Let us consider elastic transverse (bending) free vibrations of a plate having the shape of a circular ring, pinched along the inner contour of radius B, with a free outer contour of radius C...

Determination of the largest dynamic forces in hoisting ropes is associated with the study of oscillatory processes in a variable length thread with a load at the end. Differential equations of longitudinal vibrations of an elastic weighted thread were first derived and solved by N. P. Neronov. These equations and their exact solution obtained by the method of characteristics are complicated and inconvenient for practical application. However, brought to a numerical example, they can be used to compare approximate methods with the exact solution of the problem .

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.

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.

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.

Let us imagine several moving unchanging media S1, S2, ... Sn and a material point M moving relative to these media. Let us consider the motion of the point M relative to the medium S1, the medium S1 relative to the medium S2, . . . . the medium Sn-1 relative to the medium Sn . It is required to determine the motion of the point M relative to the medium Sn (n ≥ 3).

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.

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.

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.

When preparing ores for beneficiation, as well as in the construction of various structures are widely used machines for crushing large pieces of rocks. Among them a prominent place is occupied by the so-called jaw crushers, in which pieces of rocks are crushed by periodically pressing on them two rectangular jaws - swinging and stationary.For the normal operation of such a crusher is necessary that when pressing the jaws on a piece of ore, the latter is not pushed upward by them, but wedged between them. This is not possible at any angle between the jaws, but only at angles smaller than some of the largest angle.

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

It is known that if we neglect the vertical acceleration of fluid particles compared to the acceleration of gravity and consider the horizontal components of vertical velocity to be unchanging, then for an approximate solution of the problem of motion of a heavy incompressible ideal fluid, steady uninterrupted pre-critical flow in a channel with a horizontal bottom and vertical walls, we can use the gas-hydrodynamic analogy. This problem is solved, for example, by the method of Academician S. A. Khristianovich for gas flows with subsonic velocities. According to this method, the desired flow is found by means of a plane-parallel flow of incompressible fluid, the boundaries and velocity field of which are close to the boundaries and velocity field of the actual fluid flow in the channel under appropriate conditions. In this paper, we will construct the plane-parallel flow required to study fluid motion in transient smoothly tapering sections of channels with rectilinear vertical walls at the upstream and downstream ends.