Asymptotic method for investigating resonant regimes of nonlinear bending vibrations of elastic shaft

Abstract

Асимптотичний метод дослідження резонАнсних режимів неліній них згинАльних коливАнь пружного вАлА Purpose. To develop a method for determining resonant modes of industrial equipment of elastic shaft type, which is widely used in the mining industry, through the study of mathematical model of nonlinear oscillations. Mathematical models of oscillatory systems previously were studied in the literature mainly based on the numerical and experimental approaches. This paper proposes using a combination of the wave theory of motion and asymptotic methods of nonlinear mechanics using special apparatus of periodic functions to investigate the vibrational dynamics of the system and conditions of resonance phenomena in it, as well as to describe the method for determining the resonance curves to increase the margin of safety of industrial equipment. Methodology. Methods for studying resonance amplitudes and frequencies, determining the strength characteristics of equipment are based on the use of asymptotic methods of nonlinear mechanics, wave motion theory and theory of special Ateb-functions. Findings. In this work the conditions of resonance amplitude and frequency depending on the system parameters were obtained analytically for these nonlinear vibrational systems of elastic shaft and the overall method for determining the resonance curves was described. Originality. For the first time a complete analysis of the impact of physical, mechanical and geometrical factors of the dynamic pricess on the resonant frequency and amplitude in systems such as elastic shaft was conducted on the UDC 534.1

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