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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