Generalized Masing Approach to Modeling Hysteretic Deteriorating Behavior
Publication: Journal of Engineering Mechanics
Volume 133, Issue 5
Abstract
The modeling of hysteretic behavior is of significant importance in several areas, including civil engineering and mechanics. This paper focuses on finding a method for modeling hysteretic behavior that is simple and efficient in terms of capturing the response and retaining the memory, if any, and at the same time is proper for use in physically meaningful modeling and identification of the system with few parameters. A distributed-element model (DEM) capable of capturing deterioration is used as a starting point, and its characteristics are studied, with a particular focus on the way memory is stored in the model. It is observed that keeping track of the response at a few of the past extremes of input displacement, called the Sequence of Dominant Alternating Extremes, is enough for representing the effect of history. The relation of this behavior to a generalized Masing model is studied. A set of rules is proposed which is a generalization of the Masing rules and can capture the deteriorating (or nondeteriorating) response of DEMs with any distribution of element yield displacement thresholds to any arbitrary loading. The presented formulation provides a framework for efficient modeling and identification of dynamic models of very different characteristics with only a few physically meaningful parameters.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers acknowledge partial support for this research by National Science Foundation through Grant No. NSFCAREER CMS0134333.
References
Al-Bender, F., Symens, W., Swevers, J., and Van Brussel, H. (2004). “Theoretical analysis of the dynamic behavior of hysteresis elements in mechanical systems.” Int. J. Non-Linear Mech., 39, 1721–1735.
Ashrafi, S. A., and Smyth, A. W. (2006). “An adaptive parametric identification scheme for a class of nondeteriorating and deteriorating nonlinear hysteretic behavior.” J. Eng. Mech., in press.
Ashrafi, S. A., Smyth, A. W., and Betti, R. (2006). “A parametric identification scheme for nondeteriorating and deteriorating nonlinear hysteretic behavior.” Structural Control and Health Monitoring, 13(1), 108–131.
Baber, T. T., and Wen, Y. K. (1981). “Random vibration of hysteretic, degrading systems.” J. Engrg. Mech. Div., 107(6), 1069–1087.
Capecchi, D., and de Felice, G. (2001). “Hysteretic systems with internal variables.” J. Eng. Mech., 127(9), 891–898.
Chiang, D. Y. (1992). “Parsimonious modeling of inelastic systems.” Ph.D. dissertation, California Institute of Technology, Pasadena, Calif.
Chiang, D. Y. (1997). “A phenomenological model for cyclic plasticity.” J. Eng. Mater. Technol., 119(1), 7–11.
Chiang, D. Y., and Beck, J. L. (1994a). “A new class of distributed-element models for cyclic plasticity. I: Theory and application.” Int. J. Solids Struct., 31(4), 469–484.
Chiang, D. Y., and Beck, J. L. (1994b). “A new class of distributed-element models for cyclic plasticity. II: On important properties of material behavior.” Int. J. Solids Struct., 31(4), 485–496.
Cifuentes, A. O., and Iwan, W. D. (1986). “On the modeling of a class of deteriorating structures subject to severe earthquake loading.” Proceedings, 3rd U.S. National Conf. on Earthquake Engineering, Earthquake Engineering Research Institute, Vol. 2, 967–978.
Cifuentes, A. O., and Iwan, W. D. (1989). “Nonlinear system identification based on modelling of restoring force behavior.” Soil Dyn. Earthquake Eng., 8(1), 2–8.
Fan, W. R. S. (1968). “The damping properties and the earthquake response spectrum of steel frames.” Ph.D. dissertation, Univ. of Michigan, Ann Arbor, Mich.
Iwan, W. D. (1966). “A distributed-element model for hysteresis and its steady-state dynamic response.” J. Appl. Mech., 33(4), 893–900.
Iwan, W. D. (1967). “On a class of models for the yielding behavior of continuous and composite systems.” J. Appl. Mech., 34(3), 612–617.
Iwan, W. D., and Cifuentes, A. O. (1986). “A model for system identification of degrading structures.” Earthquake Eng. Struct. Dyn., 14(6), 877–890.
Jayakumar, P. (1987). “Modeling and identification in structural dynamics, Report No. eerl 87-01.” Ph.D. dissertation, California Institute of Technology, Pasadena, Calif.
Jennings, P. C. (1963). “Response of simple yielding structures to earthquake excitation.” Ph.D. dissertation, California Institute of Technology, Pasadena, Calif.
Kleinberg, T. (1997). “A generalized approach for modeling the nonlocal memory of hysteresis systems.” J. Magn. Magn. Mater., 166, 315–320.
Lampaert, V., and Swevers, J. (2001). “On-line identification of hysteresis functions with nonlocal memory.” Proc., 2001 IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, Como, Italy, 833–837.
Masing, G. (1926). “Eigenspannungen und verfestigung beim messing (self stretching and hardening for brass).” Proc., 2nd Int. Congress for Applied Mechanics, Zurich, Switzerland, 332–335.
Mayergoyz, I. (2003). Mathematical models of hysteresis and their applications, Elsevier, New York.
Pisarenko, G. S. (1962). “Vibrations of elastic systems taking account of energy dissipation in the material.” Technical Documentary Rep. No. wadd tr 60-582.
Preisach, F. (1935). “Über die magnetische nachwirkung (on magnetic aftereffect).” Z. Phys., 97, 277–302.
Rosenblueth, E., and Herrera, I. (1964). “On a kind of hysteretic damping.” J. Engrg. Mech. Div., 90(4), 37–48.
Skelton, R. P., Maier, H. J., and Christ, H.-J. (1997). “The Bauschinger effect, Masing model and the Ramberg-Osgood relation for cyclic deformation in metals.” Mater. Sci. Eng., A, 238, 377–390.
Thyagarajan, R. S. (1990). “Modeling and analysis of hysteretic structural behavior, Report No. eerl 89-03.” Ph.D. dissertation, California Institute of Technology, Pasadena, Calif.
Vucetic, M. (1990). “Normalized behavior of clay under irregular cyclic loading.” Can. Geotech. J., 27(1), 29–46.
Wei, J. D., and Sun, C. T. (2000). “Constructing hysteretic memory in neural networks.” IEEE Trans. Syst., Man, Cybern., Part B: Cybern., 30(4), 601–609.
Wen, K. K. (1986). “Stochastic response and damage analysis of inelastic structures.” Probab. Eng. Mech., 1(1), 49–57.
Özdemir, H. (1976). “Nonlinear transient dynamic analysis of yielding structures.” Ph.D. dissertation, Univ. of California, Berkeley, Calif.
Information & Authors
Information
Published In
Copyright
© 2007 ASCE.
History
Received: May 6, 2005
Accepted: Apr 3, 2006
Published online: May 1, 2007
Published in print: May 2007
Notes
Note. Associate Editor: Raimondo Betti
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.