30, No. 5, pp. 412–422, DOI:10.1016/j.soildyn.2009.12.013.
Moutinho, C. (2012). “An alternative methodology for designing tuned mass dampers to reduce seismic vibrations in building structures.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 41, No. 14, pp. 2059–2073, DOI: https://doi.org/10.1002/eqe.2174.
Nigdeli, S. M. and Begdas, G (2017). “Optimum tuned mass damper design in frequency domain for structures.” KSCE Journal of Civil Engineering, KSCE, Vol. 21, No. 3, pp.912–922, DOI: https://doi.org/10.1007/S12205-016-0829-2.
Ok, S. Y, Song, J., and Park, K. S. (2008). “Optimal performance design of bi-tuned mass damper systems using multi-objective optimization.” KSCE Journal of Civil Engineering, KSCE, Vol. 12, No. 5, pp. 313–322, DOI 10.1007/sl2205-008-0313-8.
Ormondroyd, J. and Den Hartog, J. P. (1928). “The theory of dynamic vibration absorber.” Transactions of the American Society of Mechanical Engineers, ASME, Vol. 50, No. 7, pp. 9–22.
Ozsariyildiz, S. S. and Bozer, A. (2015). “Finding optimal parameters of tuned mass dampers.” The Structural Design of Tall and Special Buildings, Wiley, Vol. 24, No. 6, pp. 461–475, DOI: 10.1002/tal.1174.
Penunuri, E, Escalante, R. P., Villanueva, C., and Oy, D. P. (2011). “Synthesis of mechanisms for single and hybrid tasks using differential evolution.” Mechanism and Machine Theory, Elsevier, Vol. 46, No. 10, pp. 1335–1349, DOI: https://doi.org/10.1016/j.mechmachtheory.2011.05.013.
Pinkaew, T., Lukkunaprasit, P., and Chatupote, P. (2003). “Seismic effectiveness of tuned mass dampers for damage reduction of structures.” Engineering Structures, Elsevier, Vol 25, No. 1, pp. 39–46, DOI: 10.1016/S0141-0296(02)00115-3.
Poh’sie, G. H., Chisari, C., Rinaldin, G., Amadio, C., and Fragiacomo, M. (2016). “Optimal design of tuned mass dampers for a multistorey cross laminated timber building against seismic loads.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 45, No. 12, pp. 1977–1995, DOI: https://doi.org/10.1002/eqe.2736.
Rana, R. and Soong, T. T (1998). “Parametric study and simplified design of tuned mass dampers.” Engineering Structures, Elsevier, Vol. 20, No. 3, pp. 193–204, DOI: 10.1016/S0141-0296(97)00078-3.
Ronkkonen, J., Kukkonen, S., and Price, K. V (2005). “Real-parameter optimization with differential evolution.” IEEE Congress on Evolutionary Computation, pp. 506–513, DOI: https://doi.org/10.1109/CEC.2005.1554725.
Sadek, E, Mohraz, B., Taylor, A. W, and Chung, R. M. (1997). “A method of estimating the parameters of tuned mass dampers for seismic applications.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 26, No. 6, pp. 617–635, DOI: 10.1002/(SICI)1096-9845(199706)26:63.0.CO;2-Z.
Sgobba, S. and Marano, G. C. (2010). “Optimum design of linear tuned mass dampers for structures with nonlinear behavior.” Mechanical System and Signal Processing, Elsevier, Vol. 24, No. 6, pp. 1739–1755, DOI: https://doi.org/10.1016/j.ymssp.2010.01.009.
Soong, T. T. and Dargush, G. F. (1997). Passive energy dissipation systems in structural engineering, John Wiley & Sons Ltd., Chichester, UK, and New York NY, pp. 227–317.
Birito, R. S. and Ruiz, S. E. (1999). “Influence of ground motion intensity on the effectiveness of tuned mass dampers.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 28, No. 11, pp. 1255–1271, DOI: 10.1002/(SICI)1096-9845(199911)28:1K1255::AID-EQE865> 3.0.CO;2-C.
Storn, R. and Price, K. V (1997). “Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces.” Journal of Global Optimization, Springer, Vol. 11, No. 4, pp. 341–359, DOI: 10.1023/a:1008202821328.
Takewaki, I. (2009). Building control with passive dampers: Optimal performance-based design for earthquakes, John Wiley & Sons, Ltd. (Asia), Singapore, pp. 51–75, DOI: https://doi.org/10.1002/9780470824931.
Thompson, A. G. (1981). “Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system.” Journal Sound Vibration, Elsevier, Vol. 77, No. 3, pp. 403–415, DOI: 10.1016/S0022-460X(81)80176-9.
Tigli, O. F. (2012). “Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads.” Journal of Sound and Vibration, Elsevier, Vol. 331, No. 13, pp. 3035–3049, DOI: https://doi.org/10.1016/j.jsv.2012.02.017.
Villaverde, R. and Koyama, L. A. (1993). “Damped resonant appendages to increase inherent damping in buildings.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 22, No. 6, pp. 491–507, DOI: https://doi.org/10.1002/eqe.4290220603.
Warburton, G. B. (1982). “Optimal absorber parameters for various combinations of response and excitation parameters.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 10, No. 3, pp. 381–401, DOI: https://doi.org/10.1002/eqe.4290100304.
Warburton, G. B. and Ayorinde, E. O. (1980). “Optimum absorber parameters for simple systems.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 8, No. 3, pp. 197–217, DOI: https://doi.org/10.1002/eqe.4290080302.
Wu, G, Shen, X., Li, H., Chen, H., Lin, A., and Suganthan, P. N. (2018). “Ensemble of differential evolution variants.” Information Science, Elsevier, Vol. 423, pp. 172–186, DOI: 1016/j.ins.2017.09.053.
Wu, J., Chen, G, and Lou, M. (1999). “Seismic effectiveness of tuned mass dampers considering soil-structure interaction.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 28, No. 11, pp. 1219–1233, DOI: doi.org/10.1002/(SICI)1096-9845(199911)28: 11<1219::AID-EQE861>3.0.CO;2-G.
Xiang, P. and Nishitani, A. (2015). “Optimum design and application of non-traditional tuned mass damper toward seismic response control with experimental test verification.” Earthquake Engineering and Structural Dynamics, Wiley, Vol. 44, No. 13, pp. 2199–2220, DOI: https://doi.org/10.1002/eqe.2579.
Yang, X. S., Bekdas, G, and Nigdeli, S. M. (2016). Metaheuristics and Optimization in Civil Engineering, Springer, Switzerland, pp. 1–42.
Acknowledgements
Not Applicable
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cetin, H., Aydin, E. A New Tuned Mass Damper Design Method based on Transfer Functions. KSCE J Civ Eng 23, 4463–4480 (2019). https://doi.org/10.1007/s12205-019-0305-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-019-0305-x