Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops
The double grazing periodic motions and bifurcations are investigated for a two-degree-of-freedom vibroimpact system with symmetrical rigid stops in this paper. From the initial condition and periodicity, existence of the double grazing periodic motion of the system is discussed. Using the existence...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/642589 |
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| author | Qunhong Li Limei Wei Jieyan Tan Jiezhen Xi |
| author_facet | Qunhong Li Limei Wei Jieyan Tan Jiezhen Xi |
| author_sort | Qunhong Li |
| collection | DOAJ |
| description | The double grazing periodic motions and bifurcations are investigated for a two-degree-of-freedom vibroimpact system with symmetrical rigid stops in this paper. From the initial condition and periodicity, existence of the double grazing periodic motion of the system is discussed. Using the existence condition derived, a set of parameter values is found that generates a double grazing periodic motion in the considered system. By extending the discontinuity mapping of one constraint surface to that of two constraint surfaces, the Poincaré map of the vibroimpact system is constructed in the proximity of the grazing point of a double grazing periodic orbit, which has a more complex form than that of the single grazing periodic orbit. The grazing bifurcation of the system is analyzed through the Poincaré map with clearance as a bifurcation parameter. Numerical simulations show that there is a continuous transition from the chaotic band to a period-1 periodic motion, which is confirmed by the numerical simulation of the original system. |
| format | Article |
| id | doaj-art-161318bb3e6b41719943aa63cfed66e5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-161318bb3e6b41719943aa63cfed66e52025-02-03T06:14:08ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/642589642589Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral StopsQunhong Li0Limei Wei1Jieyan Tan2Jiezhen Xi3College of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaThe double grazing periodic motions and bifurcations are investigated for a two-degree-of-freedom vibroimpact system with symmetrical rigid stops in this paper. From the initial condition and periodicity, existence of the double grazing periodic motion of the system is discussed. Using the existence condition derived, a set of parameter values is found that generates a double grazing periodic motion in the considered system. By extending the discontinuity mapping of one constraint surface to that of two constraint surfaces, the Poincaré map of the vibroimpact system is constructed in the proximity of the grazing point of a double grazing periodic orbit, which has a more complex form than that of the single grazing periodic orbit. The grazing bifurcation of the system is analyzed through the Poincaré map with clearance as a bifurcation parameter. Numerical simulations show that there is a continuous transition from the chaotic band to a period-1 periodic motion, which is confirmed by the numerical simulation of the original system.http://dx.doi.org/10.1155/2014/642589 |
| spellingShingle | Qunhong Li Limei Wei Jieyan Tan Jiezhen Xi Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops Abstract and Applied Analysis |
| title | Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops |
| title_full | Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops |
| title_fullStr | Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops |
| title_full_unstemmed | Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops |
| title_short | Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops |
| title_sort | double grazing periodic motions and bifurcations in a vibroimpact system with bilateral stops |
| url | http://dx.doi.org/10.1155/2014/642589 |
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