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

A procedure for obtaining closed-form homogeneous solutions for the problem of vibration of 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 viscoelastic beam.