Viscoelastic constitutive relationships incorporating fractional derivatives have been previously shown to be extremely useful in describing the frequency dependent behavior of common damping materials. However, the implementation of such models in the analysis of damped mechanical systems is somewhat complicated by the fact that polynomial equations with noninteger order exponents must be solved. This paper develops accurate approximations from which the damping factor and damped natural frequency of such systems may be obtained by evaluating relatively simple algebraic expressions.

1.
Bagley
R. L.
, and
Torvik
P. J.
,
1983
, “
Fractional Calculus - A Different Approach to the Analysis of Viscoelastically Damped Structures
,”
AIAA Journal
, Vol.
21
, No.
5
, pp.
741
748
, May.
2.
Bagley
R. L.
, and
Torvik
P. J.
,
1985
, “
Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures
,”
AIAA Journal
, Vol.
23
, No.
6
, pp.
918
925
, June.
3.
Bagley
R. L.
, and
Torvik
P. J.
,
1986
, “
On the Fractional Calculus Model of Viscoelastic Behavior
,”
Journal of Rheology
, Vol.
30
, No.
1
, pp.
133
155
.
4.
Christiansen, Richard M., 1982, Theory of Viscoelasticity, 2nd Ed. Academic Press, N.Y., pp. 14–27.
5.
Drake, M. L., 1988, Damping Properties of Various Materials, AFWAL-TR-88-4248, Air Force Wright Aeronautical Laboratories, Wright-Patterson AFB, OH, p. A-2.
6.
Findley, W. N., J. S. Lai, and Konaran, 1989, Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover Publications, New York, pp. 78–96.
7.
Jones, D. I. G., 1980, “Viscoelastic Materials for Damping Applications,” Damping Applications for Vibration Control, ed. P. J. Torvik, ASME, New York, pp. 33–47.
8.
Lewis, T., A. D. Nashif and D. I. G. Jones, 1989, “Frequency Dependance of Polymer Complex Modulus Properties,” Proceedings of Damping ’89, WRDC TR-89-3116 Vol. II, Wright Research and Development Center, WPAFB, OH, p FAC-32.
9.
Murdock, J. A., 1991, Perturbations: Theory and Methods, Wiley, N.Y., pp. 33–43.
10.
Torvik
P. J.
, and
Bagley
R. L.
,
1984
, “
On the Appearance of the Fractional Derivative in the Behavior of Real Materials
,”
ASME Journal of Applied Mechanics
, Vol.
51
, pp.
294
298
, June.
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