(Видавництво Львівської політехніки, 2022-02-22) Topilnytskyy, Volodymyr; Kabanov, Kostiantyn; Lviv Polytechnic National University
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.
