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

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Zhengbing Hu 1,* Viktor Legeza 2 Ivan Dychka 3 Dmytro Legeza 4

1. School of Educational Information Technology, Central China Normal University, Wuhan, China

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

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

4. Powerhouse, part of Essent Energy Group, Netherlands

* Corresponding author.


Received: 10 May 2017 / Revised: 15 Jun. 2017 / Accepted: 6 Jul. 2017 / Published: 8 Jan. 2018

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


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


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