H∞ optimization of multiple tuned mass dampers for multimodal vibration control

[en] In this paper, a new computational method for the purpose of multimodal vibration mitigation using multiple tuned mass dampers is proposed. Classically, the minimization of the maximum amplitude is carried out using direct H∞ optimization. However, as shall be shown in the paper, this approach is prone to being trapped in local minima, in view of the nonsmooth character of the problem at hand. This is why this paper presents an original alternative to this approach through norm-homotopy optimization. This approach, combined with an efficient technique to compute the structural response, is shown to outperform direct H∞ optimization in terms of speed and performance. Essentially, the outcome of the algorithm leads to the concept of all-equal-peak design for which all the controlled peaks are equal in amplitude. This unique design is new with respect to the existing body of knowledge.

Disciplines :

Civil engineering
Aerospace & aeronautics engineering
Mechanical engineering

Author, co-author :

Raze, Ghislain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

H∞ optimization of multiple tuned mass dampers for multimodal vibration control

Publication date :

May 2021

Journal title :

Computers and Structures

ISSN :

0045-7949

Publisher :

Elsevier, United Kingdom

Volume :

248

Pages :

106485

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 17 January 2021

Statistics

Number of views

96 (14 by ULiège)

Number of downloads

679 (9 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

Frahm H. Device for damping vibrations of bodies; 1911. https://patents.google.com/patent/US989958A/en.
Ormondroyd, J., Den Hartog, J., Theory of the dynamic vibration absorber. J Appl Mech 50:7 (1928), 11–22.
Brock, J.E., A note on the damped vibration absorber. Trans ASME, J Appl Mech, 13(4), 1946 A—-284.
Den Hartog, J.P., Mechanical vibrations. 1985, Courier Corporation.
Warburton, G.B., Optimum absorber parameters for various combinations of response and excitation parameters. Earthq Eng Struct Dyn 10:3 (1982), 381–401, 10.1002/eqe.4290100304 http://doi.wiley.com/10.1002/eqe.4290100304.
Nishihara, O., Asami, T., Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors). J Vib Acoust, 124(4), 2002, 576, 10.1115/1.1500335 http://vibrationacoustics.asmedigitalcollection.asme.org/article.aspx?articleid=1470453.
Gutierrez Soto, M., Adeli, H., Tuned mass dampers. Arch Comput Meth Eng 20:4 (2013), 419–431, 10.1007/s11831-013-9091-7 http://link.springer.com/10.1007/s11831-013-9091-7.
Elias, S., Matsagar, V., Research developments in vibration control of structures using passive tuned mass dampers. Annu Rev Control 44 (2017), 129–156, 10.1016/j.arcontrol.2017.09.015 https://linkinghub.elsevier.com/retrieve/pii/S1367578817301372.
De Angelis, M., Perno, S., Reggio, A., Dynamic response and optimal design of structures with large mass ratio TMD. Earthquake Eng Struct Dyn 41:1 (2012), 41–60, 10.1002/eqe.1117 http://doi.wiley.com/10.1002/eqe.1117.
De Domenico, D., Ricciardi, G., An enhanced base isolation system equipped with optimal tuned mass damper inerter (TMDI). Earthquake Eng Struct Dyn 47:5 (2018), 1169–1192, 10.1002/eqe.3011 http://doi.wiley.com/10.1002/eqe.3011.
Dell'Elce, L., Gourc, E., Kerschen, G., A robust equal-peak method for uncertain mechanical systems. J Sound Vib 414 (2018), 97–109, 10.1016/j.jsv.2017.10.038 https://linkinghub.elsevier.com/retrieve/pii/S0022460X17307629.
