An Advanced Exponential Model for Seismic Isolators Having Hardening or Softening Behavior at Large Displacements

In this paper, an advanced Nonlinear Exponential
Model (NEM), able to simulate the uniaxial dynamic behavior of
seismic isolators having a continuously decreasing tangent stiffness
with increasing displacement in the relatively large displacements
range and a hardening or softening behavior at large displacements, is
presented. The mathematical model is validated by comparing the
experimental force-displacement hysteresis loops obtained during
cyclic tests, conducted on a helical wire rope isolator and a recycled
rubber-fiber reinforced bearing, with those predicted analytically.
Good agreement between the experimental and simulated results
shows that the proposed model can be an effective numerical tool to
predict the force-displacement relationship of seismic isolation
devices within the large displacements range. Compared to the
widely used Bouc-Wen model, unable to simulate the response of
seismic isolators at large displacements, the proposed one allows to
avoid the numerical solution of a first order nonlinear ordinary
differential equation for each time step of a nonlinear time history
analysis, thus reducing the computation effort. Furthermore, the
proposed model can simulate the smooth transition of the hysteresis
loops from small to large displacements by adopting only one set of
five parameters determined from the experimental hysteresis loops
having the largest amplitude.

Authors:

• Nicolò Vaiana
• Giorgio Serino

Keywords:

• Base isolation
• hardening behavior
• nonlinear exponential model
• seismic isolators
• softening behavior.

References:

[1] F. Naeim and J. M. Kelly, Design of Seismic Isolated Structures: From
Theory to Practice. New York: John Wiley & Sons, 1999.
[2] M. C. Constantinou, A. S. Whittaker, Y. Kalpakidis, D. M. Fenz and G.
P. Warn, “Performance of seismic isolation hardware under service and
seismic loading,” Technical Report MCEER-07-0012, State University
of New York, Buffalo, 2007.
[3] M. Spizzuoco, V. Quaglini, A. Calabrese, G. Serino and C. Zambrano,
“Study of wire rope devices for improving the re-centering capability of
base isolated buildings,” Structural Control and Health Monitoring, to
be published.
[4] C. S. Tsai, T. C. Chiang, B. J. Chen and S. B. Lin, “An advanced
analytical model for high damping rubber bearings,” Earthquake
Engineering and Structural Dynamics, vol. 32, pp. 1373-1387, 2003.
[5] N. Vaiana, M. Spizzuoco and G. Serino, “Influence of displacement
amplitude and vertical load on the horizontal dynamic and static
behavior of helical wire rope isolators,” Proceedings of the 19th
International Conference on Earthquake and Structural Engineering,
London, United Kingdom, 2017.
[6] M. Spizzuoco, A. Calabrese and G. Serino, “Innovative low-cost
recycled rubber-fiber reinforced isolator: experimental tests and finite
element analyses,” Engineering Structures, vol. 76, pp. 99-111, 2014.
[7] M. C. Constantinou, A. Mokha and A. M. Reinhorn, “Teflon bearings in
base isolation II: modeling,” Journal of Structural Engineering, vol.
116, no. 2, pp. 455-474, 1990.
[8] S. Nagarajaiah, A. M. Reinhorn and M. C. Constantinou, “Nonlinear
dynamic analysis of 3-D base-isolated structures,” Journal of Structural
Engineering, vol. 117, no. 7, pp. 2035-2054, 1991.
[9] G. F. Demetriades, M. C. Constantinou and A. M. Reinhorn, “Study of
wire rope systems for seismic protection of equipment in buildings,”
Engineering Structures, vol. 15, no. 5, pp. 321-334, 1993.
[10] Y. Q. Ni, J. M. Ko, C. W. Wong and S. Zhan, “Modelling and
identification of a wire-cable vibration isolator via a cyclic loading test.
Part 1: experiments and model development,” Journal of Systems and
Control Engineering, vol. 213, no. I3, pp. 163-171, 1999.
[11] N. Vaiana, F. C. Filippou and G. Serino, “Nonlinear dynamic analysis of
base-isolated structures using a partitioned solution approach and an
exponential model,” Proceedings of the 19th International Conference
on Earthquake and Structural Engineering, London, United Kingdom,
2017.
[12] G. Serino, “Modelli per la determinazione delle proprietà meccaniche
degli isolatori elastomerici armati,” Convenzione di ricerca con
l’ENEL/DSR/CRIS, Rapporto Tecnico fase 1/94, Napoli, 1994.
[13] R. Bouc, “Modele mathematique d’hysteresis,” Acustica, vol. 24, pp. 16-
25, 1971.
[14] Y. K. Wen, “Method for random vibration of hysteretic systems,”
Journal of the Engineering Mechanics Division, vol. 102, no. EM2, pp
249-263, 1976.
[15] Y. K. Wen, “Equivalent linearization for hysteretic systems under
random excitation,” Journal of Applied Mechanics, vol. 47, pp 150-154,
1980.
[16] N. Vaiana and G. Serino, “Speeding up nonlinear time history analysis
of base-isolated structures using a nonlinear exponential model,”
Proceedings of the 19th International Conference on Earthquake
Engineering, Barcelona, Spain, 2017.
[17] S. Pagano, M. Russo, S. Strano and M. Terzo, “A mixed approach for
the control of a testing equipment employed for earthquake isolation
systems,” Journal of Mechanical Engineering Science, vol. 228, no. 2,
pp. 246-261, 2014.