Investigation of Harmonic Waves in the Viscoelastic Layer

The paper deals with the study of harmonic waves in the viscoelastic layer. The properties of the material are described by the constitutive equations in the integral form. The fractional exponential function of Rabotnov is chosen as a kernel of integral operator. Two cases are considered: symmetric stress-strain state (SSS) and asymmetric SSS. The properties of modes which change in time harmonically are investigated for the purpose of studying of the free vibrations. Dispersion equations for both cases are derived. The numerical solutions of dispersion equations are obtained. Asymptotics of the roots of the dispersion equations for small and large values of frequencies are obtained. Analysis of the solutions is done. The influence of viscosity factors on the behavior of the dispersion curves is established. Comparative analysis of numerical solutions and asymptotics of the roots of dispersion equations are made.