The paper considers the static pressure of the
environment on the parallel pipe. The environment is elastic and homogeneous bodies. To determine the ambient
pressure, the finite element method is used. An algorithm was developed and a
computer program was compiled. Based on the compiled program, numerical results
are obtained. The numerical results obtained for two to five parallel pipes are
compared with known theoretical and experimental results.

Abstract:
We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work force, including the force of inertia obtain equations vibrations of mechanical systems. Frequency equation is solved numerically by the method of Muller. According to the result of numerical analysis we established nonmonotonic dependence damping coefficients of the system parameters.

Abstract:
The paper solves the problem of the variation formulation of the steady-linear oscillations of structurally inhomogeneous viscoelastic plate system with point connections. Under the influence of surface forces, range of motion and effort varies harmonically. The problem is reduced to solving a system of algebraic equations with complex parameters. The system of inhomogeneous linear equations is solved by the Gauss method with the release of the main elements in columns and rows of the matrix. For some specific problems, the amplitude-frequency characteristics are obtained.

Abstract:
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.

In this paper, a conjugate spectral problem and
biorthogonality conditions for the problem of extended plates of variable
thickness are constructed. A technique for solving problems and numerical
results on the propagation of waves in infinite extended viscoelastic plates of
variable thickness is described. The viscous properties of the material are
taken into account using the Voltaire integral operator. The investigation is
carried out within the framework of the spatial theory of viscoelasticity. The
technique is based on the separation of spatial variables and the formulation
of a boundary value problem for Eigen values which are solved by the Godunov
orthogonal sweep method and the Muller method. Numerical values of the real and
imaginary parts of the phase velocity are obtained depending on the wave
numbers. In this case, the coincidence of numerical results with known data is
obtained.

The vibrations of deformed bodies interacting with
an elastic medium are considered. The
problem reduces to finding those values of complex Eigen frequencies for which
the system of equations of motion and the radiation conditions have a nonzero
solution to the class of infinitely differentiable functions. It is shown that
the problem has a discrete spectrum located on the lower complex plane and the
symmetric spectrum is an imaginary axis.

The propagation of natural
waves in a cylindrical shell (elastic or viscoelastic) that is in contact with
a viscous liquid is considered. The problem reduces to solving spectral
problems with a complex incoming parameter. The system of ordinary differential
equations is solved numerically, using the method of orthogonal rotation of
Godunov with a combination of the Muller method. The dissipative processes in
the mechanical system are investigated. A mechanical effect is obtained that
describes the intensive flow of mechanical energy.

Abstract:
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 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.

Abstract:
The main features are the length of the waveguide in one direction, as well as limitations and localization of the wave beam in other areas. There is described the technique of the solution of tasks on distribution of waves in an infinite cylindrical waveguide with a radial crack. Also numerical results are given in the article. 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 sweep Godunov. In the given paper we obtain numeric values of the phase velocity depending on of wave numbers. The obtained numerical results are compared with the known data. This work is continuation of article [1]. Statement of the problem and methodology of partial solutions are described in [1]. In this work, we present a complete statement of the problem, methods of solution and discuss the numerical results.

Abstract:
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.