Habib, G., Detroux, T., Viguié, R., Kerschen, G., Nonlinear generalization of Den Hartog's equal-peak method. Mech Syst Signal Process 52–53:1 (2015), 17–28, 10.1016/j.ymssp.2014.08.009.
Snowdon, J.C., Steady-state behavior of the dynamic absorber—addendum. J Acoust Soc Am 36:6 (1964), 1121–1123, 10.1121/1.1919171 http://asa.scitation.org/doi/10.1121/1.1919171.
Iwanami, K., Seto, K., An optimum design method for the dual dynamic damper and its effectiveness. Bull JSME 27:231 (1984), 1965–1973, 10.1299/jsme1958.27.1965 http://joi.jlc.jst.go.jp/JST.Journalarchive/jsme1958/27.1965?from=CrossRef.
Igusa, T., Xu, K., Vibration control using multiple tuned mass dampers. J Sound Vib 175:4 (1994), 491–503, 10.1006/jsvi.1994.1341 https://linkinghub.elsevier.com/retrieve/pii/S0022460X84713411.
Yamaguchi, H., Harnpornchai, N., Fundamental characteristics of Multiple Tuned Mass Dampers for suppressing harmonically forced oscillations. Earthq Eng Struct Dyn 22:1 (1993), 51–62, 10.1002/eqe.4290220105 http://doi.wiley.com/10.1002/eqe.4290220105.
Abé, M., Fujino, Y., Dynamic characterization of multiple tuned mass dampers and some design formulas. Earthq Eng Struct Dyn 23:8 (1994), 813–835, 10.1002/eqe.4290230802 http://doi.wiley.com/10.1002/eqe.4290230802.
Neubert, V.H., Dynamic absorbers applied to a bar that has solid damping. J Acoust Soc Am 36:4 (1964), 673–680, 10.1121/1.1919039 http://asa.scitation.org/doi/10.1121/1.1919039.
Snowdon, J.C., Vibration of cantilever beams to which dynamic absorbers are attached. J Acoust Soc Am 39:5A (1966), 878–886, 10.1121/1.1909966 http://asa.scitation.org/doi/10.1121/1.1909966.
Kitis, L., Wang, B., Pilkey, W., Vibration reduction over a frequency range. J Sound Vib 89:4 (1983), 559–569, 10.1016/0022-460X(83)90357-7 https://linkinghub.elsevier.com/retrieve/pii/0022460X83903577.
Özgüven, H., Çandir, B., Suppressing the first and second resonances of beams by dynamic vibration absorbers. J Sound Vib 111:3 (1986), 377–390, 10.1016/S0022-460X(86)81399-2 https://linkinghub.elsevier.com/retrieve/pii/S0022460X86813992.
Rana, R., Soong, T., Parametric study and simplified design of tuned mass dampers. Eng Struct 20:3 (1998), 193–204, 10.1016/S0141-0296(97)00078-3 https://linkinghub.elsevier.com/retrieve/pii/S0141029697000783.
Clark AJ. Multiple passive tuned mass damper for reducing earthquake induced building motion. In: 9th world conf. earthq. eng.; 1988. p. 779–84.
Yau, J.-D., Yang, Y.-B., A wideband MTMD system for reducing the dynamic response of continuous truss bridges to moving train loads. Eng Struct 26:12 (2004), 1795–1807, 10.1016/j.engstruct.2004.06.015 https://linkinghub.elsevier.com/retrieve/pii/S0141029604001993.
Krenk, S., Høgsberg, J., Tuned resonant mass or inerter-based absorbers: unified calibration with quasi-dynamic flexibility and inertia correction. Proc R Soc A Math Phys Eng Sci, 472(2185), 2016, 20150718, 10.1098/rspa.2015.0718 http://rspa.royalsocietypublishing.org/lookup/doi/10.1098/rspa.2015.0718.
Li, C., Qu, W., Optimum properties of multiple tuned mass dampers for reduction of translational and torsional response of structures subject to ground acceleration. Eng Struct 28:4 (2006), 472–494, 10.1016/j.engstruct.2005.09.003 https://linkinghub.elsevier.com/retrieve/pii/S0141029605003196.
