Optimal placement of damping devices in buildings

  • Wilson Emilio David SánchezEmail author
  • Suzana Moreira Avila
  • José Luís Vital de Brito
Technical Paper


The appropriate use of energy dissipating devices improves the behavior of structures when subjected to external loads, defining the optimal location of the dampers; therefore, it is crucial to ensure their efficiency. In this work, the mathematical expressions of an efficient and systematic procedure proposed by Takewaki were adapted and detailed to find the optimum location of dampers when a structural damper is used. This procedure consists of minimizing the sum of the amplitudes of the transfer functions evaluated at the undamped fundamental frequency of a structural system subject to constraints on the sum of the damping coefficients of the added dampers. For instance, at the beginning and end of the calculation, the sum of the damping coefficients entered must be the same. A series of numerical examples on shear building models within a range of two to six stories are used to verify the efficiency of the systematic procedure. The results showed that the optimal placement method is efficient due to the amplitude reduction of the transfer function after the optimal distribution of the damping coefficients in the structure.


Structural damping Incremental inverse problem Optimal placement of dampers Passive control Transfer function 



The authors gratefully acknowledge the financial support of CNPq, CAPES and Ingenieria Especializada (ieb—COL), which made this research possible.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Kasai K, Maison BF (1997) Building pounding damage during the 1989 Loma Prieta earthquake. Eng Struct 19:195–207CrossRefGoogle Scholar
  2. 2.
    Rosenblueth E, Meli R (1986) The 1985 Mexico earthquake. Concr Int 8:23–34Google Scholar
  3. 3.
    Ogata K (2010) Ingeniería de Control Moderna, 5th edn. Pearson, MadridGoogle Scholar
  4. 4.
    Takewaki I (1997) Optimal damper placement for minimum transfer functions. Earthq Eng Struct Dyn 26:1113–1124CrossRefGoogle Scholar
  5. 5.
    Takewaki I (1997) Efficient redesign of damped structural systems for target transfer functions. Comput Methods Appl Mech Eng 147:275–286CrossRefzbMATHGoogle Scholar
  6. 6.
    Takewaki I (1998) Optimal damper positioning in beams for minimum dynamic compliance. Comput Methods Appl Mech Eng 156:363–373CrossRefzbMATHGoogle Scholar
  7. 7.
    Takewaki I (2000) Optimal damper placement for critical excitation. Probab Eng Mech 15:317–325CrossRefGoogle Scholar
  8. 8.
    Takewaki I, Uetani K (1999) Optimal damper placement for building structures including surface ground amplification. Soil Dyn Earthq Eng 18:363–371. CrossRefGoogle Scholar
  9. 9.
    Aydin E, Boduroglu MH, Guney D (2007) Optimal damper distribution for seismic rehabilitation of planar building structures. Eng Struct 29:176–185CrossRefGoogle Scholar
  10. 10.
    Aydin E, Boduroglu MH (2008) Optimal placement of steel diagonal braces for upgrading the seismic capacity of existing structures and its comparison with optimal dampers. J Constr Steel Res 64:72–86CrossRefGoogle Scholar
  11. 11.
    Aydin E (2012) Optimal damper placement based on base moment in steel building frames. J Constr Steel Res 79:216–225CrossRefGoogle Scholar
  12. 12.
    Martinez CA, Curadelli O, Compagnoni ME (2013) Optimal design of passive viscous damping systems for buildings under seismic excitation. J Constr Steel Res 90:253–264CrossRefGoogle Scholar
  13. 13.
    Martínez CA, Curadelli O, Compagnoni ME (2014) Optimal placement of nonlinear hysteretic dampers on planar structures under seismic excitation. Eng Struct 65:89–98CrossRefGoogle Scholar
  14. 14.
    Sonmez M, Aydin E, Karabork T (2013) Using an artificial bee colony algorithm for the optimal placement of viscous dampers in planar building frames. Struct Multidiscip Optim 48:395–409. CrossRefGoogle Scholar
  15. 15.
    Uetani K, Tsuji M, Takewaki I (2003) Application of an optimum design method to practical building frames with viscous dampers and hysteretic dampers. Eng Struct 25:579–592. CrossRefGoogle Scholar
