Mathematical Model of the Dynamics in a One Nonholonomic Vibration Protection System

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Author(s)

Viktor Legeza 1,* Ivan Dychka 1 Ruslan Hadyniak 1 Liubov Oleshchenko 1

1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2018.10.03

Received: 11 Jun. 2018 / Revised: 15 Jul. 2018 / Accepted: 2 Aug. 2018 / Published: 8 Oct. 2018

Index Terms

Heavy Homogeneous Sphere, Pure Rolling, Appell’s Formalism, Translational Motion, Spherical Recess, Energy Conservation Integral, Roller Absorbers

Abstract

Dynamic behavior of a heavy homogeneous sphere in a spherical cavity of a supporting body that performs specified translational movements in space has been studied. Using the Appel formalism, the equations of ball motion in a moving spherical cavity without slip are constructed and a numerical analysis of the evolution of the ball motion is carried out.

Cite This Paper

Viktor Legeza, Ivan Dychka, Ruslan Hadyniak, Lіubov Oleshchenko, "Mathematical Model of the Dynamics in a One Nonholonomic Vibration Protection System", International Journal of Intelligent Systems and Applications(IJISA), Vol.10, No.10, pp.20-26, 2018. DOI:10.5815/ijisa.2018.10.03

Reference

[1]Den Hartog J.P. Mechanical Vibrations. McGraw-Hill, New York, 1956. – 436 p.
[2]Dynamic calculation of buildings and structures: Handbook of the designer (in Russian) / Ed. B.G. Korenev, I.M. Rabinovich. – Moscow: Stroiizdat, 1984. – 304 p.
[3]Dynamic calculation of special engineering buildings and structures: Handbook of the designer (in Russian) / Ed. B.G. Korenev, A.F. Smirnov. – M.: Stroiizdat, 1986. – 185 p.
[4]N.A.Fufaev. A sphere rolling on a horizontal rotating plane // Journal of Applied Mathematics and Mechanics, 1983, V.47, Issue 1, p.p. 27 – 29.
[5]N.A.Fufaev. Theory of the motion of systems with rolling // Journal of Applied Mathematics and Mechanics, 1985, V.49, Issue 1, p.p. 49 – 53.
[6]N.A.Fufaev. Rolling of a heavy homogeneous ball over a rough sphere rotating around a vertical axis // Soviet Applied Mechanics, 1987, V.23, Issue 1, p.p. 86 – 89.
[7]Korenev B.G., Reznikov L.M. Dynamic Vibration Absorbers – Theory and Technical Applications. Chichester. – John Willey and Sons‖. – 1993. – 296 p.
[8]Legeza V.P. Vibration protection of dynamic systems with roller absorbers (in Ukrainian). – Kyiv, "The Fourth Wave", 2010. – 280 p.
[9]Legeza V.P. Numerical analysis of the motion of a ball in an ellipsoidal cavity with a moving upper bearing // Soviet Applied Mechanics. – 1987. – Vol. 23, №2. – P. 191 – 195.
[10]Legeza V.P. Kinematics and dynamics of a mechanical system on rollers that provide nonholonomic constraints // Journal of Mathematical Sciences (Kluwer Academic Publishers–Plenum Publishers). –1994. – Vol. 72, №5. – P. 3299 – 3305.
[11]Legeza V.P. Plane problem on a heavy ball rolling in a spherical recess of an inverted pendulum // Int. Appl. Mech. – 2001. – Vol. 37, №8. – P. 1089 – 1093.
[12]Li J., Zhang Z., Chen J. Experimental Study on Vibration Control of Offshore Wind Turbines Using a Ball Vibration Absorber // J. Energy and Power Engineering, 2012, № 4. – P. 153 – 157.
[13]Lobas L.G. On Rolling Systems // Int. Appl. Mech. – 2000. – 36, № 5. – P. 691 – 696.
[14]Lurie A.I. Analytical mechanics. – Berlin: Springer – Verlag, 2002. – 864 p.
[15]Neimark Yu.I., Fufayev N.A. Dynamics of nonholonomic systems. – Providence: Amer. Mathem. Society, 2004. – 518 p.
[16]Obradovic A., Savinic S., Radulovic R. The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip // Theoretical and applied mechanics, V. 44 (2017), Issue 2, p.p. 237 – 254.
[17]Pirner M. Actual Behaviour of a Ball Vibration Absorber // Wind Engineering and Industrial Aerodynamics. – 2002, Vol. 90, №8. – P. 987 – 1005.
[18]Pirner M., Fischer O. One prototype of the ball absorber and its effect on the tower // Int. Association for Shell and Spatial Struct. Proc. Working Group IV Masts and Towers. 19th Meeting in Krakow, Poland, September, 1999. – P. 187–196.
[19]Pirner M., Fischer O. The development of a ball vibration absorber for the use on towers // IASS, Jour. Of the Int. Association for shell and spatial structures, 2000, Vol. 41, №2. – P. 91 – 99.
[20]Weaver W., Timoshenko S.P., Young D.H. Vibration Problems in Engineering, 5th Edition. – John Wiley (N.Y.), 1990. – 624 p.
[21]Zhang Z. –L., Chen J.–B., Li J. Theoretical study and experimental verification of vibration control of offshore wind turbines by a ball vibration absorber // Structure and Infrastructure Engineering, Taylor & Francis, 2014, Vol. 10, № 8. – P. 1087 – 1100.
[22]Zhang Z. –L., Li J., Nielsen S.R.K., Basu B. Mitigation of edgewise vibrations in wind turbine blades by means of roller dampers // J. of Sound and Vibration, 333 (2014). – P. 5283 – 5298.
[23]Zhengbing Hu, Viktor Legeza, Ivan Dychka, Dmytro Legeza. Mathematical Model of the Damping Process in a One System with a Ball Vibration Absorber // International Journal of Intelligent Systems and Applications (IJISA), Vol. 10, No. 1, Jan. 2018, p.p. 24 – 33.