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Open AccessArticle

Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers

1
Ministry of education and science of Kazakhstan, Institute Mechanics and Mechanical Engineering, Almaty 050010, Kazakhstan
2
Ministry of education and science of Kazakhstan, Abai Kazakh National Pedagogical University, Almaty 050000, Kazakhstan
*
Author to whom correspondence should be addressed.
Machines 2019, 7(3), 58; https://doi.org/10.3390/machines7030058
Received: 27 June 2019 / Revised: 2 September 2019 / Accepted: 3 September 2019 / Published: 6 September 2019
(This article belongs to the Special Issue Advances of Italian Machine Design)
This article considers the oscillation of a solid body on kinematic foundations, the main elements of which are rolling bearers bounded by high-order surfaces of rotation at horizontal displacement of the foundation. Equations of motion of the vibro-protected body have been obtained. It is ascertained that the obtained equations of motion are highly nonlinear differential equations. Stationary and transitional modes of the oscillatory process of the system have been investigated. It is determined that several stationary regimes of the oscillatory process exist. Equations of motion have been investigated also by quantitative methods. In this paper the cumulative curves in the phase plane are plotted, a qualitative analysis for singular points and a study of them for stability are performed. In the Hayashi plane a cumulative curve of a body protected against vibration forms a closed path which does not tend to the stability of a singular point. This means that the vibration amplitude of a body protected against vibration does not remain constant in a steady state, but changes periodically. View Full-Text
Keywords: vibroprotection; seismic; rolling bearer; vibration; non-linear vibrations; cumulative curves; singular point vibroprotection; seismic; rolling bearer; vibration; non-linear vibrations; cumulative curves; singular point
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MDPI and ACS Style

Bissembayev, K.; Jomartov, A.; Tuleshov, A.; Dikambay, T. Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers. Machines 2019, 7, 58.

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