Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

RESEARCH PAPER

Abstract

In this paper we discuss the adjoint sensitivity analysis and optimization of hysteretic systems equipped with nonlinear viscous dampers and subjected to transient excitation. The viscous dampers are modeled via the Maxwell model, considering at the same time the stiffening and the damping contribution of the dampers. The time-history analysis adopted for the evaluation of the response of the systems relies on the Newmark-β time integration scheme. In particular, the dynamic equilibrium in each time-step is achieved by means of the Newton-Raphson and the Runge-Kutta methods. The sensitivity of the system response is calculated with the adjoint variable method. In particular, the discretize-then-differentiate approach is adopted for calculating consistently the sensitivity of the system. The importance and the generality of the sensitivity analysis discussed herein is demonstrated in two numerical applications: the retrofitting of a structure subject to seismic excitation, and the design of a quarter-car suspension system. The MATLAB code for the sensitivity analysis considered in the first application is provided as “Supplementary Material”.

Keywords

Adjoint sensitivity analysis Nonlinear dynamic systems Viscous dampers Gradient-based optimization 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments. The research presented in this paper was founded by the Israeli Ministry of Science, Technology and Space. The authors gratefully acknowledge this financial support.

Supplementary material

158_2017_1858_MOESM1_ESM.zip (1.3 mb)
(ZIP 1.25 MB)

