Hysteretic Beam Model for Steel Wire Ropes Hysteresis Identification

  • Biagio Carboni
  • Carlo Mancini
  • Walter Lacarbonara
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 168)


A nonlinear hysteretic beam model based on a geometrically exact planar beam theory combined with a continuum extension of the Bouc-Wen model of hysteresis is proposed to describe the memory-dependent dissipative response of short wire ropes which have the unique feature of exhibiting hysteretic energy dissipation due to the interwire friction. With the proposed model, hysteresis is introduced in the constitutive equation between the bending moment and the curvature within the special Cosserat theory of shearable beams. The model is indeed capable of describing the hysteretic behavior exhibited by short steel wire ropes subject to flexural cycles. The model parameters which best fit a series of experimental measurements for selected wire ropes are identified employing the Particle Swarm Optimization method . The identified parameters are used to reproduce other experimental tests on the same wire ropes obtaining a good accuracy.


Particle Swarm Optimization Particle Swarm Optimization Algorithm Displacement Amplitude Tangent Stiffness Hysteretic Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was partially supported by the Italian Ministry of Education, University and Scientific Research (2010-2011 PRIN Grant No. 2010BFXRHS-002) and by a FY 2013 Sapienza Grant N. C26A13JPY9.


  1. 1.
    Baber, T., Noori, M.: Random vibration of degrading, pinching systems. J. Eng. Mech. 111(8), 1010–1026 (1985)CrossRefGoogle Scholar
  2. 2.
    Baber, T., Wen, Y.: Random vibration hysteretic, degrading systems. J. Eng. Mech. Div. 107(6), 1069–1087 (1981)Google Scholar
  3. 3.
    Bouc, R.: Forced vibration of mechanical systems with hysteresis. In: Proceedings of the Fourth Conference on Non-linear oscillation, Prague, Czechoslovakia (1967)Google Scholar
  4. 4.
    Carboni, B., Lacarbonara, W.: A new vibration absorber based on the hysteresis of multi-configuration nitinol-steel wire ropes assemblies. In: MATEC Web of Conferences, vol. 16, p. 01004. EDP Sciences (2014)Google Scholar
  5. 5.
    Carboni, B., Lacarbonara, W., Auricchio, F.: Hysteresis of multiconfiguration assemblies of nitinol and steel strands: experiments and phenomenological identification. J. Eng. Mech. 141, 04014135 (2014)Google Scholar
  6. 6.
    Carpineto, N., Lacarbonara, W., Vestroni, F.: Hysteretic tuned mass dampers for structural vibration mitigation. J. Sound Vib. 333(5), 1302–1318 (2014)CrossRefADSGoogle Scholar
  7. 7.
    Casciati, F.: Stochastic dynamics of hysteretic media. Struct. Saf. 6(2), 259–269 (1989)CrossRefGoogle Scholar
  8. 8.
    Charalampakis, A., Dimou, C.: Identification of bouc-wen hysteretic systems using particle swarm optimization. Comput. Struct. 88(21), 1197–1205 (2010)CrossRefGoogle Scholar
  9. 9.
    Costello, G.: Theory of Wire Rope. Springer, New York (1990)Google Scholar
  10. 10.
    Crawley, E.F., ODonnell, K.J.: Identification of nonlinear system parameters in joints using the force-state mapping technique. AIAA Pap 86(1013), 659–667 (1986)Google Scholar
  11. 11.
    Demetriades, G., Constantinou, M., Reinhorn, A.: Study of wire rope systems for seismic protection of equipment in buildings. Eng. Struct. 15(5), 321–334 (1993)CrossRefGoogle Scholar
  12. 12.
    Dimou, C., Koumousis, V.: Reliability-based optimal design of truss structures using particle swarm optimization. J. Comput. Civil Eng. 23(2), 100–109 (2009)CrossRefGoogle Scholar
  13. 13.
    Eberhart, R.C., Shi, Y.: Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 Congress on Evolutionary Computation, 2001, vol. 1, pp. 81–86. IEEE (2001)Google Scholar
  14. 14.
    Fourie, P., Groenwold, A.: The particle swarm optimization algorithm in size and shape optimization. Struct. Multi. Optim. 23(4), 259–267 (2002)CrossRefGoogle Scholar
  15. 15.
    Fourie, P., Groenwold, A.A.: Particle swarms in topology optimization. In: Proceedings of the Fourth World Congress of Structural and Multidisciplinary Optimization, Dalian, China (2001)Google Scholar
  16. 16.
    Gerges, R.: Model for the force-displacement relationship of wire rope springs. J. Aerosp. Eng. 21(1), 1–9 (2008)CrossRefGoogle Scholar
  17. 17.
    Gerges, R., Vickery, B.: Parametric experimental study of wire rope spring tuned mass dampers. J. Wind Engi. Ind. Aerodyn. 91(12), 1363–1385 (2003)CrossRefGoogle Scholar
  18. 18.
    Gerges, R., Vickery, B.: Optimum design of pendulum-type tuned mass dampers. Struct. Des. Tall Spec. Build. 14(4), 353–368 (2005)CrossRefGoogle Scholar
  19. 19.
    Gholizadeh, S., Salajegheh, E.: Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel. Comput. Methods Appl. Mech. Eng. 198(37), 2936–2949 (2009)CrossRefADSGoogle Scholar
  20. 20.
    Gnanavel, B., Gopinath, D., Parthasarathy, N.: Effect of friction on coupled contact in a twisted wire cable. J. Appl. Mech. 77(2), 024501 (2010)Google Scholar
  21. 21.
