In work questions of distribution of waves in a viscoelastic wedge with any corner of top is considered. The elastic cylinder with a radial crack is a wedge 180 ϕ <  corner. The regional task for system of the differential equations in private derivatives is decided by means of a method of straight lines that allows using a method of orthogonal prorace.

On the basis of the method of orthogonal sweep and the Mueller method, the solution of the problem of intrinsic oscillation of a Toroidal shell with a flowing liquid is discussed. The problem of determining the frequencies and forms of intrinsic bending vibrations in the plane of curvature of curvilinear sections of thin-walled Toroidal shells of large diameter with a flowing liquid, with different conditions for fixing the end sections is solved. The behavior of complex Eigen frequencies as a function of the curvature of the shell axis is studied.

In this paper we consider of natural oscillations cylindrical bodies with external friction. Complex rates changes from friction parameters are shown. Rate equations are solved numerically-by method of Muller.

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 we construct conjugate spectral problem and the conditions of biorthogonality for distribution in extended plates of variable thickness of the problem considered. It describes the procedure of solving problems and a numerical result is on wave propagation in an infinitely large plate of variable thickness. Viscous properties of the material are taken into account by means of an integral operator Voltaire. Research is conducted in the framework of the spatial theory of visco elastic. The technique is based on the separation of spatial variables and formulates the boundary eigenvalue problem that can be solved by the method of orthogonal pivotal condensation Godunov. Numerical values obtained the real and imaginary parts of the phase velocity depending on the wave numbers. The numerical result coincides with the known data.