  16. 16.
    Uz ME, Hadi MNS (2014) Optimal design of semi active control for adjacent buildings connected by MR damper based on integrated fuzzy logic and multi-objective genetic algorithm. Eng Struct 69:135–148. CrossRefGoogle Scholar
  17. 17.
    Murakami Y, Noshi K, Fujita K et al (2015) Optimal Placement of Hysteretic Dampers via Adaptive Sensitivity-Smoothing Algorithm. Eng Appl Sci Optim 38:233–247CrossRefGoogle Scholar
  18. 18.
    Pu W, Liu C, Zhang H, Kasai K (2016) Seismic control design for slip hysteretic timber structures based on tuning the equivalent stiffness. Eng Struct 128:199–214. CrossRefGoogle Scholar
  19. 19.
    Leu LJ, Chang JT (2011) Optimal allocation of non-linear viscous dampers for three-dimensional building structures. Procedia Eng 14:2489–2497. CrossRefGoogle Scholar
  20. 20.
    Garcia DL (2001) A simple method for the design of optimal damper configurations in MDOF structures. Earthq. Spectra 17:387–398CrossRefGoogle Scholar
  21. 21.
    Landi L, Conti F, Diotallevi PP (2015) Effectiveness of different distributions of viscous damping coefficients for the seismic retrofit of regular and irregular RC frames. Eng Struct 100:79–93. CrossRefGoogle Scholar
  22. 22.
    Kim J, Bang S (2002) Optimum distribution of added viscoelastic dampers for mitigation of torsional responses of plan-wise asymmetric structures. Eng Struct 24:1257–1269. CrossRefGoogle Scholar
  23. 23.
    Xu ZD, Shen YP, Zhao HT (2003) A synthetic optimization analysis method on structures with viscoelastic dampers. Soil Dyn Earthq Eng 23:683–689. CrossRefGoogle Scholar
  24. 24.
    Xu ZD, Zhao HT, Li AQ (2004) Optimal analysis and experimental study on structures with viscoelastic dampers. J Sound Vib 273:607–618. CrossRefGoogle Scholar
  25. 25.
    Main JA, Krenk S (2005) Efficiency and tuning of viscous dampers on discrete systems. J Sound Vib 286:97–122CrossRefGoogle Scholar
  26. 26.
    Lang ZQ, Guo PF, Takewaki I (2013) Output frequency response function based design of additional nonlinear viscous dampers for vibration control of multi-degree-of-freedom systems. J Sound Vib 332:4461–4481CrossRefGoogle Scholar
  27. 27.
    Alibrandi U, Falsone G (2015) Optimal design of dampers in seismic excited structures by the Expected value of the stochastic Dissipated Power. Probabilistic Eng Mech 41:129–138. CrossRefGoogle Scholar
  28. 28.
    Kandemir-Mazanoglu EC, Mazanoglu K (2017) An optimization study for viscous dampers between adjacent buildings. Mech Syst Signal Process 89:88–96. CrossRefGoogle Scholar
  29. 29.
    Lin CC, Lu LY, Lin GL, Yang TW (2010) Vibration control of seismic structures using semi-active friction multiple tuned mass dampers. Eng Struct 32:3404–3417. CrossRefGoogle Scholar
  30. 30.
    Lin G-L, Lin C-C, Chen B-C, Soong T-T (2015) Vibration control performance of tuned mass dampers with resettable variable stiffness. Eng Struct 83:187–197. CrossRefGoogle Scholar
  31. 31.
    Lu LY (2004) Predictive control of seismic structures with semi-active friction dampers. Earthq Eng Struct Dyn 33:647–668. CrossRefGoogle Scholar
  32. 32.
    Park HS, Lee E, Choi SW et al (2016) Genetic-algorithm-based minimum weight design of an outrigger system for high-rise buildings. Eng Struct 117:496–505. CrossRefGoogle Scholar
  33. 33.
    Park K-S, Ok S-Y (2015) Optimal design of hybrid control system for new and old neighboring buildings. J Sound Vib 336:16–31CrossRefGoogle Scholar
  34. 34.
    Rama Mohan Rao A, Sivasubramanian K (2008) Optimal placement of actuators for active vibration control of seismic excited tall buildings using a multiple start guided neighbourhood search (MSGNS) algorithm. J Sound Vib 311:133–159CrossRefGoogle Scholar
  35. 35.
    Meirovitch L (1986) Elements of Vibration Analysis. McGraw-HillGoogle Scholar
  36. 36.
    Whittle J, Williams M, Karavasilis T (2012) Optimal placement of viscous dampers for seismic building design.

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.University of BrasiliaBrasiliaBrazil
  2. 2.University of BrasiliaBrasiliaBrazil

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