Non-Linear Model of the Damping Process in a System with a two-mass Pendulum Absorber

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Zhengbing Hu 1,* Viktor Legeza 2 Ivan Dychka 2 Mykola Onai 2

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

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

* Corresponding author.


Received: 10 Aug. 2018 / Revised: 9 Oct. 2018 / Accepted: 23 Nov. 2018 / Published: 8 Jan. 2019

Index Terms

Damping System in the Non-Linear Formulation, Two-Mass Pendulum Absorber, Amplitude-Frequency Characteristic (AFC), Parameters of Tuning of Absorber, Determining the Optimum Parameters


In this paper, the dynamic behavior of the damping system is analyzed with a two-mass pendulum absorber, the equations of motion of non-linear mechanical systems are built accordingly. AFC equation systems have been identified in the non-linear formulation. To obtain the frequency response, the Ritz averaging method is used. A new numerical method of determining the parameters of optimal tuning two-mass pendulum absorber in the non-linear formulation has been Proposed and implemented.

Cite This Paper

Zhengbing Hu, Viktor Legeza, Ivan Dychka, Mykola Onai, "Non-Linear Model of the Damping Process in a System with a two-mass Pendulum Absorber", International Journal of Intelligent Systems and Applications(IJISA), Vol.11, No.1, pp.67-72, 2019. DOI:10.5815/ijisa.2019.01.07


[1]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, p.p.18 – 25, 2017. DOI: 10.5815/ijisa. 2017.03.03.
[2]Legeza V.P.Vibration protection of dynamic systems with roller absorbers (in Ukrainian). Kyiv, “Fourth wave”, 2010. – 280 p.
[3]Legeza V.P. The theory of vibration protection systems using isochronous roller dampers (models, methods, dynamic analysis, technical solutions) (in Russian). – Saarbrücken (Deutschland): LAMBERT Academic Publishing, 2013. – 116 p.
[4]Ritz W. eine neue Methode zur gewisser Variations – Probleme der mathemati-schen Physik. – Journal die reine und angewandte Mathematik (Grelle), 1909, B. 135, N.1, S. 1 – 61.
[5]Klotter K. Non-linear vibration problems treated by the averaging method of W.Ritz //Proc. 1st U.S. Nath. Congr., Appl. Mech., Chicago, Illinois: Edwards Brothers Inc., 1951, p.p. 125 – 131.
[6]Weaver W.,Timoshenko S.P.,Young D.H. Vibration Problems in Engineering, 5th Ed. – J. Wiley, 1990. – 624 p.
[7]Den Hartog J.P. Mechanical Vibrations. McGraw- Hill, New York, 1956. – 436 p.
[8]Korenev B.G., Reznikov L.M. Dynamic Vibration Absorbers – Theory and Technical Applications. Chichester. –John Willey and Sons. –1993. – 296 p.
[9]State building norms of Ukraine. Loads and effects (SBN В.1.2-2:2006). Kyiv, Ministry of Construction of Ukraine. – 2006. – 78 p.
[10]Dynamic calculation of structures for special effects: Handbook of the designer (Ed. Korenev B.G, Rabinovich I.M). (in Russian). – M .: Stroiizdat, 1981. – 216 p.
[11]Fisher O. Some experience with the use of vibration absorbers on aerial masts. – Acta Technica CSAV. – 1974, Roc. 19. – №2. – S. 32 – 38.
[12]Kolousek V, et al. Wind effect on Civil Engineering Structures. – Academia Praha. – 1983. – 125 p.
[13]Da-Xue Chen,Guang-Hui Liu,"Oscillatory Behavior of a Class of Second-order Nonlinear Dynamic Equations on Time Scales", IJEM, vol.1, no.6, pp.72-79, 2011.
[14]Mehdi Rouissat,Riad .A Borsali,Mohammed Chick-Bled,"Dual Amplitude-Width PPM for Free Space Optical Systems", IJITCS, vol.4, no.3, pp.45-50, 2012.