Han, B., Li, C., Characteristics of linearly distributed parameter-based multiple-tuned mass dampers. Struct Control Heal Monit 15:6 (2008), 839–856, 10.1002/stc.222 http://doi.wiley.com/10.1002/stc.222.
Rade, D.A., Steffen, V., Optimisation of dynamic vibration absorbers over a frequency band. Mech Syst Signal Process 14:5 (2000), 679–690, 10.1006/mssp.2000.1319 https://linkinghub.elsevier.com/retrieve/pii/S0888327000913190.
Zuo, L., Nayfeh, S., Minimax optimization of multi-degree-of-freedom tuned-mass dampers. J Sound Vib 272:3–5 (2004), 893–908, 10.1016/S0022-460X(03)00500-5 https://linkinghub.elsevier.com/retrieve/pii/S0022460X03005005.
Hoang, N., Warnitchai, P., Design of multiple tuned mass dampers by using a numerical optimizer. Earthq Eng Struct Dyn 34:2 (2005), 125–144, 10.1002/eqe.413 http://doi.wiley.com/10.1002/eqe.413.
Li, H.-N., Ni, X.-L., Optimization of non-uniformly distributed multiple tuned mass damper. J Sound Vib 308:1–2 (2007), 80–97, 10.1016/j.jsv.2007.07.014 https://linkinghub.elsevier.com/retrieve/pii/S0022460X07005561.
Salvi, J., Rizzi, E., Optimum tuning of Tuned Mass Dampers for frame structures under earthquake excitation. Struct Control Health Monitor 22:4 (2015), 707–725, 10.1002/stc.1710 http://doi.wiley.com/10.1002/stc.1710.
De Domenico, D., Ricciardi, G., Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems. Earthquake Eng Struct Dyn 47:12 (2018), 2539–2560, 10.1002/eqe.3098 http://doi.wiley.com/10.1002/eqe.3098.
Piccirillo, V., Tusset, A.M., Balthazar, J.M., Optimization of dynamic vibration absorbers based on equal-peak theory. Lat Am J Solids Struct 16:4 (2019), 1–22, 10.1590/1679-78255285 http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252019000400506&lng=en&tlng=en.
Štepánek, J., Máca, J., Design of tuned mass dampers for large structures using modal analysis. Acta Polytechnica CTU Proceedings 26 (2020), 100–106, 10.14311/APP.2020.26.0100 https://ojs.cvut.cz/ojs/index.php/APP/article/view/6396.
Leung, A.Y.T., Zhang, H., Cheng, C.C., Lee, Y.Y., Particle swarm optimization of TMD by non-stationary base excitation during earthquake. Earthq Eng Struct Dyn 37:9 (2008), 1223–1246, 10.1002/eqe.811 http://doi.wiley.com/10.1002/eqe.811.
Leung, A., Zhang, H., Particle swarm optimization of tuned mass dampers. Eng Struct 31:3 (2009), 715–728, 10.1016/j.engstruct.2008.11.017 https://linkinghub.elsevier.com/retrieve/pii/S0141029608003817.
Hadi, M.N.S., Arfiadi, Y., Optimum design of absorber for MDOF structures. J Struct Eng 124:11 (1998), 1272–1280, 10.1061/(ASCE)0733-9445(1998)124:11(1272) http://ascelibrary.org/doi/10.1061/%28ASCE%290733-9445%281998%29124%3A11%281272%29.
Arfiadi, Y., Hadi, M.N.S., Optimum placement and properties of tuned mass dampers using hybrid genetic algorithms. Int J Optim Civ Eng 1 (2011), 167–187 http://ijoce.iust.ac.ir/article-1-14-en.html.
Mohebbi, M., Shakeri, K., Ghanbarpour, Y., Majzoub, H., Designing optimal multiple tuned mass dampers using genetic algorithms (GAs) for mitigating the seismic response of structures. J Vib Control 19:4 (2013), 605–625, 10.1177/1077546311434520 http://journals.sagepub.com/doi/10.1177/1077546311434520.
Bekdas, G., Nigdeli, S.M., Estimating optimum parameters of tuned mass dampers using harmony search. Eng Struct 33:9 (2011), 2716–2723, 10.1016/j.engstruct.2011.05.024 https://linkinghub.elsevier.com/retrieve/pii/S0141029611002343.
