Issue №: 4(95)
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.
ON THE POSSIBILITY OF STAGNATION OF FREE OSCILLATIONS OF A NONLINEARLY ELASTIC OSCILLATOR WITH A LINEAR VISCOUS RESISTANCE
Olshanskiy Vasyl Pavlovych – Doctor of Physical and Mathematical Sciences, Full Professor, Petro Vasilenkj Kharkiv National Technical University of Agriculture, Tel. (066) 010-09-55, е-mail: OlshanskiyVP@gmail.com
Olshanskiy Stanislav Vasilevich – Phd in Physical and Mathematical Sciences, Petro Vasilenkj Kharkiv National Technical University of Agriculture, Tel. (057) 343-29-41, е-mail: stasolsh77@gmail.com
The free oscillations of an oscillator with a power-nonlinear elasticity characteristic under the action of linear viscous resistance are considered. Using the energy balance method, which is widespread in mechanics, the calculation of the amplitudes of free damped oscillations is reduced to calculating the roots of an algebraic equation, which has an exact analytical solution only with linear elasticity of the oscillator. In the case of an arbitrary positive indicator of nonlinear elasticity, a numerical solution of the equation is required. For this, the Newton's iterative method was used in the work, which has fast convergence of iterations at an arbitrary initial approximation. According to the results of the analysis of the coefficients of the equation established, that in the case of a rigid characteristic of elasticity, when the nonlinearity is greater than unity, the oscillations are reduced to a finite number of decaying ranges, that is, they are limited in time, and in the case of a soft characteristic of elasticity, when the nonlinearity is less than unity, they continue to infinity, as linear dissipative oscillator. The research is given by the method of energy balance and numerical integration of the differential equation of oscillations on a computer. The work of the force of viscous resistance is calculated approximately using periodic Ateb functions that accurately describe free undamped oscillations in the absence of resistance. As a result, approximate iterative dependences are obtained for calculating the amplitudes of the ranges that decay during movement. The numerical results obtained using approximate formulas and numerical computer integration of the nonlinear Cauchy problem are compared. Their satisfactory agreement was noted. A satisfactory agreement was noted between the results for both hard and soft elastic characteristics, which confirmed the adequacy of approximate analytical solutions to the dynamics problem. The main advantage of the described approximate calculation method is that there is no need to build an analytical solution to the nonlinear differential equation of motion of the oscillator, which is a rather complicated mathematical problem. Furthermore, it made it possible to establish conditions under which the oscillator with a viscous and dry friction resistance have similar oscillation properties.
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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.
