Oscillations of a viscoelastic medium with a cylindrical cavity are studied. The viscosity is taken into account in the form of an additional term in the constitutive equation, proportional to a fractional derivative of variable order. In the considered examples the order function corresponds to dependences obtained for real materials. A damping effect is observed in the amplitude behavior. The field which determines the order function demonstrates the viscoelastic behavior of the material under load.

Issue Section:
Technical Briefs
Keywords:
damping, stress-strain relations, nonlinear differential equations, viscoelasticity, oscillations, vibrations, elastic deformation
Topics:
Cavities, Damping, Oscillations, Stress, Viscoelasticity, Deformation, Viscosity
1.
Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, Inc., New York.
2.
Bagley
,
R. L.
, and
Torvak
,
P. J.
,
1979
, “
A generalized Derivative Model for an Elastomer Damper
,”
The Shock and Vibration Bulletin
49
, Part. 2., pp.
135
–
143
.
3.
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
.
4.
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
.
5.
Koeller
,
R. C.
,
1984
, “
Applications of Fractional Calculus to the Theory of Viscoelasticity
,”
ASME J. Appl. Mech.
51
, pp.
299
–
307
.
6.
Markis
,
N.
,
1997
, “
Three-Dimensional Constitutive Viscoelastic Laws With Fractional Order Time Derivatives
,”
J. Rheol.
41
(
5
), pp.
1007
–
1020
.
7.
Ingman
,
D.
,
Suzdalnitsky
,
J.
, and
Zeifman
,
M.
,
2000
, “
Constitutive Dynamic-Order Model for Nonlinear Contact Phenomena
,”
ASME J. Appl. Mech.
67
, pp.
383
–
390
.
8.
Zukas, J. A., Nicholas, T., Swift, H. F., Greszczuk, L. B., and Curran, D. R., 1982, Impact Dynamics, Wiley-Interscience Publ., NY.
9.
Field
,
J. S.
, and
Swain
,
M. V.
,
1993
, “
A Simple Predictive Model for Spherical Indentation
,”
J. Mater. Res.
8
(
2
), pp.
297
–
305
.
10.
Barlow
,
D. A.
,
1973
, “
The Indentation and Scratch Hardness of Plastics
,”
ASME J. Eng. Mater. Technol.
95
, pp.
243
–
251
.
11.
Cherepanov, G. P., and Ershov, L. V., 1977, Fracture Mechanics, Mashinostroenie, Moscow (in Russian).
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