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.

Issue Section:
Technical Papers
Topics:
Eigenvalues, Vibration, Laplace transforms, Relaxation (Physics)
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