Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers
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 ascertain...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/7/3/58 |
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| author | Kuatbay Bissembayev Assylbek Jomartov Amandyk Tuleshov Tolegen Dikambay |
| author_facet | Kuatbay Bissembayev Assylbek Jomartov Amandyk Tuleshov Tolegen Dikambay |
| author_sort | Kuatbay Bissembayev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T12:01:40Z |
| format | Article |
| id | doaj.art-5fea48077b6f456b8d64784dc13c8053 |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-04-13T12:01:40Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-5fea48077b6f456b8d64784dc13c80532022-12-22T02:47:46ZengMDPI AGMachines2075-17022019-09-01735810.3390/machines7030058machines7030058Analysis of the Oscillating Motion of a Solid Body on Vibrating BearersKuatbay Bissembayev0Assylbek Jomartov1Amandyk Tuleshov2Tolegen Dikambay3Ministry of education and science of Kazakhstan, Institute Mechanics and Mechanical Engineering, Almaty 050010, KazakhstanMinistry of education and science of Kazakhstan, Institute Mechanics and Mechanical Engineering, Almaty 050010, KazakhstanMinistry of education and science of Kazakhstan, Institute Mechanics and Mechanical Engineering, Almaty 050010, KazakhstanMinistry of education and science of Kazakhstan, Abai Kazakh National Pedagogical University, Almaty 050000, KazakhstanThis 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.https://www.mdpi.com/2075-1702/7/3/58vibroprotectionseismicrolling bearervibrationnon-linear vibrationscumulative curvessingular point |
| spellingShingle | Kuatbay Bissembayev Assylbek Jomartov Amandyk Tuleshov Tolegen Dikambay Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers Machines vibroprotection seismic rolling bearer vibration non-linear vibrations cumulative curves singular point |
| title | Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers |
| title_full | Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers |
| title_fullStr | Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers |
| title_full_unstemmed | Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers |
| title_short | Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers |
| title_sort | analysis of the oscillating motion of a solid body on vibrating bearers |
| topic | vibroprotection seismic rolling bearer vibration non-linear vibrations cumulative curves singular point |
| url | https://www.mdpi.com/2075-1702/7/3/58 |
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