Том 63, № 10 (2018)

The problem of the spectral emissivity of the Soyuz-TM descent module during its entry into the dense layers of the atmosphere at altitudes of 90–45 km with an orbital velocity has been solved. The results of three-dimensional numerical simulations are compared with experimental data.

A new method for the design of inhomogeneous materials and block structures with complex physicomechanical properties is stated. This approach based on the method of a block element can conveniently complement different numerical approaches used for these purposes and reveal the boundary problem solution properties, which either are complicated or cannot be analyzed by other methods. It is proven that a crucial role in the construction of this new approach is played by packed block elements as topological manifolds with a boundary, which can form similar new topological manifolds as a result of conjugation. It is demonstrated how homeomorphisms, which represent the mappings of topological manifolds of block elements onto real number spaces and further enable the construction of quotient topologies, which “glue” together both block elements and boundary problem solution fragments on block elements as carriers, are constructed for these purposes.

The translational motion of a thermoelastic web under small transverse deformations is considered. It is assumed that a web moving with a constant translational velocity is described by the model of a thermoelastic orthotropic plate, which is rectangular-shaped in plan and supported at two opposite edges of the span under consideration. The plate is subject to combined thermomechanical loading, which involves purely mechanical planar tension, as well as centrifugal forces and unsteady reactions. The investigation of transverse buckling (divergence) of the orthotropic thermoelastic material using the static method of investigation of the stability is reduced to solving the boundary-value problem on eigenvalues. An example of applying the obtained defining relations in the analytical determination of the critical divergence rate and the corresponding form of stability loss is given.

The problem of finding the equilibrium configurations of a heavy inextensible closed thread (chain) on a smooth surface is considered. The surface is a unilateral constraint for the thread and represents either a circular cone, the axis of which is in parallel to the vertical (gravity) or a sphere. It is shown that the equilibrium nonhorizontal configurations of the thread-chain are possible only when the cone half-angle is in the range from 30° to 45°. In the case of a sphere, it is shown that equilibrium nonhorizontal configurations of the thread-chain are impossible.

In this work, plane problems of numerical simulation of wave motion are studied. Potential flows of a perfect incompressible fluid are considered. A numerical algorithm for calculating the shape of a free boundary is proposed. The algorithm is based on the boundary element method with the use of quadrature formulas with no saturation. The algorithm is used for studying the breaking of capillary gravity waves and calculating thin cumulative jets. The stability of the scheme and high accuracy in calculations of sharp cumulative jets are achieved due to special control for the distribution of grid points and a decrease in the grid step in the neighborhood of the forward end of the cumulative jet with an ultimately rapid growth of the curvature.

The motion of a pendulum mounted on a platform that rotates around a vertical line with a constant velocity and simultaneously makes specified harmonic oscillations along this vertical line is considered. The platform angular velocity is assumed to be precisely equal to the frequency of small oscillations of the pendulum in the case of an immobile platform. There are relative equilibrium positions of the pendulum when it is oriented along the platform rotation axis (in the hanging or inverted state). The nonlinear problem of stability of these relative equilibria is considered.