The study of the stress state in the ceilings and the related issue of determining their durable dimensions are still relevant in the mining industry. As is known, the stability of the ceiling is determined by the tensile stresses that occur in it, the greatest value of which is achieved on the production circuit. The magnitude of these stresses depends on the thickness of the ceiling, on the elastic properties of the roofing rocks, on the depth of the excavation, and other reasons...

The modern development of rock mechanics has put forward the important task of studying the effect of strain rate on rock properties. The study of rock fracture processes under dynamic loading is of great importance for the improvement of mining technology. Mechanical properties under dynamic loading is important to know when designing mining machines, drilling wells at high speeds, destruction of rocks by explosion.

In the present article the basic laws of operation of viroploading machine type 2PNV-1, the design of which is developed by Gipronickel.The working body of the machine is a vibroloading chute. The impact of the vibro tray, embedded in the stack of rock, causes vibrofluidity in it, as a result of which the rock enters the tray and moves up to the transfer conveyor ...

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.

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.

In this article, it is intended to consider in detail the question of the distribution of stresses in a rock massif, which is assumed to be homogeneous elastic isotropic and subject to Hooke's law. The specific gravity of the rock is assumed to be constant. It is assumed that the rock in the section under consideration is bounded from above by a horizontal plane to which no forces are applied.

When lifting a load lying on a fixed base, the rope is sometimes not only unloaded, but also has an overhang. It is practically important to determine under these conditions the greatest tension of the rope in the first moments of driving the drum into rotational motion. This issue is devoted to the works of V. V. Georgievskaya, who divides the process of lifting the load into three stages: 1) selection of the rope tension; 2) removal of the load from the fixed base; 3) lifting the load. It is assumed that in all three stages, the drum, on which the rope is wound, rotates at an equal speed, having left the state of rest. The author neglects the change in rope length and the influence of internal resistances in the rope.

Approximate determination of the tension of hoisting mine ropes is used in order to overcome the two main difficulties arising in justifying the calculation of ropes for strength. If with a known approximation can justify the application of Hooke's law for the tension of the rope, taken in theory as a perfectly elastic thread of constant cross-section, then to account for internal resistance in the rope, as well as in a rectilinear homogeneous rod, quite reasonable formula is not available. The source of the second difficulty lies in the complex form of one of the boundary conditions of the problem of mathematical physics about the longitudinal vibrations of an elastic thread of variable length with a load at the lower end, to which the determination of the tension of hoisting mine ropes is given. It is about the upper end of the rope, which due to the coiling on the drum and the assumed absence of sliding on the drum should have a given speed, coinciding with the speed of the points of the outer surface of the rotating drum.

The numerical evaluation of rope tension is of great practical importance, but is far from being fully completed. In the present work an attempt is made to estimate the rope tension at the load suspension point during the period of uniform drum rotation, provided that this period was preceded by a period of uniformly accelerated drum rotation, accompanied from the very beginning of the load lifting by oscillatory motion of the system. Due to the action of internal resistance forces, these oscillations will be damped, and by the end of the period of uniformly accelerated drum rotation, all points of the vertical part of the rope and the load will receive the same acceleration, equal to the tangential” acceleration of the points of the drum surface. At the beginning of uniform rotation of the drum due to the change of the rotation mode the oscillations of the system are resumed and the forces of internal resistances are again manifested. However, they can be disregarded if we consider the motion of the system in a time interval close to the initial time.

When designing a dredge and selecting the main parameters that determine its operation, an important issue is the choice of angular speed of rotation of the motor and the length of the bottom of the scoop. For normal operation of the dredge it is necessary to select these parameters so that the material, pouring out of the scoop, falls into the receiving device. To solve this issue, the movement of material along the bottom of the scoop should be studied.

In the present work, the question of stress distribution from own weight in a rock massif with an unsupported horizontal excavation of circular cross-section and a free day surface is considered.

The work aims to find out quantitatively and qualitatively the main circumstances of motion of some vibrating machine intended for transportation and sorting of material, and both pre-resonance and post-resonance modes of operation of this machine are considered.The problem is reduced to integration of a system of linear differential equations with variable coefficients. Integration of the system is carried out by means of decomposition of unknown functions in series by powers of a small parameter.The obtained integrals make it possible to determine the frequencies of free oscillations of the material system under consideration, and hence the conditions of resonance. The totality of the obtained data makes it possible to calculate the strength of the vibrating parts of the structure and to give such ratios of parameters that allow to reduce the angular displacements of its two frames, which are undesirable in the proper functioning of the vibrating machine

_{Let’s consider a homogeneous isotropic prismatic layer of rectangular cross-section under the action of its own weight. Let the layer extend infinitely in the direction perpendicular to the cross-section. Two sides of the cross section are embedded and the other two sides are free (Fig. 1). In this case, the layer will be under plane strain conditions. Let us place the origin at the center of gravity of the layer cross-section and denote: layer height 2c, layer width 2l, weight per unit volume of material g, elastic constants E, n, G.}

The problem of stress distribution in a prismatic rod rotating around one of the main central axes of inertia of the cross-section is reduced to solving two independent problems. One of them does not depend on the shape of the cross-section contour and is solved once. The second problem depends on the shape of the cross-section contour and is reduced to determining the plane strain state. With an accuracy quite sufficient for practice, the value of the main design stress can be obtained using the simplified formula (7) (see article). Assuming in the obtained expressions for stresses a = 0 and bр = r, we obtain stresses for a rod of circular cross-section.

Neglecting the influence of the spokes, we will consider the flywheel as a ring with a circular meridional cross-section (Fig. 1). Let r₁ be the cross-section radius; r₂ be the radius of the circle containing the cross-section centers. We will take the oz axis as the axis of rotation and assume that the angular velocity is constant and sufficiently large. Using the kinetostatic method, we will apply an inertial force to each element of the rod and determine its elastic equilibrium. To simplify the boundary conditions, we will move to bipolar coordinates.

In our work "Distribution of stresses in rotating prismatic rods" the problem of determining the stresses in a rod rotating about an axis lying in the plane of the cross-section is solved. This question is reduced to solving two independent problems: the first of them does not depend on the shape of the cross-section contour and can be solved once; the second is reduced to considering a plane strain state. The general solution of the equations of elasticity theory was obtained after long and painstaking calculations by the method of E. Almanzi. We will show that this solution can be easily obtained using the general integral of the equations of elasticity theory in the Papkovich-Grodsky form.

In this paper, we solve the problem of stress distribution in a rod rotating about an axis lying in the plane of the cross-section. We show that in this case the problem is reduced to two completely independent problems. The first of these problems does not depend on the shape of the cross-section contour and can be solved once. The second problem depends significantly on the shape of the contour and coincides with a flat strain state, with the conditions at the ends being satisfied in the sense of Saint-Venant. In particular, we consider the cases of rotation of a hollow round shaft and a rod of elliptical cross-section.