Nonlinear Dynamic Behaviour of a Rectangular Thin Plate with a Bifurcation Diagram

Karim, Sohayb Abdul

doi:10.1007/978-3-319-79005-3_19

Engineering Design Applications

2018

DOI: 10.1007/978-3-319-79005-3_19

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Nonlinear Dynamic Behaviour of a Rectangular Thin Plate with a Bifurcation Diagram

Sohayb Abdul Karim

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2019

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Experimental Investigation of Nonlinear Vibration of a Thin Rectangular Plate

Abdulkerim

Dafnis

Riemerdes

2019

Int. J. Appl. Mechanics

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In this paper, the geometrical nonlinear vibrations of a rectangular plate have been investigated experimentally and numerically. The experiment was conducted on a thin rectangular plate. The plate was excited close to the first fundamental natural frequency. The time history of velocities of the central point has been measured by using a laser vibrometer. While the numerical investigation has been carried using the Finite Element Method (FEM), the numerical results are validated by analytical and experimental results. In order to develop and test the extraction procedure of the bifurcation plot of a dynamical system, a chaotic pendulum has been analyzed. Then, the same successful code has been used again for the experimental dynamics of the investigated plate. The plate has been forced with a sinusoidal input at a gradually stepped and increased amplitude. For every step, the phase portrait is determined, and then processed to extract the bifurcation map. The resulted map has shown successfully the linear range where the classical plate theory is adequate, and the boundary at which the transition to nonlinearity has occurred. The bifurcation has occurred when the lateral amplitude has reached 50% of the plate thickness.

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Experimental Investigation of Nonlinear Vibration of a Thin Rectangular Plate

Abdulkerim

Dafnis

Riemerdes

2019

Int. J. Appl. Mechanics

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Nonlinear Dynamic Behaviour of a Rectangular Thin Plate with a Bifurcation Diagram

Cited by 1 publication

References 21 publications

Experimental Investigation of Nonlinear Vibration of a Thin Rectangular Plate

Experimental Investigation of Nonlinear Vibration of a Thin Rectangular Plate

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