Lapshyn Ye.S., Molchanov R.N., Кhaminich A.V. Method for determining the rational parameters of dynamic dampers of low-frequency vibrations

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Parent Category: Geo-Technical Mechanics, 2019

Category: Geo-Technical Mechanics, 2019, Issue 145

Geoteh. meh. 2019, 145, 56-65

https://doi.org/10.1051/e3sconf/201910900049

METHOD FOR DETERMINING THE RATIONAL PARAMETERS OF DYNAMIC DAMPERS OF LOW-FREQUENCY VIBRATIONS

¹Lapshyn Ye.S., ²Molchanov R.N., ³Кhaminich A.V.

¹Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, ²Dnipropetrovsk Medical Academy of the Ministry of Health of Ukraine, ³OlesHoncharDniproNationalUniversity

UDC  62-752.2

Language: English

Abstract.

The problems have been considered of natural nonlinear vibrations of an absolutely rigid semiball and a semicylinder on a horizontal plane, assuming that there is no energy dissipation, sliding and tipping on foundation. To adjust the damper to a frequency close to the fundamental tone of vibrations, it is necessary to assess the natural frequency of the damper, which is determined under the assumption on smallness of the vibrations amplitude. The authors found that the damper parameters must be such that natural frequency is close to the frequency of fundamental tone of vibrations. Therefore, it is important to know the natural frequency of the vibration damper, which, as a rule, is determined under the assumption on smallness of the vibrations amplitude, which makes it possible to linearize the motion equation. At high amplitudes, the nonlinear differential motion equation is solved by numerical methods, which, however, allow to find only particular solutions for specific conditions.  This paper represents the comparison of the natural frequency of linearized and nonlinear system. The relative error has been estimated of the natural frequency calculation, which is caused by linearization. It is shown that the ratio of the natural frequency of the linearized system to the natural frequency of the nonlinear system does not depend on the mass and radius. This conclusion made it possible to generalize the results of particular computational solutions and to obtain a formula which takes into account the amplitude influence on the natural vibrations frequency and helps to determine the natural frequency for the initial angles to ninety degrees. For the first time, a method for generalizing the numerical experiments has been proposed in order to determine the influence of radii on the natural frequencies of the nonlinear vibrations of a semicylinder and a semiball. The results of numerical experiments for determining the relative frequency are approximated by a second degree polynomial of the amplitude. As a result of studies and mathematical models obtained, the authors have been determined rational radii  of dynamic dampers of vibrations.

Keywords: oscillation frequency, quencher, linearized system, hemisphere, half cylinder

 

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About the authors

Lapshyn Yevgen Semenovych, Doctor of Technical Sciences (D.Sc.), Senior Researcher, Principal Researcher sn the Department of Geodynamic Systems and Vibration Technologies, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine  (IGTM, NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Molchanov Robert Mykolaiovych, Doctor of Medical Sciences (D.Sc.), Professor, Professor of the Department of Surgery No. 1, DZ "Dnipropetrovsk Medical Academy of the Ministry of Health of Ukraine", Dnipro, Ukraine

Кhamynych Oleksandr Vasilovych, Candidate of Physical and Mathematical Sciences (Ph.D.), Professor,  Dean of the Faculty of Mechanics and Mathematics, Oles Honchar Dnipro National University, Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

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