Analytical Description of Multidegree Bilinear Hysteretic System
Publication: Journal of Engineering Mechanics
Volume 126, Issue 6
Abstract
Physically based analytical models capable of describing the behavior of general bilinear hysteretic systems are formulated. The formulation includes the effects of pinching, stiffness degradation, and load deterioration. The type of pinching considered is the one due to unequalness of strengths for loading in opposite directions. This pinching is represented in terms of a strength ratio. Stiffness degradation and load deterioration are described in terms of functions of total absorbed hysteretic energy. All of the system parameters are in terms of definite physical materials or system properties, which can be measured through tests. To show that the proposed analytical model can provide realistic descriptions of the performance of multi-degree-of-freedom systems, examples of a three-degree-of-freedom system subjected to harmonic loads as well as blast loads are presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmadi, G., Fan, F. C., and Noori, M. N. (1997). “A thermodynamically consistent model for hysteretic materials.” Trans. B, Iranian J. Sci. and Technol., Shiraz, Iran, 21(3), 257–278.
2.
Armstrong-Helouvry, B., Dupont, P., and Canudas De Wit, C. (1994). “A survey of models, analysis tools and compensation methods for the control of machines with friction.” Automatica, Pergamon, 30(7), 1083–1138.
3.
Baber, T. T., and Noori, M. N. (1985). “Random vibration of degrading, pinching systems.”J. Engrg. Mech., ASCE, 111(8), 1010– 1026.
4.
Bouc, R. (1967). “Modele mathematique d'hysteresis.” Acustica, 24(1), 16–25 (in French).
5.
Brokate, M., and Sprekels, J. (1996). Hysteresis and phase transitions. Springer, New York.
6.
Clough, R. W., and Johnston, S. B. (1966). “Effects of stiffness degradation on earthquake ductility requirements.” Proc., 2nd Japan Earthquake Engrg. Symp., 227–232.
7.
Constantinou, M. C., Mokha, A. S., and Reinhorn, A. M. (1991). “Study of sliding bearing and helical-steel-spring isolation system.”J. Struct. Engrg., ASCE, 117(4), 1257–1275.
8.
Constantinou, M. C., and Tadjbakhsh, I. G. (1985). “Hysteretic dampers in base isolation: Random approach.”J. Struct. Engrg., ASCE, 111(4), 705–721.
9.
Fan, F., Ahmadi, G., and Tadjbakhsh, I. G. (1990). “Multistory base-isolated buildings under a harmonic ground motion—Part I: A comparison of performances of various systems.” Nuclear Engrg. and Des., 123, 1–16.
10.
Foliente, G. C., Singh, M. P., and Noori, M. N. (1996). “Equivalent linearization of generally pinching hysteretic, degrading systems.” Earthquake Engrg. and Struct. Dyn., 25, 611–629.
11.
Iwan, W. D. (1965). “The steady-state response of a two-degree-offreedom bilinear hysteretic system.” J. Appl. Mech., 32(87), 151– 156.
12.
Iwan, W. D. (1966). “A distributed-element model for hysteresis and its steady-state dynamic response.” J. Appl. Mech., 33(42), 893– 900.
13.
Iwan, W. D., and Cifuentes, A. O. (1986). “A model for system identification of degrading structures.” Earthquake Engrg. and Struct. Dyn., 14, 877–890.
14.
Léger, P., and Dussault, S. (1992). “Seismic-energy dissipation in MDOF structures.”J. Struct. Engrg., ASCE, 118(5), 1251–1269.
15.
Mahin, S. A., and Lin, J. ( 1983). “Construction of inelastic response spectra for single-degree-of-freedom systems, computer programs and applications.” Rep. No. UCB/EERC-83/17, Earthquake Engineering Research Center, University of California, Berkeley, Richmond, Calif.
16.
Mokha, A. S., Constantinou, M. C., and Reinhorn, A. M. (1993). “Verification of friction model of Teflon bearings under triaxial load.”J. Struct. Engrg., ASCE, 119(1), 240–261.
17.
Mostaghel, N. (1998). “Analytical description of pinching, degrading hysteretic systems.” Rep. No. UT-CE/ST-98-102, Dept. of Civ. Engrg., University of Toledo, Toledo, Ohio.
18.
Mostaghel, N. (1999). “Analytical description of pinching, degrading hysteretic systems.”J. Engrg. Mech., ASCE, 125(2), 216–224.
19.
Mostaghel, N., and Khodaverdian, M. (1988). “Seismic response of structures supported on R-FBI system.” Earthquake Engrg. and Struct. Dyn., 16(6), 839–854.
20.
Noori, M. N., Choi, J., and Davoodi, H. (1986). “Zero and nonzero mean random vibration analysis of a new general hysteresis model.” Probabilistic Engrg. Mech., England, 1(4), 192–201.
21.
Paevere, P., Haritos, N., and Foliente, G. C. (1998). “A hysteretic MDOF model for dynamic analysis of offshore towers.” Proc., 8th Int. Offshore and Polar Engrg. Conf., Vol. IV, 513–517.
22.
Pires, J., and Tang, M. (1990). “Statistics of hysteretic energy dissipated under random dynamic loading.”J. Engrg. Mech., ASCE, 116(8), 1706–1722.
23.
Skinner, R. I., Kelly, J. M., and Heine, A. J. (1975). “Hysteretic dampers for earthquake-resistant structures.” Earthquake Engrg. and Struct. Dyn., 3, 287–296.
24.
Smyth, A. W., Masri, S. F., Chassiakos, A. G., and Caughey, T. K. (1999). “On-line parametric identification of MDOF nonlinear hysteretic systems.”J. Engrg. Mech., ASCE, 125(2), 133–142.
25.
Spencer, B. F., and Bergman, L. A. (1985). “On the reliability of simple hysteretic system.”J. Engrg. Mech., ASCE, 111(12), 1502–1514.
26.
Su, L., Ahmadi, G., and Tadjbakhsh, I. G. (1990). “Response of base-isolated shear beam structures to random excitations.” Probabilistic Engrg. Mech., England, 5(1), 35–46.
27.
Thyagarajan, R. S., and Iwan, W. D. (1990). “Performance characteristics of a widely used hysteretic model in structural dynamics.” Proc., 4th U.S. Nat. Conf. on Earthquake Engrg., Prentice-Hall, N.J., Vol. 2, 177–186.
28.
Wen, Y. K. (1976). “Method for random vibration of hysteretic systems.”J. Engrg. Mech., ASCE, 102(2), 249–263.
29.
Wen, Y. K. (1989). “Methods of random vibration for inelastic structures.” Appl. Mech. Rev., 42(2), 39–52.
30.
Wolfram, S. (1999). The mathematica book, 4th Ed., Wolfram Media/Cambridge University Press.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 126 • Issue 6 • June 2000
Pages: 588 - 598
History
Received: Sep 2, 1999
Published online: Jun 1, 2000
Published in print: Jun 2000
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.