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Advances in Materials Science and Engineering
Volume 2016, Article ID 1509384, 19 pages
Research Article

Bifurcation Study of Thin Plate with an All-Over Breathing Crack

Beijing University of Technology, No. 100, Pingleyuan, Chaoyang District, Beijing, China

Received 17 June 2016; Revised 17 September 2016; Accepted 16 October 2016

Academic Editor: Ying Li

Copyright © 2016 Lihua Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.