On the dispersion of the axisymmetric longitudinal wave propagating in a bi-layered hollow cylinder made of viscoelastic materials

Abstract

The paper deals with the study of axisymmetric longitudinal fundamental wave propagation (dispersion) in the bi-layered hollow circular cylinder made of linear viscoelastic materials. The investigations are made by utilizing the exact equations of linear viscoelasto-dynamics. The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution. Concrete numerical investigations are made for the case where constitutive relations of the layers' materials of the cylinder are described through fractional exponential operators. The influence of the viscosity of the layers' materials of the hollow cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials. Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed. As a result of the numerical investigations, in particular, it is established that in the case where the rheological parameters of the layers are the same, the viscosity of the layers' materials causes the axisymmetric wave propagation velocity to decrease. (C) 2016 Elsevier Ltd. All rights reserved.