Fracture mechanics and vibration analysis of graphene-modified auxetic functionally graded beams

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (24) : 100-107.

HE Yunxiang，SONG Mitao

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Abstract

To explore the influence of structural damage on the dynamic behavior of folded graphene-modified materials, this study employed finite element methods to calculate the stress intensity factor at the crack tip of Graphene Origami (GOri) enabled gradient beams with a negative Poisson's ratio function. Combining the rotational spring model with the first-order shear deformation theory, the free vibration equation of the beam was derived using the Ritz method and Hamilton's principle, and the natural frequencies of the beam were solved. The results indicate that, due to its gradient distribution, the folded degree of graphene origami affects the stress intensity factor at the crack tip, which correlates with the crack length. Moreover, when GOris are distributed closer to the surface of the beam, the natural frequency of the beam increases. The natural frequency of the beam also increases with the increase of GOri mass fraction. For instance, with a hydrogen coverage rate of 20% for GOri, increasing GOri by only 0.15% can lead to a 3.9% increase in the natural frequency of the beam. However, as the folded degree of GOri increases, the natural frequency of the beam decreases. Further research reveals that changing the folded degree, distribution gradient, and concentration of GOri to enhance the stiffness of the beam also makes the beam more sensitive to the crack in its vibration behavior.

Key words

Graphene Origami / Functionally Graded Beam / Negative Poisson's Ratio / Crack / Natural Frequency

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HE Yunxiang, SONG Mitao. Fracture mechanics and vibration analysis of graphene-modified auxetic functionally graded beams[J]. Journal of Vibration and Shock, 2024, 43(24): 100-107

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