Bifurcation Study of Thin Plate with an All-Over Breathing Crack
An all-over breathing crack on the plate surface having arbitrary depth and location is assumed to be nonpropagating and parallel to one side of the plate. Based on a piecewise model, the nonlinear dynamic behaviors of thin plate with the all-over breathing crack are studied to analyze the effect of...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Materials Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2016/1509384 |
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| author | Lihua Chen Jian Xue Zhijie Zhang Wei Zhang |
| author_facet | Lihua Chen Jian Xue Zhijie Zhang Wei Zhang |
| author_sort | Lihua Chen |
| collection | DOAJ |
| description | An all-over breathing crack on the plate surface having arbitrary depth and location is assumed to be nonpropagating and parallel to one side of the plate. Based on a piecewise model, the nonlinear dynamic behaviors of thin plate with the all-over breathing crack are studied to analyze the effect of external excitation amplitudes and frequencies on cracked plate with different crack parameters (crack depth and crack location). Firstly, the mode shape functions of cracked thin plate are obtained by using the simply supported boundary conditions and the boundary conditions along the crack line. Then, natural frequencies and mode functions of the cracked plate are calculated, which are assessed with FEM results. The stress functions of thin plate with large deflection are obtained by the equations of compatibility in the status of opening and closing of crack, respectively. To compare with the effect of breathing crack on the plate, the nonlinear dynamic responses of open-crack plate and intact plate are analyzed too. Lastly, the waveforms, bifurcation diagrams, and phase portraits of the model are gained by the Runge-Kutta method. It is found that complex nonlinear dynamic behaviors, such as quasi-periodic motion, bifurcation, and chaotic motion, appear in the breathing crack plate. |
| format | Article |
| id | doaj-art-41ae74b15b9f43d69502429921f333b6 |
| institution | Kabale University |
| issn | 1687-8434 1687-8442 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Materials Science and Engineering |
| spelling | doaj-art-41ae74b15b9f43d69502429921f333b62025-02-03T05:46:24ZengWileyAdvances in Materials Science and Engineering1687-84341687-84422016-01-01201610.1155/2016/15093841509384Bifurcation Study of Thin Plate with an All-Over Breathing CrackLihua Chen0Jian Xue1Zhijie Zhang2Wei Zhang3Beijing University of Technology, No. 100, Pingleyuan, Chaoyang District, Beijing, ChinaBeijing University of Technology, No. 100, Pingleyuan, Chaoyang District, Beijing, ChinaBeijing University of Technology, No. 100, Pingleyuan, Chaoyang District, Beijing, ChinaBeijing University of Technology, No. 100, Pingleyuan, Chaoyang District, Beijing, ChinaAn all-over breathing crack on the plate surface having arbitrary depth and location is assumed to be nonpropagating and parallel to one side of the plate. Based on a piecewise model, the nonlinear dynamic behaviors of thin plate with the all-over breathing crack are studied to analyze the effect of external excitation amplitudes and frequencies on cracked plate with different crack parameters (crack depth and crack location). Firstly, the mode shape functions of cracked thin plate are obtained by using the simply supported boundary conditions and the boundary conditions along the crack line. Then, natural frequencies and mode functions of the cracked plate are calculated, which are assessed with FEM results. The stress functions of thin plate with large deflection are obtained by the equations of compatibility in the status of opening and closing of crack, respectively. To compare with the effect of breathing crack on the plate, the nonlinear dynamic responses of open-crack plate and intact plate are analyzed too. Lastly, the waveforms, bifurcation diagrams, and phase portraits of the model are gained by the Runge-Kutta method. It is found that complex nonlinear dynamic behaviors, such as quasi-periodic motion, bifurcation, and chaotic motion, appear in the breathing crack plate.http://dx.doi.org/10.1155/2016/1509384 |
| spellingShingle | Lihua Chen Jian Xue Zhijie Zhang Wei Zhang Bifurcation Study of Thin Plate with an All-Over Breathing Crack Advances in Materials Science and Engineering |
| title | Bifurcation Study of Thin Plate with an All-Over Breathing Crack |
| title_full | Bifurcation Study of Thin Plate with an All-Over Breathing Crack |
| title_fullStr | Bifurcation Study of Thin Plate with an All-Over Breathing Crack |
| title_full_unstemmed | Bifurcation Study of Thin Plate with an All-Over Breathing Crack |
| title_short | Bifurcation Study of Thin Plate with an All-Over Breathing Crack |
| title_sort | bifurcation study of thin plate with an all over breathing crack |
| url | http://dx.doi.org/10.1155/2016/1509384 |
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