Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints
The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation techniqu...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2021/8854115 |
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| author | Songtao Li Qunhong Li Zhongchuan Meng |
| author_facet | Songtao Li Qunhong Li Zhongchuan Meng |
| author_sort | Songtao Li |
| collection | DOAJ |
| description | The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams. |
| format | Article |
| id | doaj-art-db4a70c38e0b4e6cbcfd2a60d5d88108 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-db4a70c38e0b4e6cbcfd2a60d5d881082025-02-03T06:07:38ZengWileyShock and Vibration1070-96221875-92032021-01-01202110.1155/2021/88541158854115Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided ConstraintsSongtao Li0Qunhong Li1Zhongchuan Meng2College 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 dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.http://dx.doi.org/10.1155/2021/8854115 |
| spellingShingle | Songtao Li Qunhong Li Zhongchuan Meng Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints Shock and Vibration |
| title | Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints |
| title_full | Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints |
| title_fullStr | Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints |
| title_full_unstemmed | Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints |
| title_short | Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints |
| title_sort | dynamic behaviors of a two degree of freedom impact oscillator with two sided constraints |
| url | http://dx.doi.org/10.1155/2021/8854115 |
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