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Purpose. For a conveyor belt, the material of which corresponds to the Maxwell-element model, to analyze the causes of the occurrence of longitudinal dynamic stresses and investigate the peculiarities of the propagation of dynamic stresses along the route of material transportation. Methodology. To calculate the value of static and dynamic stresses arising in the conveyor belt, the apparatus of mathematical physics was used. Findings. A wave equation is written that determines the propagation of longitudinal vibrations in a conveyor belt, the material of which corresponds to the Maxwell-element model. An expression is obtained for calculating the speed of propagation of elastic vibrations along the conveyor belt, the frequency of vibrations and their wavelength. The characteristic relaxation time of disturbances is determined. The method of successive approximation was used to solve the wave equation. The estimation of the characteristic time of acceleration of the conveyor belt, at which there is no destruction of the material of the conveyor belt, is given. Originality. PDE-models of conveyor-type transport systems are improved, which are used to design belt speed control systems under restrictions on speed control modes. It is shown that under the modes of acceleration or deceleration of the conveyor belt, the effects associated with the occurrence and propagation of dynamic stresses along the conveyor belt, due to the characteristics of the material corresponding to the Maxwell-element model, are insignificant. Practical value. The results obtained make it possible to determine the limitations on the modes of acceleration or deceleration of the conveyor belt, preventing its damage and increased wear. This opens up prospects for designing effective control systems for the parameters of a conveyor belt, unevenly loaded with material along the transport route.

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