Nonlinear Vibration with Volterra Series Method Used in Civil Engineering: The Bouc - Wen Hysteresis Model of Generalized Frequency Response

Abstract:

Volterra series take important role in nonlinear vibration analysis. For material hysteresis, it is proposed Bouc-Wen model to estimate frequency response function by using Volterra series in this paper: first, the component of hysteretic linear parameters was identified, then complex function was calculated, finally the differential equation of hysteretic systems was solved based on Harmonic detection method. It is not only for fast-identifying system parameters, but also providing for nonlinear seismic response.

• Periodical: Applied Mechanics and Materials (Volumes 530-531)
• Pages: 561-566
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.530-531.561
• Online since: February 2014
• Authors: Qing Ran*, Mei Ling Xiao, Yue Xin Hu
• Keywords: Generalized Frequency Response Function (GFRF), Hysteresis System, Nonlinear Vibration, Twice Identification, Volterra Series

References

[1] Kareem A, Tognarelli M. A, Gurley K.R. Modeling and analysis of quadratic term in the wind effects on structures. Journal of Wind Engineering & Industrial Aerodynamics. (1998).

DOI: 10.1016/s0167-6105(98)00101-9

[2] Worden K, Barthorpe R J. Identification of hysteretic systems using NARX models, Part I: evolutionary identification. Topics in Model Validation and Uncertainty Quantification, Volume 4. Springer New York. (2012).

DOI: 10.1007/978-1-4614-2431-4_5

[3] Franz MO, A unifying view of Wiener and Volterra theory and polynomial kernel regression. Neural Computation. (2006).

DOI: 10.1162/neco.2006.18.12.3097

[4] A.K. Swain S.A. Billings. Accrate Prediction of Non-linear wave force: PartⅠ: Fixed Cylinder. Mechanical System and Signal Processing. (1998).

[5] Bedrosian E, Rice S.O. The output properties of Volterra systems driven by harmonic and Gaussian input. Proceedings of the IEEE,. (1971).

[6] Tsang K M, Billings S.A. Reconstruction of linear and non-linear continuous time models from discrete sampled-data systems. Mechanical System and Signal Processing. (1992).

DOI: 10.1016/0888-3270(92)90057-p

[7] Peyton J JC, Billings S A. A recursive algorithm for the computing the frequency response of a class of nonlinear difference equation models. International Journal of Control, (1989).

[8] Chen S, Billings S.A. Representation of non-linear system: the NARMAX model. (1989).

[9] Victor J.D. Knight B.W. Nonlinear analysis with an arbitrary stimulus ensemble. Quarterly of Applided Mathematics. (1979).

[10] Billings S A, Chen S, Backhouse R J. The identification of linear and non-linear models of a turbocharged automotive diesel engine. Mechanical Systems and Signal Processing, (1989).

DOI: 10.1016/0888-3270(89)90012-5

[11] Cheng changing. Study on the theory and application of Volterra series(in Chinese). Shanghai Jiao Tong University, Shanghai. (2012).