Modeling of wave propagation in a viscoelastic medium

The contribution presents a study of the propagation of waves in a hollow finite cylinder provoked by a transient load. The viscose behavior is superimposed to linear elasticity in terms of the linear Boltzmann-Volterra model. The proposed semi-analytical algorithm includes Laplace transform with respect to time applied to the wave equation with an account for the specified stress-strain relationship, boundary, and initial conditions. The solution is found in the space of images and is then `projected back’ into the space of originals. Alternatively, the wave propagation is investigated by monitoring the stress and the displacement evolution in a specified location within a transient, finite element analysis. Viscoelasticity is modeled by modifying the material parameters according to a predefined time-dependent constitutive relation. Both analyses employ the same geometry and comparable boundary conditions, assuming isotropic viscoelasticity and constant Poisson’s ratio.