    Gnanavel, B., Parthasarathy, N.: Effect of interfacial contact forces in radial contact wire strand. Arch. Appl. Mech. 81(3), 303–317 (2011)CrossRefADSzbMATHGoogle Scholar
  22. 22.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference of Neural Network IV, Perth, AustraliaGoogle Scholar
  23. 23.
    Kwok, N., Ha, Q., Nguyen, T., Li, J., Samali, B.: A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization. Sens. Actuators A: Phys. 132(2), 441–451 (2006)CrossRefGoogle Scholar
  24. 24.
    Lacarbonara, W.: Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling. Springer, New York (2013)Google Scholar
  25. 25.
    Liu, B., Wang, L., Jin, Y.H., Tang, F., Huang, D.X.: Directing orbits of chaotic systems by particle swarm optimization. Chaos, Solitons Fractals 29(2), 454–461 (2006)MathSciNetCrossRefADSzbMATHGoogle Scholar
  26. 26.
    Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Cambridge University Press, Cambridge (2013)Google Scholar
  27. 27.
    Ma, J., Ge, S.R., Zhang, D.K.: Distribution of wire deformation within strands of wire ropes. J. China Univ. Min. Technol. 18(3), 475–478 (2008)CrossRefGoogle Scholar
  28. 28.
    Masri, S., Caughey, T.: A nonparametric identification technique for nonlinear dynamic problems. J. Appl. Mech. 46(2), 433–447 (1979)CrossRefADSGoogle Scholar
  29. 29.
    Multiphysics, C.: Version 3.5 a (2008)Google Scholar
  30. 30.
    Nucera, C., di Scalea, F.L.: Monitoring load levels in multi-wire strands by nonlinear ultrasonic waves. Struct. Health Monit. 10(6), 617–629 (2011)CrossRefGoogle Scholar
  31. 31.
    Quaranta, G., Monti, G., Marano, G.C.: Parameters identification of van der pol-duffing oscillators via particle swarm optimization and differential evolution. Mech. Syst. Sig. Process. 24(7), 2076–2095 (2010)CrossRefADSGoogle Scholar
  32. 32.
    Sauter, D., Hagedorn, P.: On the hysteresis of wire cables in stockbridge dampers. Int. J. Nonlinear Mech. 37(8), 1453–1459 (2002)CrossRefADSzbMATHGoogle Scholar
  33. 33.
    Schutte, J., Groenwold, A.: Sizing design of truss structures using particle swarms. Struct. Multi. Optim. 25(4), 261–269 (2003)CrossRefGoogle Scholar
  34. 34.
    Simeonov, V.K., Sivaselvan, M.V., Reinhorn, A.M.: Nonlinear analysis of structural frame systems by the state-space approach. Comput. Aided Civil Infrastruct. Eng. 15(2), 76–89 (2000)CrossRefGoogle Scholar
  35. 35.
    Sivaselvan, M.V., Reinhorn, A.M.: Hysteretic models for deteriorating inelastic structures. J. Eng. Mech. 126(6), 633–640 (2000)CrossRefGoogle Scholar
  36. 36.
    Stockbridge, G.: Vibration damper. US patent 1,675,391 (1928)Google Scholar
  37. 37.
    Tinker, M., Cutchins, M.: Damping phenomena in a wire rope vibration isolation system. J. Sound Vib. 157(1), 7–18 (1992)CrossRefADSGoogle Scholar
  38. 38.
    Triantafyllou, S., Koumousis, V.: Bouc-wen type hysteretic plane stress element. J. Eng. Mech. 138(3), 235–246 (2011)CrossRefGoogle Scholar
  39. 39.
    Triantafyllou, S., Koumousis, V.: Small and large displacement dynamic analysis of frame structures based on hysteretic beam elements. J. Eng. Mech. 138(1), 36–49 (2011)CrossRefGoogle Scholar
  40. 40.
    Triantafyllou, S.P., Koumousis, V.K.: An hysteretic quadrilateral plane stress element. Arch. Appl. Mech. 82(10–11), 1675–1687 (2012)CrossRefADSzbMATHGoogle Scholar
  41. 41.
    Venter, G., Sobieszczanski-Sobieski, J.: Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization. Struct. Multi. Optim. 26(1–2), 121–131 (2004)CrossRefGoogle Scholar
  42. 42.
    Version, M.: 7.10. 0.499 (r2010a) (2010)Google Scholar
  43. 43.
    Vestroni, F., Lacarbonara, W., Carpineto, N.: Hysteretic tuned mass damper for passive control of mechanical vibration. Sapienza University of Rome, Italian Patent No. RM2011A000434 (2011)Google Scholar
  44. 44.
    Waisman, H., Montoya, A., Betti, R., Noyan, I.: Load transfer and recovery length in parallel wires of suspension bridge cables. J. Eng. Mech. 137(4), 227–237 (2010)CrossRefGoogle Scholar
  45. 45.
    Wen, Y.: Method for random vibration of hysteretic systems. J. Eng. Mech. Div. 102(2), 249–263 (1976)zbMATHGoogle Scholar
  46. 46.
    Worden, K.: Data processing and experiment design for the restoring force surface method, part i: integration and differentiation of measured time data. Mech. Syst. Sig. Process. 4(4), 295–319 (1990)CrossRefADSGoogle Scholar
  47. 47.
    Worden, K.: Data processing and experiment design for the restoring force surface method, part ii: choice of excitation signal. Mech. Syst. Sig. Process. 4(4), 321–344 (1990)CrossRefADSGoogle Scholar
  48. 48.
    Ye, M.: Parameter identification of dynamical systems based on improved particle swarm optimization. In: Intelligent Control and Automation, pp. 351–360. Springer, Berlin (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Biagio Carboni
    • 1
  • Carlo Mancini
    • 1
  • Walter Lacarbonara
    • 1
  1. 1.Department of Structural and Geotechnical EngineeringSapienza University of RomeRomeItaly

Personalised recommendations