Fractional‐Derivative Maxwell Model for Viscous Dampers
Publication: Journal of Structural Engineering
Volume 117, Issue 9
Abstract
A fractional‐derivative Maxwell model is proposed for viscous dampers, which are used for vibration isolation of piping systems, forging hammers, and other industrial equipment, as well as for vibration and seismic isolation of building structures. The development and calibration of the model is based on experimentally observed dynamic characteristics. The proposed model is validated by dynamic testing and very good agreement between predicted and experimental results is obtained. Numerical algorithms for the solution of the constitutive relation in either the frequency or the time domain are presented. Some analytical results for a single‐degree‐of‐freedom viscodamper system are presented. These results are useful to the design of vibration‐isolation systems. Furthermore, an equivalent viscous oscillator is defined whose response is essentially the same as that of the viscodamper isolator. Finally, the model is employed in the analysis of a base‐isolated model structure that has been tested on a shake table.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bagley, R. L., and Torvic, P. J. (1983). “Fractional calculus—a different approach to the analysis of viscoelastically damped structures.” AIAA J., 21(5), 741–748.
2.
Bird, B., Armstrong, R., and Hassager, O. (1987). Dynamics of polymeric liquids. John Wiley and Sons, New York, N.Y.
3.
Constantinou, M. C., Mokha, A., and Reinhorn, A. M. (1991). “Study of a sliding bearing and helical steel spring isolation system.” J. Struct. Engrg., ASCE, 117(4), 1257–1275.
4.
Gemant, A. (1936). “A method of analyzing experimental results obtained from elastoviscous bodies.” Physics, 7(8), 311–317.
5.
Higashino, M., Aizawa, S., and Hayamizu, Y. (1988). “The study of base isolation system for actual use.” Proc., 9th World Conf. on Earthquake Engrg., International Association for Earthquake Engineering, Tokyo, Japan, V705‐V710.
6.
Huffmann, G. (1985). “Full base isolation for earthquake protection by helical springs and viscodampers.” Nuclear Engrg. and Design, 84, 331–338.
7.
Koh, C. G., and Kelly, J. M. (1990). “Application of fractional derivatives to seismic analysis of base‐isolated models.” Earthquake Engrg. and Struct. Dynamics, 19(2), 229–241.
8.
Makris, N., and Constantinou, M. C. (1990). “Viscous dampers: Testing, modeling and application in vibration and seismic isolation.” Report No. NCEER‐90‐0028, National Center for Earthquake Engineering Research, State University of New York, Buffalo, N.Y.
9.
Oldham, K. B., and Spanier, J. (1974). The fractional calculus: Mathematics in science and engineering, Vol. III. Academic Press, New York, N.Y.
10.
“Pipework dampers.” (1986). Tech. Report, GERB Vibration Control, Westmont, Ill.
11.
Schwahn, K. J., Reinsch, K. H., and Weber, F. M. (1988). “Description of the features of viscous dampers on the basis of equivalent rheological models, presented for pipework dampers.” Proc., Pressure, Vessel and Piping Conference, Seismic Engineering, American Society of Mechanical Engineers, New York, N.Y., Vol. 127, 477–484.
12.
Veletsos, A. S., and Ventura, C. E. (1985). “Dynamic analysis of structures by the DFT method.” J. Struct. Engrg., ASCE, 111(2), 2625–2642.
Information & Authors
Information
Published In
Copyright
Copyright © 1991 ASCE.
History
Published online: Sep 1, 1991
Published in print: Sep 1991
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.