Asymptotic Method for Studying Mathematical Models of Resonant and Nonresonant Nonlinear Vibrations for Some 1D Moving Bodies

The mathematical model of nonlinear oscillations of an elastic moving one - dimensional body is investigated. The method of research of the specified model in case of resonant and nonresonant modes of fluctuations is developed. The oscillatory systems considered in the work simulate, in particular, dynamic processes in auger electromechanical machines, technological equipment used in drilling works, etc. The equations in standard form, which determine the parameters of the dynamic process for nonlinear oscillations of a moving body, are considered and investigated. Asymptotic approaches to the study of these mathematical models of oscillations make it possible to obtain and analyze the conditions of resonant and non-resonant modes of operation of the above technological systems.