INFORMATION CHANGE THE WORLD

International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.10, No.1, Jan. 2018

Mathematical Model of the Damping Process in a One System with a Ball Vibration Absorber

Full Text (PDF, 572KB), PP.24-33


Views:49   Downloads:0

Author(s)

Zhengbing Hu, Viktor Legeza, Ivan Dychka, Dmytro Legeza

Index Terms

Damping Mechanical System;Carrier Body;Working Body;External Harmonic Excitation;Ball Vibration Absorber (BVA);Kinematic Ties;Nonholonomic Ties; Appell's Formalism;Amplitude-Frequency Characteristic (AFC);Parameters Settings of Absorber;Determining the Optimum Parameters;Rolling of a Heavy Ball Without Sliding

Abstract

The forced oscillations of the damping mechanical system of solids "Ball Vibration Absorber (BVA) with linearly viscous resistance – a movable carrier body" under the influence of external harmonic excitation are considered. Based on Appell's formalism, the dynamic equations for the joint motion of a heavy ball without sliding into a spherical cavity of a carrier body are formulated and numerically studied. The amplitude-frequency characteristic of the damping mechanical system and the curves of the dependences of the maximum amplitude of the oscillations of the carrier body on the values of the radius of the spherical cavity and the coefficient of viscous resistance of the BVA are obtained. The conditions and restrictions on the rolling of a heavy ball in the spherical recess of the absorber without sliding are determined.

Cite This Paper

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, pp.24-33, 2018. DOI: 10.5815/ijisa.2018.01.04

Reference

[1]Dynamic calculation of buildings and structures: Handbook of the designer (in Russian) / Ed. B.G. Korenev, I.M. Rabinovich. – Moscow: Stroiizdat, 1984. – 304 p.

[2]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.

[3]Adhikari S., Ali F. Energy Harvesting Dynamic Vibration Absorbers // J. App. Mech., 2013, Vol. 80, P. 1 – 9. 

[4]Chang C.C. Mass dampers and their optimal designs for building vibration control // Eng. Struct. – 1999. – 21. – P. 454 – 463.

[5]Den Hartog J.P. Mechanical Vibrations. McGraw-Hill, New York, 1956. – 436 p.

[6]Kärnä T. Damping methods to mitigate wind-induced vibrations // J. Struct. Mech. –2009. – 42, N1. – P. 38 – 47.

[7]Keutgen R., Lilien J.–L. A new damper to solve galloping on bundled lines. Theoretical background, laboratory and field results // IEEE Transactions on Power Delivery, 1998, Vol.13, №1. – P. 260 – 265.

[8]Korenev B.G., Reznikov L.M. Dynamic Vibration Absorbers – Theory and Technical Applications. Chichester. “John Willey and Sons”. – 1993. – 296 p.

[9]Kwok K.C.S. Damping increase in building with tuned mass damper // ASCE J. Eng. Mech. – 1984. – 110, N11. – P. 1645 – 1649.

[10]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.

[11]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.

[12]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. 

[13]Legeza V.P. Rolling of a Heavy Ball in a Spherical Recess of a Translationally Moving Body // Int. Appl. Mech. – 2002. – Vol. 38, №6. – P. 758 – 764.

[14]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.

[15]Lobas L.G. On Rolling Systems // Int. Appl. Mech. – 2000. – 36, № 5. – P. 691 – 696.

[16]Lurie A.I. Analytical mechanics. – Berlin: Springer – Verlag, 2002. – 864 p.

[17]Naprstek J., Fisher C., Pirner M., Fisher O. Non-linear dynamic behavior of a ball vibration absorber // 3rd ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2011). Corfu, Greece, 26 – 28 May 2011. – P. 1 – 14.

[18]Neimark Yu.I., Fufayev N.A. Dynamics of nonholonomic systems. – Providence: Amer. Mathem. Society, 2004. – 518 p.

[19]Pirner M. Actual Behaviour of a Ball Vibration Absorber // Wind Engineering and Industrial Aerodynamics. – 2002, Vol. 90, №8. – P. 987 – 1005.

[20]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.

[21]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.

[22]Weaver W., Timoshenko S.P., Young D.H. Vibration Problems in Engineering, 5th Edition. – John Wiley (N.Y.), 1990. – 624 p.

[23]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.

[24]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.

[25]Zhengbing Hu, V.P.Legeza, I.A.Dychka, D.V.Legeza, "Mathematical Modeling of the Process of Vibration Protection in a System with two-mass Damper Pendulum", International Journal of Intelligent Systems and Applications(IJISA), Vol.9, No.3, pp.18-25, 2017. DOI: 10.5815/ijisa.2017.03.03