THEIR UDC 622.61Damping of the oscillatious over the length of metal strips of a vibrating belt is due to dispersion of energy in the material of the strip, to interaction of the belt with the base and the load being transported, and to compression of the strip against the base by the weight of the belt and the load. The latter is the most important and is the only factor which we need to take into account in an analytical investigation of damping.The necessity to investigate damping arises, for example, in the problem of the transverse oscillations of beams.The oscillations of beams with fixed supports or mounted on an elastic base are represented by a fourth-order partial differential equation. However, this equation is difficult to me for investigating the decrease in the amplitude of oscillations of a vibrating belt with increasing distance from the vibrator. This is due to the fact that a vibrating belt does not have fixed supports and is located on a rigid base. Damping of the oscillations may be investigated by the methods of elasticity theory; here the solution is songht in finished form and the problem reduces to finding one parameter of the solution.In Fig. 1, the solid wavy line represents a vibrating belt at a fixed time.For the longitudinal cross section of a vibrating belt, formed by the plane xOy, we will write the fundamental equations of elasticity theory in the displacements a2u.

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VIBRATORYVibratory belt conveyers are a promising method of carrying broken rock along an inclined working. Owing to its low weight, high reliability, and adequate throughput, a vibratory belt conveyer can carry loads under conditions in which other conveyers are unsuitable -under fallen rock, without access for servicing and repair, in steeply dipping workings, etc. Much interest therefore is attached to the creation of a method of calculating the amplitude of transverse vibrations, on which the throughput of a vibratory belt conveyer largely depends. To obtain reliable results it is necessary to take account of the influence of take-off and landing of fragments of the load on the operation of conveyer. This can be done by using the method in [1 ]. Figure 1 shows a vibratory belt conveyer carrying a layer of load with a characteristic thickness of 15-30 cm. The belt 1 lies freely on the base 4 made of beams fixed with anchor bolts 7 to the floor of the working. Between the beams on the underside a vibration exciter 3 is attached to the belt. To increase the amplitude of transverse vibrations the discharge end rests on spring 5 and can be pressed away from the base.In a long working a vibratory belt conveyer takes the form of.sections; to the discharge end of each section is welded a cover plate 6 to prevent the load from falling into the joint between the sections. Sliding is prevented by support 2. Let us introduce a system of coordinates xy with its origin at the point of attachment of the vibration exciter, and let us write the equation Of the v~brations in the formErW' + ~y; + ys cos =-R = (P cos o~t -,.,,y;) e (x), where EI is the flexural rigidity, y is the density, S is the cross-sectional area of the belt, g is the acceleration due to gravity, ~ is the angle of inclination, R is force per unit length exerted by the load on the belt, and P and m v are the exciting force and the mass of the vibration exciter. The function s (x) represents the distributionofpointforces on the section and has the dimensions 1/L.Thus, as well as the first two terms in the Bernoulli-Euler equation for small transverse vibrations, the added terms express the transverse components of the mass of the belt and load and also the forces due to the vibration exciter.Having in view the implicit difference method of solution, we replace x by m and s (x) by the integer function s(m}, where m is the n,rmher of a node of a difference net along the x axis, and we introduce the function ~3Wining Institute, Siberian Branch of the Academy of Sciences of the USSR (IGD SO AN SSSR), Novosibirsk.

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This book gives the remits of many years of research by the author on transportation, loading, bunkering, and discharge of loose materials by means of vibration.A special place in the book is occupied by original models, suggested by the author, of the loose transported medium. Their appearance is not fortuitous.