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: email@example.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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The journal "Vibrations in engineering and technology" presents materials on the following issues
• Theory of processes and machines
• Mechanical Engineering and materialprocessing
• Processing and food production
The certificateof massmediaState registration:kv no 16643-5115 from 30.04.2010 .
Founder of the journal: Vinnytsia National Agrarian University
Kaletnik Hryhorii Mykolaiovych
Ph.D., Prof., academician of NAAS, VNAU (Vinnytsia)
Chief Editor Deputy
DsCProf., NSC IMEG NAAS of Ukraine (Kyiv)
Ph.D., Assoc., VNAU (Vinnytsia)
Members of the editorial board
Bulgakov V.M.- Doctor of Technical Sciences, Professor, Acad.NAAS, National University of Life and Environmental Sciences of Ukraine
Veselovskaya N.R.- Doctor of Technical Sciences, Professor, Vinnytsia National Agrarian University
Derevenko A.I.- Ph.D., Associate Professor, Vinnytsia National Agrarian University
Zinkovsky A.P.- Doctor of Technical Sciences, Professor, the Institute of Strength Problems named after H.S.Pysarenko, NAS of Ukraine
Iskovych-Lototskyi R.D.- Doctor of Technical Sciences, Professor, Vinnytsia National Technical University
Kupchuk I.M.- Ph.D, Senior Lecturer, Vinnytsia National Agrarian University
Nadutyi V.P. - Doctor of Technical Sciences, Professor, Geotechnical Mechanics Institute named after PolyakovM.S. NAS of Ukraine
Matveyeyv V.V. - Ph.D., Professor, Academician of the National Academy of Sciences of Ukraine, the Institute of Strength Problems named after H.S.PysarenkoNAS of Ukraine
Olshanskyi V.P. - Ph.D, Professor, Kharkiv National Technical University of Agriculture named after Petro Vasylenko
PoleyvodaYu.A. - Ph.D., Associate Professor, Vinnytsia National Agrarian University
Spirin A.V.- Ph.D., Associate Professor, Vinnytsia National Agrarian University
Tverdohlib I.V. - Ph.D., Associate Professor, Vinnytsia National Agrarian University
Tokarchuk O.A.- Ph.D., Associate Professor, Vinnytsia National Agrarian University
Tsurkan O.V.- Ph.D. Associate Professor., Vinnytsia National Agrarian University
Jordan Todorov Maksimov - Doctor of Technical Sciences, Prof., Gabrovo Technical University (Bulgaria)
Kind of publication: journal
Type of publication : Scientific
Publication status: Domestic
Year of founding:
Periodicity: 4 times a year
Extent: 18.75 nominal printed pages
ISSN: 2306-8744 (printed version), (online)
Language of edition : (mixed languages) Ukrainian, Russian, English
The scope of the distribution and the category of readers: national, foreign, teaching staff, scientists, businessmen.
Periodical is included in the list of scientific professional editions of Ukraine approved by the Order of Ministry of Education and Sciences of Ukraine from 21.12.2015 No. 1328.
The journal "Vibrations in engineering and technology" is included in the "Catalogue of periodicals of Ukraine".
Journal subscription can be executed in each post office department.
Subscription Index is 99720.
Old version of site: http://vibrojournal.vsau.edu.ua/
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 94 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Kaletnik H.M PhD , professor, academician NAAS 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.