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

• Published in: Natsional'nyi Hirnychyi Universytet. Naukovyi Visnyk Vol. 1; no. 1; pp. 68 - 73
• Main Authors: Pukach, P.Ya, Kuzio, I.V., Nytrebych, Z.M., Il’kiv, V.S.
• Format: Journal Article
• Language: English
• Published: Dnipropetrosk State Higher Educational Institution "National Mining University" 2018
• Subjects: Asymptotic methods; Asymptotic properties; Design engineering; Drilling; Drilling equipment; Drilling machines (tools); Excavation; Impact analysis; Industrial equipment; Investigations; Mathematical models; Mechanical properties; Mechanics; Mechanics (physics); Methods; Mining; Mining engineering; Mining industry; Nonlinear analysis; Nonlinear systems; Numerical analysis; Numerical methods; Oscillations; Partial differential equations; Periodic functions; Resonance; Theory; Vibrations; Waves
• ISSN: 2071-2227; 2223-2362
• DOI: 10.29202/nvngu/2018-1/9

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. 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. 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. 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 basis of analytical approaches that allow, in contrast to numerical methods and experimental approaches, exploring features of dynamics of such systems more precisely. The proposed technique allows solving important practical problems of developing oscillatory engineering systems at the design stage, selecting the elastic characteristics of shafts, counting modes and screw drilling equipment in view of possible resonance phenomena. Determination of resonance modes of the equipment in turn allows for efficient and safe mining.