Using the apparatus of the special periodic Ateb-functions in combination with the asymptotic methods of nonlinear mechanics, the nonlinear mathematical models of motion of working environment of the oscillation system, which dependences take into account resilient and viscid making tensions from descriptions of the deformation state of environment, her physical and mechanical properties and features of co-operation of environment with the oscillation system, are worked out. The nonlinear model for describing the dynamics of the working environment of oscillating systems is more flexible, because the nonlinearity index, which depends on the type of working load, significantly affects the results of the oscillating loading process. It allows us to take into account the type of load, and, accordingly, increase the level of adequacy of the constructed analytical model of the oscillatory process that needs to be investigated. Taking into account this model, the study of various processes in oscillating systems can be carried out, in particular in different modes of vibration processing.
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