Issue №: 2(117)
The journal deals with the problems of vibration technologies and machines, mathematical methods of vibration process studies, information on design and technological development, presents teaching and methodological aspects of teaching in the Higher School of Applied Sciences, where vibration machines and technologies are studied.
A MATHEMATICAL MODEL OF AN ELASTIC-DAMPER SYSTEM BASED ON THE EXAMPLE OF A KELVIN-VOIGT BODY
Dmytriv Vasyl - Doctor of Engineering Sciences, Professor, Head of Department of Desing Machine and Automotive Engineering, Lviv Polytechnic National University, 79013, 12 Stepan Bandera Str., Lviv, Ukraine, е-mail: Vasyl.T.Dmytriv@lpnu.ua, https://orcid.org/0000-0001-9361-6418
Berehuliak Stepan - recipient of the PhD degree of Department of Desing Machine and Automotive Engineering, Lviv Polytechnic National University, 79013, 12 Stepan Bandera Str., Lviv, Ukraine, е-mail: Stepan.T.Berehuliak@lpnu.ua, https://orcid.org/0009-0005-6597-9752
Mechanical systems that combine structural elements with elastic and viscous properties and operate under dynamic and impulse loads require accurate mathematical models to predict their oscillatory behaviour. The purpose of this study was to develop a mathematical model of an elastic-damper system based on the Kelvin-Voigt body, aimed at describing viscoelastic material behaviour and analysing the influence of stiffness and damping parameters on the dynamic response of the system. The research applied analytical methods for solving differential equations, analysis of characteristic equations for both real and complex roots, as well as algebraic transformations for constructing general and particular solutions. As a result, an analytical solution was obtained for determining the dynamic response of the masses under impulse loading. The proposed model took into account variable stiffness, damping, and mass parameters, and distinguishes between regimes with real and complex eigenvalues. It was established that increasing the damping coefficient reduces amplitude and accelerates oscillation decay, while increasing mass extends the decay duration. The influence of pulse duration and repetition frequency on the oscillation profile was investigated. The simulation results confirmed the accuracy of the analytical expressions and enable the modelling of transient processes under various conditions. Compared to purely numerical approaches, the proposed method provides broader opportunities for system analysis and control. The developed model can be applied in the study of technical systems with arbitrary configurations of elastic-viscous element connections and varying numbers of components, making it possible to optimise the design of systems that utilise oscillations, vibrations, damping.
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About the journal
The journal "Vibrations in Engineering and Technologies" is included in the list of technical scientific publications of Ukraine
(Category "B", Order of the Ministry of Education and Science of Ukraine dated July 2, 2020 No. 886)
Old version of the site: http://vibrojournal.vsau.edu.ua/
The journal "Vibrations in Engineering and Technology" is indexed by the following databases and catalogs:
The certificateof massmedia State registration:kv no 16643-5115 from 30.04.2010 .
Founder of the journal: Vinnytsia National Agrarian University
The journal is devoted to highlighting current issues in engineering, mechanical engineering, and technological processes, including the study of dynamic and oscillatory phenomena in technical systems, the application of mathematical methods for process modeling and analysis, as well as the presentation of results of design-engineering and technological developments. Particular attention is given to the study of vibration processes and their application in modern technologies.
The purpose of the scientific journal “Vibrations in Engineering and Technologies” is to disseminate the results of fundamental and applied research in the field of engineering sciences aimed at developing theoretical foundations and practical approaches to the design, analysis, and improvement of machines, materials, and technological processes, including the use of vibration and oscillatory effects in various sectors of production.
The publication is focused on the formation of a modern scientific and informational environment for the effective exchange of research results, support of innovative development, and implementation of advanced technical solutions in industry, agro-industrial production, and related fields.
The journal promotes the development of interdisciplinary research, the integration of modern engineering approaches, and the enhancement of the efficiency of technological processes and technical systems, including through the rational use of vibration phenomena.
Objectives of the Scientific Journal
To achieve its stated purpose, the journal addresses the following key objectives:
dissemination of results of fundamental and applied scientific research in the fields of mechanics, mechanical engineering, technological processes, machine dynamics, and equipment, as well as in areas related to the application of vibration phenomena in engineering and technologies;
promotion of research aimed at the creation and improvement of machines, mechanisms, and technological equipment based on oscillatory and vibration processes;
support for the implementation of modern technological solutions focused on improving productivity, energy efficiency, and reliability of technical systems;
обеспечение scientific exchange of research results among research institutions, higher education establishments, and industrial enterprises;
development of interdisciplinary cooperation among researchers in the fields of mechanics, materials science, material processing technologies, and automation of technological processes;
dissemination of modern scientific achievements and advanced technologies related to the application of vibration processes in production and technical systems.
Publisher Vinnytsia National Agrarian University
In June 1994 the 2nd International Scientific and Technical Conference "Application of vibrations for technological purposes" was organized on the basis of Vinnytsia State Agricultural Institute. Leading experts in this field, noting the significant contribution to the school of Vibration Engineering under the leadership of P. S. Bernyk, proposed to create a professional all-Ukrainian scientific and technical journal "Vibration in engineering and technology..The journal was foundedat Vinnytsia State Agricultural Institute and P.S. Bernyk was elected to be the chief editor .
For all these years (since 1994) theJournal "vibration in engineering and technology" published 119 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Ihor Kupchuk, Candidate of Technical Sciences, Associate professor, Associate Professor of the Department of Engineering Mechanics and Technological Processes in the Agricultural Industry Faculty of Engineering and Technology Vinnytsia National Agrarian University is the chief editor of the "Vibrations in engineering and Technology"
The journal "Vibration in Engineering and technology", which has no analogues on the territory of Ukraine, is well known abroad.
