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Equivalent damping of SDOF structure with Maxwell damper

  • Chuangdi LiEmail author
  • Tun Li
  • Dingwei Ban
  • Xinguang Ge
Technical Paper
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Abstract

To predict the maximum earthquake response of an SDOF structure with a Maxwell fluid damper or supplemental brace-viscous damper system using the seismic design response spectrum technique, a new approach is presented to determine the first- and second-order equivalent viscous damping and stiffness, the peak responses, and the damper force of the above structure. Based on the fact that the dynamic characteristics of a general linear viscoelastically damped structure are fully determined by its free vibration properties and the relaxation time constants of a Maxwell fluid damper and supplemental brace-viscous damper system in engineering practice are all small, the method of improved multiple time scales and the equivalent criterion in which all free vibration properties are the same are used to obtain the first- and second-order equivalent viscous damping and stiffness of the above structure in closed form. The accuracy of the proposed method is higher and significantly better than that of the modal strain energy method. Furthermore, in the parametric range of the requirements of the Chinese "Code for Seismic Design of Buildings", the error of the proposed second-order equivalent system for the above-mentioned engineering structure is not more than 0.5%.

Keywords

Maxwell damper supplemental brace-viscous damper system equivalent viscous damping response spectrum method maximum response of damper force 
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Notes

Acknowledgement

This work was financially supported by the National Natural Science Foundation of China under Grant No. 51468005 and 51368008, Guangxi Natural Science Foundation under Grant No. 2014GXNSFAA118315, and the Innovative Research Team Program of Guangxi University of Science and Technology (2015).

