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This paper presents a study on the natural vibration of circular double-layer graphene sheets (DLGSs) using circular plate theory. The circular DLGSs are assumed to be coupled together through the carbon–carbon van der Waals (vdW) force between their two layers. An analytical solution of coupled governing equations is proposed to predict the natural frequencies of circular DLGSs. The vibration behaviors in circular DLGSs are found to have an in-phase mode (IPM) associated with the classical natural frequency, and an anti-phase mode (APM) owing to the influence of the vdW interaction. The natural frequencies of the IPM are independent of vdW interactions between adjacent layers, while those of the APM depend on the vdW interaction, and are larger. Based on the exact solution, the influences of wavenumbers (m, n) on the natural frequencies of simply supported circular DLGSs are also investigated in detail.
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Natsuki et al. (2012) studied this question.
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