Abstract:The work is devoted to the study of harmonic waves in a hereditarily elastic plate with two viscoelastic coatings, the properties of the material, which are described by the equations of state in integral form. The fractional exponential function of Rabotnov and Koltunov-Rzhanitsyn was chosen as the kernel of the integral operator. Two cases are considered: the case of a stress-strain state symmetric and antisymmetric in the normal coordinate (VAT). In the study of natural oscillations, the properties of those modes that are time-dependent by harmonic law are investigated. For both cases, dispersion equations are derived, which are solved numerically. Asymptotics of the roots of dispersion equations for small and large frequencies are also obtained. The analysis of the obtained solutions made it possible to draw conclusions about the influence of hereditary factors on the behavior of dispersion curves. A comparative analysis of numerical solutions and their asymptotics is carried out.

In this paper, the case of the interaction of a flat compression pulse with a layered cylindrical body in an infinite homogeneous and isotropic elastic medium is studied. The problem by the methods of integral Fourier transforms is solved. The inverse transform numerically by the Romberg method is calculated. With a time of toast and a decrease in momentum, the accuracy is not less than 2%. Taking into account the diffracted waves the results are obtained.

An infinitely long circular cylinder, consisting generally of a finite number of coaxial viscoelastic layers, surrounded by a deformable medium is considered. The dynamic stress-the deformed state of a piecewise-homogeneous cylindrical layer from a harmonic wave is investigated. The numerical results of stress, depending on the wavelength are obtained.