References

  1. Abramowitz M and Stegun IA (1965), Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, New York: Dover Publication Inc.Google Scholar
  2. Cacciola P, Colajanni P and Muscolino G (2004), “Combination of Modal Response Consistent with Seismic Input Representation,” Journal of Structural Engineering, 130(1): 47–55.CrossRefGoogle Scholar
  3. Chang KC, Soong TT, Oh ST and Lai ML (1995), “Seismic Behavior of Steel Frame with Added Viscoelastic Damper,” Journal of Structural Engineering, 121(10): 1418–1426.CrossRefGoogle Scholar
  4. Chang TS and Singh MP (2009), “Mechanical model parameter for viscoelastic damper,” Journal of Engineering Mechanics, 135(6): 581–584.CrossRefGoogle Scholar
  5. Chen YT and Chai YH (2011), “Effects of Brace Stiffness on Performance of Structures with Supplemental Maxwell Model-Based Brace-Damper Systems,” Earthquake Engineering and Structural Dynamics, 40: 75–92.CrossRefGoogle Scholar
  6. Christopoulos C and Filiatrault A (2006), Principle of Passive Supplemental Damping and Seismic Isolation, Pavia, Italy: IUSS Press.Google Scholar
  7. Fu Y amd Kasai K (1998), “Comparative Study of Frames Using Viscoelastic and Viscous Dampers,” Journal of Structural Engineering, 124(5): 513–522.CrossRefGoogle Scholar
  8. GB50011-2010 (2010), Code for Seismic Design of Buildings, Beijing: China Architecture and Building Press. (in Chinese)Google Scholar
  9. Huang HC (2009), “Efficiency of the Motion Amplification Device with Viscous Dampers and its Application in High-rise Building,” Earthquake Engineering and Engineering Vibration, 8(4): 521–536.CrossRefGoogle Scholar
  10. Lewandowski R and Lasecka-Plura M (2016), “Design Sensitivity Analysis of Structures with Viscoelastic Dampers,” Computers and Structures, 164: 95–107.CrossRefGoogle Scholar
  11. Li CD, Zou WJ, Ge XG and Li T (2013), “Random Response and Equivalent Damping of MDOF Dissipation Structures with General Integral Model Viscoelastic Dampers,” Engineering Mechanics, 30(4): 136–145. (in Chinese)Google Scholar
  12. Li CD, Chen OY, Ge XG and Li T (2014a), “Analytic Method of Earthquake Action Calculation for Multistory Isolated Structure,” Chinese Journal of Applied Mechanics, 31(3): 326–331. (in Chinese)Google Scholar
  13. Li CD, Chen OY, Ge XG and Li T (2014b), “Decoupling in a Real Space and Earthquake Action Analysis for High-rise Isolated Structures,” Journal of Vibration and Shock, 33(15): 119–125. (in Chinese)Google Scholar
  14. Li CD, Li T, Ge XG and Zou WJ (2015), “Exact Non-Orthogonal Modal Superposition Solutions of Transient Response of MDOF Dissipation Structures with Ggeneral Linear Viscoelastic Dampers,” Engineering Mechanics, 32(11): 140–149. (in Chinese)CrossRefGoogle Scholar
  15. Li CD, Li T, Wei XT and Ge XG (2016), “Exact Response Analysis of Energy Dissipation Structures with Maxwell Dampers under Non-Stationary Seismic Excitation,” Journal of Vibration and Shock, 35(19): 172–180. (in Chinese)Google Scholar
  16. Lin YY and Chang KC (2003), “Study on Damping Reduction Factor for Building under Earthquake Ground Motions,” Journal of Structural Engineering, 129(3): 206–214.CrossRefGoogle Scholar
  17. Londono JM, Neild SA and Wagg DJ (2013), “A Noniterative Design Procedure for Supplement Brace-Damper Systems in Single-Degree-of-Freedom Systems,” Earthquake Engineering and Structural Dynamics, 42: 2361–2367.CrossRefGoogle Scholar
  18. Nayfeh A H (1973), Perturbation Methods, New York: Wiley.Google Scholar
  19. Ou JP, Wu B and Long X (1998), “A Seismic Design Methods of Passive Energy Dissipation Systems,” Earthquake Engineering and Engineering Vibration, 18(2): 98–107. (in Chinese)Google Scholar
  20. Ou JP, Long X and Li Q S (2007), “Seismic Response Analysis of Structures with Velocity-Dependent Dampers,” Journal of Constructional Steel Research, 63: 628–638.CrossRefGoogle Scholar
  21. Palmeri A and Ricciardelli F (2003), “State Space Formulation for Linear Viscoelastic System with Memory,” Journal of Engineering Mechanics, 129(7): 715–724.CrossRefGoogle Scholar
  22. Palmeri A (2006), “Correlation Coefficients for Structures with Viscoelastic Dampers,” Engineering Structures, 28: 1197–1208.CrossRefGoogle Scholar
  23. Park SW (2001), “Analytical Modeling of Viscoelastic Damper for Structural and Vibration Control,” Journal of Solid and Structures, 38: 8065–8092.CrossRefGoogle Scholar
  24. Ras A and Boumechra N (2016), “Seismic Energy Dissipation Study of Linear Fluid Viscous Damper in Steel Structure Design,” Alexandria Engineering Journal, 55: 2821–2832.CrossRefGoogle Scholar
  25. Singh MP, Verma NP and Moreschi LM (2003), “Seismic Analysis and Design with Maxwell Dampers,” Journal of Engineering Mechanics, 129(3): 273–282.CrossRefGoogle Scholar
  26. Soong TT and Grigoriu M (1993), Random Vibration of Mechanical and Structural Systems, Englewwod Cliffs, NJ, Prentice-Hall.Google Scholar
  27. Soong TT and Dargush GF (1997), Passive Energy Dissipation Systems in Structural Engineering, New York: Wiley.Google Scholar
  28. Soong TT and Spencer BF (2002), “Supplemental Energy Dissipation: State-of-the-Art and State-of-the-Practice,” Engineering Structures, 24: 243–259.CrossRefGoogle Scholar
  29. Spencer BF and Nagarajaiah S (2003), “State of the Art in Structural Control,” Journal of Structural Engineering, 129(7): 845–856.CrossRefGoogle Scholar
  30. Takewaki I (2009), Building Control with Passive Dampers: Optimal Performance-based Design for Earthquake, Singapore: Wiley.CrossRefGoogle Scholar
  31. Tubaldi E (2015), “Dynamic Behavior of Adjacent Buildings Connected by Linear Viscous/Viscoelastic Dampers,” Structural Control and Health Monitoring, 22(8):1086–1102.CrossRefGoogle Scholar
  32. Yamada K (2008), “Dynamic Characteristics of SDOF Structure with Maxwell Element,” Journal Engineering Mechanics, 134(5): 396–404.CrossRefGoogle Scholar
  33. Zanmbrano A, Inaudi JA and Kelly JM (1996), “Modal Coupling and Accuracy of Modal Strain Energy Method,” Journal of Engineering Mechanics, 122(7): 603–612.CrossRefGoogle Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil EngineeringGuangxi University of Science and TechnologyLiuzhou, GuangxiChina

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