# Mechanics

## The Global Solvability of the Problem of Nonlinear Diffusion and Slow Convection in Slightly Compressible Viscous Fluid

The paper deals with Stokes system, corresponding to the motion of slightly compressible viscous fluid where kinematic viscous depends on the admixture concentration. The system also contains the convective diffusion equation. The article proves the existence of generalized solution of the initial-boundary problem for this system in the limited domain with the homogeneous Dirichlet condition for the fluid velocity and the homogeneous Neumann condition for the concentration of admixture on the boundary of domain.

## Propagation of Pressure Waves in Finite-Size Bubbles Zones

Peculiarities of pressure waves propagation in liquids with bubbly zones have been studied. The problem is studied taking into account two-dimensional effects. Results of the research of a wave impulse influence on the firm wall partially covered with a bubble screen are presented.

## The Comparative Analysis of Calculation of Durability and Stability of the Supported Shells on the Basis of the PC OBOLOCHKA and PC ANSYS

To substantiate the efficiency of the PC OBOLOCHKA use for research of durability and stability of the supported shells the article compares the received results of calculation with the results found through PC ANSYS use.

## On One Case of Reducibility of the Equations of Motion of a Complex Mechanical System

A mechanical system, consisting of a non-variable rigid body (a carrier) and a subsystem, the configuration and composition of which may vary with time (the motion of its elements with respect to the carrier is specified), is considered. The system moves in a uniform gravitational field around a fixed point of the carrier. Obtained are conditions for the existence of the integral, which is a generalization of the kinetic moment projection integral in the case of variable mass. The system is reduced to an autonomous type.

## Modified Spline Collocation Method in the Problems of Thin Rectangular Viscoelastic Plate Vibration

Numerical method for evaluation of critical frequencies during steadystate bending vibrations of viscoelastic plate is presented. The solution is based on applying modified spline collocation method for lowering the problem’s dimension and numerical solving of the obtained problem via discrete orthogonalization method. The application of this approach with different boundary conditions is examined in detail.

## Development of the Decomposition Method in Mechanics of Solids

The orthogonal projection method for solution of boundary value problem of theory of elasticity with eigenstrain is presented. The main feature of the method is that the orthogonal decomposition is performed in the Hilbert function space of eigenstrains instead of function space of stresses, which is commonly accepted.

## On Wavenumbers of Plane Harmonic Type III Thermoelastic Waves

The present study is devoted to propagation of plane harmonic GNIII thermoelastic waves by the coupled system of linear equations of motion and heat transport based on the Green & Naghdi theory of thermoelasticity. Analytical findings and exact solutions are primarily related to complex wavenumbers, phase velocities and attenuation coefficients of the plane GNIII-thermoelastic waves. Complete analysis of all analytical branches of the wavenumbers is given.

## Flow around the Wing Section in Channel under the Interface of Two Ponderable Liquids

In this paper, we examine a flow around the wing section under the interface of two bounded layers of liquids under gravity. We present here some results of the calculation of real hydrofoil hydrodynamic characteristics subject to Froude number. Comparisons with cases of semi-infinite channel — with no top border and with no bottom border — are given.

## Homentropic Model of Spherical Shock Wave Reﬂection from the Center of Convergence

An implosive shock wave on a based gas the particular case of motion with zero pressure, but with variable density is discussed. The density is described by degree relation to distance up to a point of focusing of a shock wave. Such selection of an exponent in this relation that the entropy in all area of flow after passage of a shock wave was a constant (homentropic case) is offered. Thus qualitatively different behaviour of temperature in comparison with classical case Guderley – Landau – Stanjukovich is obtained.

## Elastic Mode Mixity Parameters for Semi-Elliptical Crack under Biaxial Loading

A method for solution and result of calculations for the elastic mode mixity parameters. The energy release rate is suggested for complex loading including modes I+II+III. The behavior of the edge inclined semi-circular and semi-elliptical surface cracks is considered under biaxial loading of arbitrary direction. The algorithm is based on application to the full elliptical crack solution of the correcting functions accounting for the crack front intersection of the plate free surface.