### Abstract

The relevance of the research is caused by the fact that vibration electromagnetic activators are promising for use in various technolo' gies. These technologies are associated with extraction and transportation of georesources, including preparation of drilling fluids and liquefaction of viscous oil products. Vibrating electromagnetic activator is an electric machine of reciprocating motion with an armature' activator, which forms turbulent submerged jets in a treated liquid medium. In the first half'period, the armature'activator is attracted to the wall due to a current pulse in the coils and potential energy is accumulated in the elastic spring. This is a mode of forced oscilla' tions in mechanical system of a vibrating electromagnetic activator. In the second half'period there is no current in the coils and the ar' mature'activator is repelled from the walls due to the spring energy. This is the mode of free oscillations in the mechanical system. Vi' bration electromagnetic activators should be tuned to the resonant frequency to maximize energy efficiency. The resonant frequency is not constant and depends on the properties of the treated fluid. The shape of the force'induced oscillation must provide oscillations in mechanical system at the resonant frequency with a limiting amplitude. This fact will increase the energy efficiency and performance of a vibration electromagnetic activator. The main aim of the research is to conduct analytical research to provide resonant oscillations with a limiting amplitude in a vibration electromagnetic activator. Methods of the research are based on using ordinary differential equations, Laplace transform, amplitude'frequency characteristics, systems of nonlinear algebraic equations, spectral analysis, comparison of analytical and experimental characteristics Results. The authors have considered the mode of free oscillations of the armature'activator with the limiting amplitude based on line' arized mathematical model of the mechanical vibration electromagnetic activator system. The mode of forced oscillations is proposed to be considered as a natural addition to the mode of free oscillations with a driving force that acts half the period and has a special form. It is shown that the modes of free and forced oscillations substantially depend on the parameters of the mechanical system. Such para' meters depend on the properties of the treated liquid medium. The authors carried out the spectral analysis of the driving force, provi' ding resonant oscillations with a limiting amplitude in the vibration electromagnetic activator mechanical system. The paper introduces the technical solution that ensures the control of the vibration electromagnetic activator with automatic tuning to the resonant frequen' cy and the limiting amplitude of oscillations of the armature'activator. This mode maximizes the energy efficiency and productivity of the mixing liquid processed media. Based on a comparison of analytical and experimental frequency characteristics the authors confir' med the hypothesis of admissibility of linearizing the mathematical model of vibration electromagnetic activator mechanical system in an analytical study of the driving force of the optimal form.

Translated title of the contribution | Resonant oscillations with a limiting amplitude in a vibration electromagnetic activator |
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Original language | Russian |

Pages (from-to) | 201-213 |

Number of pages | 13 |

Journal | Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering |

Volume | 330 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

### ASJC Scopus subject areas

- Materials Science (miscellaneous)
- Fuel Technology
- Geotechnical Engineering and Engineering Geology
- Waste Management and Disposal
- Economic Geology
- Management, Monitoring, Policy and Law

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## Cite this

*Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering*,

*330*(1), 201-213. https://doi.org/10.18799/24131830/2019/1/70