Closed-Form Solutions and the Eigenvalue Problem for Vibration of Discrete Viscoelastic Systems

[+] Author and Article Information
A. Muravyov, S. G. Hutton

Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1W5, Canada

J. Appl. Mech 64(3), 684-691 (Sep 01, 1997) (8 pages) doi:10.1115/1.2788947 History: Received September 16, 1996; Revised February 04, 1997; Online October 25, 2007


A procedure for obtaining closed-form homogeneous solutions for the problem of vibration of a discrete viscoelastic system is developed for the case where the relaxation kernel characterizing the constitutive relation of the material is expressible as a sum of exponentials. The developed procedure involves the formulation of an eigenvalue problem and avoids difficulties encountered with the application of the Laplace transform approach to multi-degree-of-freedom viscoelastic systems. Analytical results computed by using the developed method are demonstrated on an example of a viscoelastic beam.

Copyright © 1997 by The American Society of Mechanical Engineers
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