Lapshin Ye.S., Blyuss B.A., Dziuba S.V. Determination of optimal parameters for dynamic low-frequency oscillation dampers

Details

Parent Category: Geo-Technical Mechanics, 2018

Category: Collection of scientific papers «Geotekhnicheskaya Mekhanika» Issue 139

Geoteh. meh. 2018, 139, 23-30

DOI: https://doi.org/10.15407/geotm2018.02.023

DETERMINATION OF OPTIMAL PARAMETERS FOR DYNAMIC LOW-FREQUENCY OSCILLATION DAMPERS

¹Lapshin Ye.S., ¹Blyuss B.A., ¹Dziuba S.V.

¹Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine

UDC62-752.2:519.863

Language: Russian

Abstract.

The dynamic extinguishers of vibrations are widely used for the decline of loadings in different mechanisms and engineering buildings. For great-overall dimensional buildings: supports of wild-power  options, height buildings, aerials and etc – low-frequency own vibrations are characteristic (less than 10 Hertzs, and quite often and less than 1 Hertzs). The extinguishers of vibrations with the bodies of rolling, which have simple construction and high reliability, apply in this case.

In the paper, a problem of finding intrinsic frequencies of nonlinear oscillations for completely solid hemisphere on a horizontal plane is considered with the assumption that there is no energy dissipation and slipping or overturning on the base of the hemisphere.  Practical importance of this problem is highlighted for the purposes of computing parameters for dynamic dampers of low-frequency oscillations (with frequencies lower than 10 Hz, sometimes even lower than 1 Hz). The authors consider one of the simplest types of hemispherical dampers, whose oscillations are described by nonlinear differential equation. In order to tune the damper to frequency close to the main intrinsic frequency of oscillations of the facility, it is important to know intrinsic frequency of the oscillation damper. This frequency is usually determined under assumption of low-amplitude oscillations, which allows to linearize the equation of motion. Numerical methods, which are used for solving nonlinear differential equations for high amplitudes, can provide particular solutions for concrete conditions only. Therefore, this necessitates generalization of the particular solutions. It is stated that ratio of intrinsic frequency of linearized system to the intrinsic frequency of nonlinear system does not depend on mass or radius of hemisphere. This conclusion made it possible to generalize results of particular numerical solutions and derive an equation for finding optimal radius of oscillation damper with taking into account effect of amplitude on intrinsic frequency of oscillations.

A formula for determination of rational radius of the extinguisher of vibrations, executed as a semiball, is got, which takes into account influence of amplitude on own frequency of nonlinear vibrations.

Keywords: hemisphere, radius, nonlinear oscillations, intrinsic frequency.

References:

1. Chelomey, V.N. (1981), "Vibrations in engineering. Volume 6. Defence against vibrations and strikes", available at: http://www.zodchii.ws/books/info-1224.html (Accessed 10 Jan 2018).

2. Legeza, V. P. (2004), "Dynamics of vibroprotective systems with roller dampers of low-frequency vibrations", Strength of Materials., no. 2 (36), pp. 186-194.

https://doi.org/10.1023/B:STOM.0000028310.36487.e8

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.

https://doi.org/10.3103/S0025654412040024

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.

https://doi.org/10.1177/1077546307084443

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.

https://doi.org/10.1016/j.jsv.2016.01.006

7. Nadutyy, V.P. and Lapshin, Ye.S. (2005), Veroyatnostnyye protsessy vibratsionnoy klassifikatsii mineral'nogo syr'ya [Probabilistic processes in vibrational classification of natural resources], Naukova Dumka, Kyiv, Ukraine.

8. Lapshin, Ye.S. (2004), "Probabilistic estimate of the velocity of vibrational transport of a layer of loose material", Vibrations in engineering and tehnologies, no. 3(35), pp. 64–67.

9. The official site of Russian Foundation of basic Research (2014), “Dynamics of a body in contact with a solid surface”, available at: http://www.rfbr.ru/rffi/ru/books/o_1920676 (Accessed 05 Jan 2018).

10/ Bat, M.I., Dzhanelidze, G.Yu. and Kelzon, A.S. (1973), "Theoretical mechanics in examples and problems. Volume 3, Advanced Chapters of Mechanics", available at: http://www.zodchii.ws/books/info-1135.html (Accessed 11 Jan 2018).

About the authors:                       

Lapshin Yevgeny Semenovich, Doctor of Technical Sciences (D.Sc.), Senior Research, Principal Re-searcher in the Department of Geodynamic Systems and Vibration Technologies, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine  (IGTM NASU), Dnepr, Ukra-ine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Blyuss Boris Aleksandrovich, Doctor of Technical Sciences (D.Sc.), Professor, Head of Department of Geodynamic Systems and Vibration Technologies, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine (IGTM NASU), Dnepr, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Dziuba Serhii Vladimirovich, Candidate of Technical Sciences (Ph.D), Senior Researcher in  Department of Geodynamic System and Vibration Tehnologies, M.S. Polyakov Institute of Geotechnical Mechanics 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.

• < Prev
• Next >