References

  1. Almazán JL, Espinoza G, Aguirre JJ (2012) Torsional balance of asymmetric structures by means of tuned mass dampers. Eng Struct 42:308–328CrossRefGoogle Scholar
  2. Argyris JH, Mlejnek HP (1991) Dynamics of structures. North HollandGoogle Scholar
  3. Brodersen ML, Høgsberg J (2016) Hybrid damper with stroke amplification for damping of offshore wind turbines. Wind Energy 19(12):2223–2238CrossRefGoogle Scholar
  4. Caetano E, Cunha A, Moutinho C, Magalhaes F (2010) Studies for controlling human-induced vibration of the Pedro e Ines footbridge, Portugal. Part 2: implementation of tuned mass dampers. Eng Struct 32(4):1082–1091CrossRefGoogle Scholar
  5. Casado CM, Diaz IM, de Sebastian J, Poncela AV, Lorenzana A (2013) Implementation of passive and active vibration control on an in-service footbridge. Struct Control Health Monit 20(1): 70–87CrossRefGoogle Scholar
  6. Charmpis DC, Komodromos P, Phocas MC (2012) Optimized earthquake response of multi-storey buildings with seismic isolation at various elevations. Earthq Eng Struct Dyn 41(15):2289–2310Google Scholar
  7. Chopra AK (2011) Dynamics of structures: theory and applications to earthquake engineering. Prentice-Hall, Englewood CliffsGoogle Scholar
  8. Constantinou MC, Soong TT, Dargush GF (1998) Passive energy dissipation systems for structural design and retrofit. Multidisciplinary Center for Earthquake Engineering Research Buffalo, New YorkGoogle Scholar
  9. Dahl J, Jensen JS, Sigmund O (2008) Topology optimization for transient wave propagation problems in one dimension: design of filters and pulse modulators. Struct Multidiscip Optim 36(6): 585–595MathSciNetCrossRefMATHGoogle Scholar
  10. Daniel Y, Lavan O (2015) Optimality criteria based seismic design of multiple tuned-mass-dampers for the control of 3D irregular buildings. Earthq Struct 8(1):77–100CrossRefGoogle Scholar
  11. Dargush GF, Sant RS (2005) Evolutionary aseismic design and retrofit of structures with passive energy dissipation. Earthq Eng Struct Dyn 34(May):1601–1626CrossRefGoogle Scholar
  12. Elesin Y, Lazarov BS, Jensen JS, Sigmund O (2012) Design of robust and efficient photonic switches using topology optimization. Photon Nanostruct - Fundamentals Appl 10(1):153–165CrossRefGoogle Scholar
  13. Georgiou G, Verros G, Natsiavas S (2007) Multi-objective optimization of quarter-car models with a passive or semi-active suspension system. Veh Syst Dyn 45(March 2015):77–92CrossRefGoogle Scholar
  14. Gurobi Optimization Inc. (2016) Gurobi Optimizer Reference Manual. http://www.gurobi.com
  15. Haftka RT, Adelman HM (1989) Recent developments in structural sensitivity analysis. Struct Optim 1 (3):137–151CrossRefGoogle Scholar
  16. Infanti S, Castellano MG (2007) Sheikh Zayed bridge seismic protection system. In: 10th world conference on seismic isolation, energy dissipation and active vibrations control of structures, number May. Istanbul, TurkeyGoogle Scholar
  17. Infanti S, Papanikolas P, Benzoni G, Castellano MG (2004) Rion antirion bridge: design and full–scale testing of the seismic protection devices. In: 13th world conference on earthquake engineering. Vancouver, B.C., CanadaGoogle Scholar
  18. Infanti S, Robinson J, Smith R (2008) Viscous dampers for high-rise buildings. In: 14th world conference on earthquake engineering (14WCEE), number July. Beijing, ChinaGoogle Scholar
  19. Jensen JS, Nakshatrala PB, Tortorelli DA (2014) On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems. Struct Multidiscip Optim 49(2006):831–837MathSciNetCrossRefGoogle Scholar
  20. Kanno Y (2013) Damper placement optimization in a shear building model with discrete design variables: a mixed-integer second-order cone programming approach. Earthq Eng Struct Dyn 42(11):1657–1676CrossRefGoogle Scholar
  21. Kasai K, Oohara K (2001) Algorith and computer code to simulate nonlinear viscous dampers. In: Passively controlled structure symposium, Yokohama, JapanGoogle Scholar
  22. Klembczyk AR, Mosher MW (2000) Analysis, optimization, and development of a specialized passive shock isolation system for high speed planning boat seats. Technical Report, Taylor Devices Inc. and Tayco Developments Inc., North TonawandaGoogle Scholar
  23. Lavan O, Levy R (2005) Optimal design of supplemental viscous dampers for irregular shear-frames in the presence of yielding. Earthq Eng Struct Dyn 34(8):889–907CrossRefGoogle Scholar
  24. Lavan O, Levy R (2010) Performance based optimal seismic retrofitting of yielding plane frames using added viscous damping. Earthq Struct 1(3):307–326CrossRefGoogle Scholar
  25. Lavan O, Amir O (2014) Simultaneous topology and sizing optimization of viscous dampers in seismic retrofitting of 3D irregular frame structures. Earthq Eng Struct Dyn 43:1325–1342CrossRefGoogle Scholar
  26. Lavan O, Levy R (2006a) Optimal peripheral drift control of 3D irregular framed structures using supplemental viscous dampers. J Earthq Eng 10(6):903–923Google Scholar
  27. Lavan O, Levy R (2006b) Optimal design of supplemental viscous dampers for linear framed structures. Earthq Eng Struct Dyn 35(3):337–356Google Scholar
  28. Le C, Bruns TE, Tortorelli DA (2012) Material microstructure optimization for linear elastodynamic energy wave management, vol 60Google Scholar
  29. Miyamoto HK, Taylor D (2000) Structural control of dynamic blast loading. In: Proceedings from structures congress on advanced technology in structural engineering, 2000, pp 1–8Google Scholar
  30. Nakshatrala PB, Tortorelli DA (2016) Nonlinear structural design using multiscale topology optimization. Part II: Transient formulation, vol 304Google Scholar
  31. National Information Service for Earthquake Engineering - University of California Berkeley (2013) 10 pairs of horizontal ground motions for Los Angeles with a probability of exceedence of 10% in 50 yearsGoogle Scholar
  32. Oohara K, Kasai K (2002) Time-history analysis model for nonlinear viscous dampers. In: Structural engineers world congress (SEWC). Yokohama, JapanGoogle Scholar
  33. Pollini N, Lavan O, Amir O (2016) Towards realistic minimum-cost optimization of viscous fluid dampers for seismic retrofitting. Bull Earthq Eng 14(3):971–998CrossRefGoogle Scholar
  34. Pollini N, Lavan O, Amir O (2017) Minimum-cost optimization of nonlinear fluid viscous dampers and their supporting members for seismic retrofitting. Earthq Eng Struct Dyn 46:1941–1961Google Scholar
  35. Quarteroni A, Sacco R, Saleri F (2007) Numerical mathematics, volume 37 of Texts in Applied Mathematics. Springer, BerlinMATHGoogle Scholar
  36. Seleemah AA, Constantinou MC (1997) Investigation of seismic response of buildings with linear and nonlinear fluid viscous dampers. Technical Report. University at Buffalo, BuffaloGoogle Scholar
  37. Simon-Talero M, Merino RM, Infanti S (2006) Seismic protection of the Guadalfeo bridge by viscous dampers. In: 1st European conference on earthquake engineering and seismology, number September. Geneva, Switzerland, pp 3–8Google Scholar
  38. Sivaselvan MV, Reinhorn AM (2000) Hysteretic models for deteriorating inelastic structures. J Eng Mech 126(6):633–640CrossRefGoogle Scholar
  39. Smith RJ, Willford MR (2007) The damped outrigger concept for tall buildings. Struct Design Tall Special Buildings 16(4):501–517CrossRefGoogle Scholar
  40. Soong TT, Dargush GF (1997) Passive energy dissipation systems in structural engineering. Wiley, New YorkGoogle Scholar
  41. Suciu CV, Tobiishi T, Mouri R (2012) Modeling and simulation of a vehicle suspension with variable damping versus the excitation frequency. J Telecommun Info Technol 2012(1):83–89Google Scholar
  42. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(June 1986):359–373MathSciNetCrossRefMATHGoogle Scholar
  43. Takewaki I (1997) Optimal damper placement for minimum transfer functions. Earthq Eng Struct Dyn 26 (February):1113–1124CrossRefGoogle Scholar
  44. Taylor D (2015) Personal comunicationGoogle Scholar
  45. Tortorelli DA, Michaleris P (1994) Design sensitivity analysis overview and review. Inverse Prob Eng 1 (December 2013):71– 105CrossRefGoogle Scholar
  46. Turteltaub S (2005) Optimal non-homogeneous composites for dynamic loading. Struct Multidiscip Optim 30 (2):101–112MathSciNetCrossRefMATHGoogle Scholar
  47. Yang JN, Agrawal AK, Samali B, Wu J-C (2004) Benchmark problem for response control of wind-excited tall buildings. J Eng Mech 130(4):437–446CrossRefGoogle Scholar
  48. Yun K-S, Youn S-K (2017) Design sensitivity analysis for transient response of non-viscously damped dynamic systems. Struct Multidiscip Optim 55(6):2197–2210MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringTechnion - Israel Institute of TechnologyTechnion CityIsrael

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