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

Деталі
Батьківська категорія: Геотехнічна механіка, 2019
Категорія: Геотехнічна механіка, 2019, № 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

 

REFERENCES

1. Chelomey, V.N. (1981). Vibrations in the technique. Vibration and shock protection, available at:  http://www.zodchii.ws/books/info-1224.html

2. Legeza, V. P. (2006), “Dynamics of vibroprotective systems with roller dampers of low-frequency vibrations”, Strength of Materials, no. 2 (36),  pp. 186-194

3. Takei, H. and Shimazaki, Y. (2010), “Vibration control effects of tuned cradle damped mass damper”, Journal of Applied Mechanics, no. 13,  pp. 587-594

4. Legeza, V. P. (2012), “Cycloidal pendulum with a rolling cylinder”, . Mechanics of Solids, vol. 47, no. 4, pp. 380-384

5. Obata, M. and Shimazaki, Y. (2008), “Optimum parametric studies on tuned rotary-mass damper”, Journal of Vibration and Control, no. 14, pp. 867-884

6. Bransch, M. (2016), “Unbalanced oil filled sphere as rolling pendulum on a flat surface to damp horizontal structural vibrations”, Journal of Sound and Vibration, no. 368, pp. 22-35

7. Nadutyj, V.P. and Lapshin, Ye.S. (2005). The probabilistic processes of vibration classification of mineral raw materials, Naukova dumka, Kyiv, UA.

8. Lapshin, Ye.S. (2004), “The probabilistic assessment of the speed of vibro-transporting a layer of bulk material”, Vibrations in engineering and technology, no. 3 (35),  pp.  64-67

9. ESM 3124 Intermediate Dynamics, HW7 Solutions, available at: http://www2.esm.vt.edu/~sdross/pub/3124_2012/lectures/hw7_esm3124_2012_sol.pdf

10. Bransch, M. (2016), “Unbalanced oil filled sphere as rolling pendulum on a flat surface to damp horizontal structural vibrations”, Journal of Sound and Vibration, no. 368, pp. 22-35

11. Library & Information Services (2014). Dynamics of the body in contact with a solid surface, available at: http://www.rfbr.ru/rffi/ru/books/o_1920676

12. Bat, M. I., Dzhanelidze, G. Yu. and Kelzon A. S. (1973), “Theoretical mechanics in examples and problems. Special chapters of mechanics”, available at: http://www.zodchii.ws/books/info-1135.html

_______________________________________________

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, Ця електронна адреса захищена від спам-ботів. вам потрібно увімкнути JavaScript, щоб побачити її.

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, Ця електронна адреса захищена від спам-ботів. вам потрібно увімкнути JavaScript, щоб побачити її.