Robust Stochastic Design of Viscous Dampers for Base Isolation Applications

Chapter
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 21)

Abstract

Over the last decades, there has been a growing interest in the application of base isolation techniques to civil structures. Of the many relevant research topics, the efficient design of additional dampers, to operate in tandem with the isolation system, has emerged as one of the more important. One of the main challenges of such applications has been the explicit consideration of the nonlinear behavior of the isolators or the dampers in the design process. Another challenge has been the efficient control of the dynamic response under near-field ground motions. A framework is discussed in this chapter that addresses both these challenges. A probability logic approach is adopted for addressing the uncertainties about the structural model as well as the variability of future excitations. In this stochastic setting, a realistic model for the description of near-field ground motions is discussed. The design objective is then defined as the maximization of structural reliability. A simulation-based approach is implemented for evaluation of the stochastic performance and an efficient framework is discussed for performing the associated challenging design optimization and for selecting values of the controllable damper parameters that optimize the system reliability.

Keywords

Time-dependent boundary conditions Elastodynamics Penalty method Large mass method Large spring method Transient dynamics Non-linear system 

References

  1. 1.
    Christopoulos C, Filiatrault A (2006) Principles of passive supplemental damping and seismic isolation. IUSS Press, PaviaGoogle Scholar
  2. 2.
    Hall FF, Heaton TH, Halling MW, Wald DJ (1995) Near-source ground motion and its effects on flexible buildings. Earth Spectra 11:569–605CrossRefGoogle Scholar
  3. 3.
    Mavroeidis GP, Papageorgiou AP (2003) A mathematical representation of near-fault ground motions. B Seismol Soc of Am 93:1099–1131CrossRefGoogle Scholar
  4. 4.
    Bray JD, Rodriguez-Marek A (2004) Characterization of forward-directivity ground motions in the near-fault region. Soil Dyn Earth Eng 24:815–828CrossRefGoogle Scholar
  5. 5.
    Makris N, Black JB (2004) Dimensional analysis of bilinear oscillators under pulse-type excitations. J Eng Mech-ASCE 130:1019–1031CrossRefGoogle Scholar
  6. 6.
    Zhang YF, Iwan WD (2002) Protecting base isolated structures from near-field ground motion by tuned interaction damper. J Eng Mech ASCE 128:287–295CrossRefGoogle Scholar
  7. 7.
    Narasimhan S, Nagarajaiah S, Gavin HP, Johnson EA (2006) Smart base isolated benchmark building part I: problem definition. J Struct Control Health Monitor 13:573–588CrossRefGoogle Scholar
  8. 8.
    Providakis CP (2008) Effect of LRB isolators and supplemental viscous dampers on seismic isolated buildings under near fault excitation. Eng Struct 30:1187–1198CrossRefGoogle Scholar
  9. 9.
    Kelly JM (1999) The role of damping in seismic isolation. Earth Eng Struct Dyn 28:3–20CrossRefGoogle Scholar
  10. 10.
    Taflanidis AA, Scruggs JT, Beck JL (2008) Probabilistically robust nonlinear design of control systems for base-isolated structures. J Struct Control Health Monitor 15:697–719CrossRefGoogle Scholar
  11. 11.
    Taflanidis AA, Beck JL (2008) An efficient framework for optimal robust stochastic system design using stochastic simulation. Comput Method Appl Mech Eng 198:88–101MATHCrossRefGoogle Scholar
  12. 12.
    Lee D, Taylor DP (2001) Viscous damper development and future trends. Struct Des Tall Buil 10:311–320CrossRefGoogle Scholar
  13. 13.
    Park YJ, Wen YK, Ang AHS (1986) Random vibration of hysteretic systems under bi-directional ground motions. Earth Eng Struct Dyn 14:543–557CrossRefGoogle Scholar
  14. 14.
    Boore DM (2003) Simulation of ground motion using the stochastic method. Pure Appl Geophys 160:635–676CrossRefGoogle Scholar
  15. 15.
    Atkinson GW, Silva W (2000) Stochastic modeling of California ground motions. B Seismol Soc Am 90:255–274CrossRefGoogle Scholar
  16. 16.
    Alavi B, Krawinkler H (2000) Consideration of near-fault ground motion effects in seismic design. In: 12th World conference on earthquake engineering, Auckland, New ZealandGoogle Scholar
  17. 17.
    Boore DM, Joyner WB (1997) Site amplifications for generic rock sites. B Seismol Soc Am 87:327–341Google Scholar
  18. 18.
    Jaynes ET (2003) Probability theory: the logic of science. Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  19. 19.
    Taflanidis AA, Beck JL (2009) Life-cycle cost optimal design of passive dissipative devices. Struct Saf 31:508–522CrossRefGoogle Scholar
  20. 20.
    Papadimitriou C, Beck JL, Katafygiotis LS (2001) Updating robust reliability using structural test data. Probabilist Eng Mech 16:103–113CrossRefGoogle Scholar
  21. 21.
    Enevoldsen I, Sorensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15:169–196CrossRefGoogle Scholar
  22. 22.
    Royset JO, Der Kiureghian A, Polak E (2006) Optimal design with probabilistic objective and constraints. J Eng Mech ASCE 132:107–118CrossRefGoogle Scholar
  23. 23.
    Gasser M, Schueller GI (1997) Reliability-based optimization of structural systems. Math Method Oper Res 46:287–307MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Robert CP, Casella G (2004) Monte Carlo statistical methods, 2nd edn. Springer, New YorkMATHGoogle Scholar
  25. 25.
    Ruszczynski A, Shapiro A (2003) Stochastic programming. Elsevier, New YorkMATHGoogle Scholar
  26. 26.
    Spall JC (2003) Introduction to stochastic search and optimization. Wiley-Interscience, New YorkMATHCrossRefGoogle Scholar
  27. 27.
    Royset JO, Polak E (2004) Reliability-based optimal design using sample average approximations. Probabilist Eng Mech 19:331–343CrossRefGoogle Scholar
  28. 28.
    Taflanidis AA, Beck JL (2008) Stochastic subset optimization for optimal reliability problems. Probabilist Eng Mech 23:324–338CrossRefGoogle Scholar
  29. 29.
    Taflanidis AA, Beck JL (2009) Stochastic subset optimization for reliability optimization and sensitivity analysis in system design. Comput Struct 87:318–331CrossRefGoogle Scholar
  30. 30.
    Au SK, Beck JL (2003) Subset simulation and its applications to seismic risk based on dynamic analysis. J Eng Mech ASCE 129:901–917CrossRefGoogle Scholar
  31. 31.
    Berg BA (2004) Markov Chain Monte Carlo simulations and their statistical analysis. World Scientific SingaporeGoogle Scholar
  32. 32.
    Au SK, Beck JL (1999) A new adaptive importance sampling scheme. Struct Saf 21:135–158CrossRefGoogle Scholar
  33. 33.
    Au SK, Beck JL (2003) Importance sampling in high dimensions. Struct Saf 25:139–163CrossRefGoogle Scholar
  34. 34.
    Pradlwater HJ, Schueller GI, Koutsourelakis PS, Champris DC (2007) Application of line sampling simulation method to reliability benchmark problems. Struct Saf 29:208–221CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Civil Engineering and Geological SciencesUniversity of Notre DameNotre DameUSA

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