Nigdeli, S.M., Bekdas, G., Optimum tuned mass damper design in frequency domain for structures. KSCE J Civ Eng 21:3 (2017), 912–922, 10.1007/s12205-016-0829-2 http://link.springer.com/10.1007/s12205-016-0829-2.
Zhang, H.Y., Zhang, L.J., Tuned mass damper system of high-rise intake towers optimized by improved harmony search algorithm. Eng Struct 138 (2017), 270–282, 10.1016/j.engstruct.2017.02.011.
Viana, F.A.C., Kotinda, G.I., Rade, D.A., Steffen, V., Tuning dynamic vibration absorbers by using ant colony optimization. Comput Struct 86:13–14 (2008), 1539–1549, 10.1016/j.compstruc.2007.05.009 https://linkinghub.elsevier.com/retrieve/pii/S0045794907001885.
Farshidianfar, A., Soheili, S., Ant colony optimization of tuned mass dampers for earthquake oscillations of high-rise structures including soil-structure interaction. Soil Dyn Earthq Eng 51 (2013), 14–22, 10.1016/j.soildyn.2013.04.002 https://linkinghub.elsevier.com/retrieve/pii/S0267726113001048.
Liu, M.-Y., Liang, W.-C., Lin, Y.-Z., Simulated annealing optimization of tuned mass dampers for vibration control of seismic-excited buildings. Proc 9th Int Conf Appl Oper Res (ICAOR 2017) 9 (2017), 1–9.
Salcedo-Sanz, S., Camacho-Gómez, C., Magdaleno, A., Pereira, E., Lorenzana, A., Structures vibration control via Tuned Mass Dampers using a co-evolution Coral Reefs Optimization algorithm. J Sound Vib 393 (2017), 62–75, 10.1016/j.jsv.2017.01.019 https://linkinghub.elsevier.com/retrieve/pii/S0022460X17300391.
Yang, F., Sedaghati, R., Esmailzadeh, E., Vibration suppression of curved beam-type structures using optimal multiple tuned mass dampers. J Vib Control 20:6 (2014), 859–875, 10.1177/1077546312468461 http://journals.sagepub.com/doi/10.1177/1077546312468461.
Woodbury, M.A., Inverting modified matrices. Memo Rep, 42(106), 1950, 336.
Asami, T., Nishihara, O., Baz, A.M., Analytical solutions to H∞ and H2 optimization of dynamic vibration absorbers attached to damped linear systems. J Vib Acoust, 124(2), 2002, 284, 10.1115/1.1456458 http://vibrationacoustics.asmedigitalcollection.asme.org/article.aspx?articleid=1470416.
Petit, F., Loccufier, M., Aeyels, D., On the attachment location of dynamic vibration absorbers. J Vib Acoust, 131(3), 2009, 034501, 10.1115/1.3085888 http://link.aip.org/link/?VAJ/131/034501/1 http://vibrationacoustics.asmedigitalcollection.asme.org/article.aspx?articleid=1471311.
Géradin, M., Rixen, D.J., Mechanical vibrations: theory and application to structural dynamics. 2014, John Wiley & Sons.
Ozer, M.B., Royston, T.J., Extending Den Hartog's vibration absorber technique to multi-degree-of-freedom systems. J Vib Acoust, 127(4), 2005, 341, 10.1115/1.1924642 http://vibrationacoustics.asmedigitalcollection.asme.org/article.aspx?articleid=1470767.
Sherman, B.Y.J., Morrison, W.J., Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Ann Math Stat 21:1 (1950), 124–127 http://www.jstor.org/stable/2236561.
Cha, P.D., Yoder, N.C., Applying Sherman-Morrison-Woodbury formulas to analyze the free and forced responses of a linear structure carrying lumped elements. J Vib Acoust, 129(3), 2007, 307, 10.1115/1.2730537 http://vibrationacoustics.asmedigitalcollection.asme.org/article.aspx?articleid=1470946.
Nocedal, J., Wright, S.J., Numerical optimization. 2006, Springer.
Bruinsma, N., Steinbuch, M., A fast algorithm to compute the H_∞-norm of a transfer function matrix. Syst Control Lett 14:4 (1990), 287–293, 10.1016/0167-6911(90)90049-Z https://linkinghub.elsevier.com/retrieve/pii/016769119090049Z.