Asymptotic Approximations for Systems Incorporating Fractional Derivative Damping

[+] Author and Article Information
B. S. Liebst, P. J. Torvik

Air Force Institute of Technology, 2950 P Street, WPAFB, OH 45433-7765

J. Dyn. Sys., Meas., Control 118(3), 572-579 (Sep 01, 1996) (8 pages) doi:10.1115/1.2801182 History: Received March 15, 1994; Online December 03, 2007


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.

Copyright © 1996 by The American Society of Mechanical Engineers
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