Study of forced vibrations transition processes of vibration protection devices with rolling-contact bearings

  • K. Bissembayev Institute of Mechanics and Machine Science named after the Academician U.A. Dzholdasbekov
  • K. Sultanova Abai Kazakh National Pedagogical University


Many seismic isolation and vibration protection devices use asan essential element the varioustyp es of rolling-contact b earings. The rolling-contact b earing is used for creation of moving baseof b o dy protected against vibration. The most dynamic disturbances acting in the constructionsand structures have highly complex and irregular nature.This article considers the oscillation of a solid b o dy on kinematic foundations, the main elementsof which are rolling b earers b ounded by the high order surfaces of rotation at horizontal displacement of the foundation. It is ascertained that the equations of motion are highly nonlineardifferential equations. Stationary and transitional mo des of the oscillatory pro cess of the systemhave b een investigated. It is determined that several stationary regimes of the oscillatory pro cessexist. Equations of motion have b een investigated also by quantitative metho ds.In this pap er the cumulative curves in the phase plane are plotted, a qualitative analysis for singular p oints and study of them for stability is p erformed. In the Hayashi plane a cumulative curveof b o dy protected against vibration forms a closed path which do es not tend to the stability ofsingular p oint. This means that the vibration amplitude of b o dy protected against vibration is notremain constant in steady-state, but changes p erio dically.


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How to Cite
BISSEMBAYEV, K.; SULTANOVA, K.. Study of forced vibrations transition processes of vibration protection devices with rolling-contact bearings. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 105, n. 1, p. 129-144, apr. 2020. ISSN 2617-4871. Available at: <>. Date accessed: 07 june 2020.
Keywords protection against vibration, rolling-contact bearing, nonlinear vibrations, cumulative curves, singular point