Analysis of Hysteretic Damping Using Analytic Signals
Publication: Journal of Engineering Mechanics
Volume 123, Issue 7
Abstract
The purpose of this technical note is to present a time-domain formulation for linear hysteretic damping. The integro-differential equations that govern the dynamics of structures with linear hysteretic damping are transformed into ordinary differential equations in analytic signals—that is, complex-valued signals in which the real and imaginary parts are a Hilbert transform pair. The poles of this type of system show radial symmetry in the complex plane, determining that for each stable pole in the left-hand half of the complex plane, there is an “unstable” pole in the right-hand half. The impulse response functions of these unstable poles are bounded but noncausal. To illustrate the formulation, the analytic impulse response of a single-degree-of-freedom oscillator with linear hysteretic damping is obtained. The response of the structure to any loading signal can be obtained using time convolution of this impulse response function and the corresponding analytic excitation signal.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bracewell, R. N. (1986). The Fourier transform and its applications. McGraw-Hill Book Co., Inc. New York, N.Y.
2.
Caughey, T. K., and Vijayaraghavan, A.(1970). “Free and forced oscillations of a dynamic system with “linear hysteretic damping” (non-linear theory).”Int. J. Non-Linear Mech., 5(3), 533–555.
3.
Champeney, D. C. (1987). A handbook of Fourier theorems. Cambridge University Press, London, U.K.
4.
Crandall, S. H. (1963). “Dynamic response of systems with structural damping.”Air, space, and instruments, S. Lees, ed., McGraw-Hill Book Co., Inc., New York, N.Y.
5.
Crandall, S. H.(1970). “The role of damping in vibration theory.”J. Sound and Vibration, 11(1), 3–18.
6.
Crandall, S. H. (1991). “The hysteretic damping model in vibration theory.”J. Mech. Engrg. Sci., London, England, 204(C1), 23–28.
7.
Inaudi, J. A., and Hayen, J. (1995). “Research on variable-structure systems in the United States.”Proc., Post-Smirt Seminar on Base Isolation, Passive Energy Dissipation, and Active Control of Vibrations of Struct.
8.
Inaudi, J. A., and Kelly, J. M.(1995). “Linear hysteretic damping and the Hilbert transform.”J. Engrg. Mech., ASCE, 121(5), 636–632.
9.
Inaudi, J. A., and Makris, N.(1996). “Time-domain analysis of linear hysteretic damping.”Earthquake Engrg. and Struct. Dyn., 25(6), 529–545.
10.
Inaudi, J. A., Nims, D. K., and Kelly, J. M. (1993). “On the analysis of structures with energy dissipating restraints.”EERC Rep. No. 93113, Earthquake Engrg. Res. Ctr., Univ. of Calif. at Berkeley, Berkeley, Calif.
11.
Makris, N., Inaudi, J. A., and Kelly, J. M.(1996). “Macroscopic models with complex coefficients and causality.”Engrg. Mech., 122(6), 566–573.
Information & Authors
Information
Published In
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Jul 1, 1997
Published in print: Jul 1997
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.