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Study on bifurcation of thin plate with full breathing crack

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Document pages: 19 pages

Abstract: It is assumed that the full breathing crack with arbitrary depth and position on the plate surface is a non propagating crack and parallel to one side of the plate. Based on the piecewise model, the nonlinear dynamic behavior of thin plates with full breathing cracks is studied, and the effects of external excitation amplitude and frequency on cracked plates with different crack parameters (crack depth and crack position) are analyzed. Firstly, using the simply supported boundary conditions and the boundary conditions along the crack line, the vibration mode function of the cracked thin plate is obtained. Then, the natural frequency and modal function of the cracked plate are calculated and evaluated with the finite element results. The stress function of large deflection thin plate is obtained by using this equationions 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.

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