Steady‐State Oscillation of Hysteretic Differential Model. II: Performance Analysis
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VIEW THE ORIGINAL ARTICLEPublication: Journal of Engineering Mechanics
Volume 120, Issue 11
Abstract
The present study involves two aspects associated with the steady‐state performance of the versatile Bouc‐Wen hysteretic model. First, influence of the model parameters on steady‐state responses and hysteresis loops of the single‐degree‐of‐freedom (SDOF) hysteretic system is studied by the proposed Galerkin/ Levenberg‐Marquardt (GLM) method. The dynamic behavior corresponding to five kinds of hysteresis loops is identified. Second, the steady‐state characteristics of the Bouc‐Wen hysteretic model used for representing inelastic constitutive laws are recognized. As endochronic constitutive relationship, this smooth hysteretic model may locally violate the Drucker's (or Ilyushin's) stability postulate of plasticity when the steady‐state hysteresis loops are exhibited with intermediate unloading‐reloading. The study is emphasized on the energy dissipation properties in small unloading‐reloading cycles starting at an arbitrary deformation previously reached. The extent of local violation of the Drucker's postulate under steady‐state circumstances is observed through numerical analysis. The mitigation of this violation is addressed by parameter studies.
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References
1.
Bhatti, M. A., and Pister, K. S. (1981). “A dual criteria approach for optimal design of earthquake‐resistant structural systems.” Earthquake Engrg. Struct. Dyn., 9, 557–572.
2.
Bouc, R. (1967). “Forced vibrations of mechanical systems with hysteresis.” Proc. 4th Conf. on Non‐Linear Oscillation, Prague, Czechoslovakia, 315–315.
3.
Casciati, F. (1987). “Non‐linear stochastic dynamics of large structural systems by equivalent linearization.” Proc. 5th Int. Conf. on Application of Statistics and Probability in Soil and Struct. Engrg., Vol. 2, 1165–1172.
4.
Casciati, F. (1989). “Stochastic dynamics of hysteretic media.” Struct. Safety, 6(2–4), 259–269.
5.
Casciati, F., and Faravelli, L. (1989). “Non‐linear stochastic finite‐element analysis of continua.” Proc. 5th Int. Conf. on Struct. Safety and Reliab., Vol. 2, 1105–1112.
6.
Cherng, R.‐H. and Wen, Y. K. (1991). “Stochastic finite element analysis of non‐linear plane trusses.” Int. J. Non‐Linear Mech., 26(6), 835–849.
7.
Constantinou, M. C., and Tadjbakhsh, I. G. (1985). “Hysteretic dampers in base isolation: random approach.” J. Struct. Engrg., ASCE, 111(4), 705–721.
8.
Ferri, A. A., and McDowell, E. H. (1988). “Frequency domain solutions to multi‐degree of freedom, dry friction damped systems.” J. Sound Vibrations, 124(2), 207–224.
9.
Ko, J. M., Ni, Y. Q., and Tian, Q. L. (1992). “Hysteretic behavior and empirical modeling of a wire‐cable vibration isolator.” Int. J. Anal. Exp. Modal Anal., 7(2), 111–127.
10.
Lau, S. L., and Cheung, Y. K. (1981). “Amplitude incremental variational principle for nonlinear vibration of elastic systems.” J. Appl. Mech., 48(4), 959–964.
11.
Nagarajaiah, S., Reinhorn, A. M., and Constantinou, M. C. (1991). “Nonlinear dynamic analysis of 3D‐base‐isolated structures.” J. Struct. Engrg., ASCE, 117(7), 2035–2054.
12.
Ohno, N. (1990). “Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity.” Appl. Mech. Rev., 43(11), 283–295.
13.
Ozdemir, H. (1976). “Nonlinear transient dynamic analysis of yielding structures,” PhD dissertation, Dept. of Civ. Engrg., Univ. of California, Berkeley, Calif.
14.
Park, Y. J., and Reich, M. (1991). “Non‐linear 3D piping analysis under stochastic dynamic loads.” Nucl. Engrg. Des., 126, 233–243.
15.
Park, Y. J., Wen, Y. K., and Ang, A. H‐S. (1986). “Random vibration of hysteretic systems under bi‐directional ground motions.” Earthquake Engrg. Struct. Dyn., 14(4), 543–557.
16.
Pivovarov, I., and Vinogradov, O. G. (1987). “One application of Bouc's model for non‐linear hysteresis.” J. Sound Vib., 118(2), 209–216.
17.
Popov, E. P. (1980). “Seismic behavior of structural subassemblages.” J. Struct. Div., ASCE, 106(7), 1451–1474.
18.
Rivlin, R. S. (1981). “Some comments on the endochronic theory of plasticity. Int. J. Solids Struct., 17, 231–248.
19.
Sandler, I. S. (1978). “On the uniqueness and stability of endochronic theories of material behavior.” J. Appl. Mech., Trans. ASME, 45, 263–266.
20.
Shames, I. H., and Cozzarelli, F. A. (1992). Elastic and inelastic stress analysis, Prentice Hall, Englewood Cliffs, N.J., 285.
21.
Simulescu, I., Mochio, T., and Shinozuka, M. (1989). “Equivalent linearization method in nonlinear FEM.” J. Engrg. Mech., ASCE, 115(3), 475–492.
22.
Sues, R. H., Mau, S. T., and Wen, Y. K. (1988). “Systems identification of degrading hysteretic restoring forces.” J. Engrg. Mech., ASCE, 114(5), 833–846.
23.
Thyagarajan, R. S. (1989). “Modeling and analysis of hysteretic structural behavior.” Rep. No. EERL‐89‐03, Earthquake Engineering Research Lab., California Inst. of Technol., Pasadena, Calif.
24.
Valanis, K. C. (1971a). “A theory of viscoplasticity without a yield surface, Part I: general theory.” Arch. Mech., 23(4), 517–533.
25.
Valanis, K. C. (1971b). “A theory of viscoplasticity without a yield surface, Part II: application to mechanical behavior of metals.” Arch. Mech., 23(4), 535–551.
26.
Valanis, K. C. (1980). “Fundamental consequences of a new intrinsic time measure: plasticity as a limit of the endochronic theory.” Arch. Mech., 32(2), 171–191.
27.
Wen, Y. K. (1976). “Method for random vibration of hysteretic systems.” J. Engrg. Mech. Div., ASCE, 102(2), 249–263.
28.
Wong, C. W., Ni, Y. Q., and Ko, J. M. (1993). “Steady‐state dynamic response of structures with nonlinear hysteretic isolators.” Modal Anal., 8(1), 63–78.
29.
Wong, C. W., Ni, Y. Q., and Lau, S. L. (1994). “Steady‐state oscillation of hysteretic differential model. I: response analysis.” J. Engrg. Mech., ASCE, 120(10), 2271–2298.
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Published In
Journal of Engineering Mechanics
Volume 120 • Issue 11 • November 1994
Pages: 2299 - 2325
Copyright
Copyright © 1994 American Society of Civil Engineers.
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Received: Aug 25, 1992
Published online: Nov 1, 1994
Published in print: Nov 1994
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