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TECHNICAL BRIEFS

Application of Dynamic Fractional Differentiation to the Study of Oscillating Viscoelastic Medium With Cylindrical Cavity

[+] Author and Article Information
D. Ingman, J. Suzdalnitsky

QAR, Technion—I.I.T., Technion City, Haifa 32000, Israel

J. Vib. Acoust 124(4), 642-645 (Sep 20, 2002) (4 pages) doi:10.1115/1.1497364 History: Received July 01, 2001; Revised March 01, 2002; Online September 20, 2002
Copyright © 2002 by ASME
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References

Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, Inc., New York.
Bagley,  R. L., and Torvak,  P. J., 1979, “A generalized Derivative Model for an Elastomer Damper,” The Shock and Vibration Bulletin49, Part. 2., pp. 135–143.
Bagley,  R. L., and Torvik,  P. J., 1983, “Fractional Calculus - A Different Approach to the Analysis of Viscoelastically Damped Structures,” AIAA J. 21(5), pp. 741–748.
Ingman,  D., and Suzdalnitsky,  J., 2001, “Iteration Method for Equation of Viscoelastic Motion With Fractional Differential Operator of Damping,” Comput. Methods Appl. Mech. Eng. 190, pp. 5027–5036.
Koeller,  R. C., 1984, “Applications of Fractional Calculus to the Theory of Viscoelasticity,” ASME J. Appl. Mech. 51, pp. 299–307.
Markis,  N., 1997, “Three-Dimensional Constitutive Viscoelastic Laws With Fractional Order Time Derivatives,” J. Rheol. 41(5), pp. 1007–1020.
Ingman,  D., Suzdalnitsky,  J., and Zeifman,  M., 2000, “Constitutive Dynamic-Order Model for Nonlinear Contact Phenomena,” ASME J. Appl. Mech. 67, pp. 383–390.
Zukas, J. A., Nicholas, T., Swift, H. F., Greszczuk, L. B., and Curran, D. R., 1982, Impact Dynamics, Wiley-Interscience Publ., NY.
Field,  J. S., and Swain,  M. V., 1993, “A Simple Predictive Model for Spherical Indentation,” J. Mater. Res. 8(2), pp. 297–305.
Barlow,  D. A., 1973, “The Indentation and Scratch Hardness of Plastics,” ASME J. Eng. Mater. Technol. 95, pp. 243–251.
Cherepanov, G. P., and Ershov, L. V., 1977, Fracture Mechanics, Mashinostroenie, Moscow (in Russian).

Figures

Grahic Jump Location
Behavior of the circumferential stress amplitude (a) metal; (b) polymer
Grahic Jump Location
Behavior of the order function: (a) metal; (b) polymer.

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