TECHNICAL PAPERS
Jul 1, 1987

Modeling and Response of Bilinear Hysteretic Systems

Publication: Journal of Engineering Mechanics
Volume 113, Issue 7

Abstract

A differential equation model is proposed for true bilinear hysteretic systems. The stationary distribution of the response process is obtained using the stochastic averaging technique. Explicit analytical expressions are developed for various response statistics. The validity of the theoretical results is established through digital simulations.

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References

1.
Caughey, T. K., “Random Excitation of a System with Bilinear Hysteresis,” Journal of Applied Mechanics, ASME, Vol. 27, 1960, pp. 649–652.
2.
Gerald, C. F., and Wheatley, P. O., “Applied Numerical Analysis,” 3rd ed., Addison‐Wesley Publishing Co., Reading, Mass., 1984.
3.
Iwan, W. D., and Spanos, P. T. D., “Response Envelope Statistics for Nonlinear Oscillators with Random Excitation,” Journal of Applied Mechanics, ASME, Vol. 45, 1978, pp. 170–174.3.
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Roberts, J. B., “The Response of an Oscillator with Bilinear Hysteresis to Stationary Random Excitation,” Journal of Applied Mechanics, ASME, Vol. 45, 1978, pp. 922–928.
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Roberts, J. B., “The Yielding Behavior of a Randomly Excited Elastoplastic Structure,” Journal of Sound and Vibration, Vol. 72, No. 1, 1980, pp. 71–854.
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Spanos, P. T. D., “Hysteretic Structural Vibrations under Random Load,” Journal of the Acoustical Society of America, Vol. 65, pp. 404–410.
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Stratonovich, R. L., “Topics in the Theory of Random Noise,” Vol. 2, 1967, Gordon and Beach, New York, N.Y.
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Wen, Y. K., “Method for Random vibration of Hysteretic Systems,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. 2, Feb., 1976, pp. 249–263.
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Wen, Y. K., “Equivalent Linearisation for Hysteretic Systems under Random Excitation,” Journal of Applied Mechanics, ASME, Vol. 47, No. 1, 1980, pp. 150–154.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 113Issue 7July 1987
Pages: 1000 - 1013

History

Published online: Jul 1, 1987
Published in print: Jul 1987

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Authors

Affiliations

Mohammad Yar
Res. Fellow, Inst. of Sound and Vibration Res., Univ. of Southampton, U.K.
Joseph K. Hammond
Sr. Lect., Inst. of Sound and Vibration Res., Univ. of Southampton, U.K.

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