Vol 44 Iss. 3

The article aims to outline the history of the successive development of the theory of determining dynamic forces in mine hoisting ropes, noting all the most significant points reflected in the works of various teams of the USSR, and omitting some interesting works relating to issues of private or controversial nature.

The condition of continuity (continuity) was first given for the general case in analytical form by Euler, and then later in a different form by Lagrange.In this paper, the motion of the medium is described by means of Euler variables, which are related by Taylor series with Lagrange variables. The first part of the paper relates to a one-component fluid, the second to a two-component fluid.

The identity of X-ray radiographs of plastically deformed annealed and unannealed crystals indicates that elastic changes in the orientation of neighboring sections of a plastically deformed unannealed crystal play an insignificant role in the formation of tails on the radiographs. The investigation of the nature of rotation led to a detailed study of tails on X-ray radiographs, since the reorientation of individual sites in a deformed crystal is most reliably established by means of X-ray radiographs. From a crystal, whose lattice is distorted, X-rays with blurred and split spots are obtained, asterisms and bridges between bright spots appear.

Among the works of Prof. M. I. Akimov, his thesis “On Bessel functions of many variables and their applications in mechanics” occupies the first place in importance.

Forces at the point of the rope running over the drum. To consider the scheme of lifting the load, we introduce the notations: ...

Consider the plane vortex-free motion of a boundless fluid in the presence of a stationary cylindrical solid. The fluid is assumed to be ideal and incompressible, and its velocity at an infinitely large distance from the solid body is assumed to be constant in magnitude and direction. Let us restrict ourselves to the case of continuous steady motion.

The theory of the ball mill was basically developed by Davis in the first quarter of the present century after an experimental study of the ball mill. Much later corrections and additions were made to it. At that time the question arose of taking into account the factor of pushing by the underlying balls of those balls which had already separated from the wall of the drum and were making their relative motion in it, forming a chain of balls disintegrating at the top. Due to the error made, the researchers did not give a correct solution to this question. The error was eliminated and the true shape of the chain of balls was established somewhat later. However, this error is also found in the new foreign literature, so it is reasonable to return to this issue once again and to outline the kinematics and dynamics of the ball mill from the point of view of the theory of chains of balls (refined theory of the ball mill) and give a critical assessment of the latter.

The problem of the calculation of a shell loaded along the formant was first solved in the study of the stresses arising in cylindrical shells used for slabs. As a result of neglecting the values of Mx and Mxy, a simple differential equation for Mx is obtained. Further development of this issue is related to works based on the assumption that Mx and Mxy are insignificant in the overall balance of forces and moments in a long shell under distributed load. Along with this, there were data indicating that this is not the case when linear or concentrated loads are applied to the shell. For example, when the load was transferred to the shell through a relatively large diameter pipe, the ratio of the maximum longitudinal bending stresses to the maximum circumferential bending stresses was half.

Motion of particles and fluid bounded by parallel planes. We have already considered the problem of motion of suspended particles in the particular case of absence of obstacles. In this paper we consider the one-dimensional motion of particles and gas bounded by two parallel planes - walls.

In the present work we consider, firstly, the motion of a system of three solid bodies rotating around a fixed point and having a common geometrical axis of proper rotations, and secondly, the motion of a system consisting of two solid bodies rotating around a fixed point and also having a common geometrical axis of proper rotations.

When bodies move with large supersonic velocities, the gas between the body surface and the shock wave is heated to several thousand degrees Celsius. At such temperatures, the heat exchange by radiation between gas particles, as well as between the gas and the body surface, has a significant effect on the gas parameters in the shock layer. In this case, in order to solve the problem of streamline of a blunt-nosed body by a hypersonic gas flow, it is necessary to involve the full system of gas dynamics equations taking into account gas viscosity and thermal conductivity and radiation field.

At present, there are many numerical methods for calculating the laminar boundary layer. Among them, the finite difference method, the method of straight lines and the method of integral relations of A. A. Dorodnitsyn should be especially emphasized.

The calculation of flat frame systems with irregular quadrilateral contours by the displacement method is complicated for a number of reasons, including the kinematic calculation. Usually in such cases, a kinematic solution by graphical means is recommended. The advantages and disadvantages of graphical methods are well known.

Although a large number of works have been devoted to the study of RaD emission, still little is known about the intensities of RaD β-spectra and their shape. The study of RaD β-spectra is a difficult experimental problem because RaD β-particles have very low energies. This energy region is strongly affected by electron scattering on the walls and apertures of the instrument, electron scattering from the source lining, energy losses in the radioactive preparation itself, in the film on the window of the Geiger-Muller counter. Very intense conversion lines of nuclear transition with energy 46.5 kev are located close to the boundary of β-spectra. In the 5-12 kev region, there are a large number of Auger L-series electron lines that overlap with the RaD β-spectra. All this makes it very difficult to determine the boundary and shape of the spectra.

The year 1963 marked 40 years of scientific and pedagogical activity of the Head of the Department of Theoretical Mechanics, Doctor of Technical Sciences, Professor Nikolai P. Neronov.