**Free vibration of single-layered MoS2 suspended over a circular hole**

JN Jiang and LF Wang and YQ Zhang, JOURNAL OF APPLIED PHYSICS, 126, 135106 (2019).

DOI: 10.1063/1.5110758

The vibrational behaviors of circular single-layered molybdenum disulfide (CSLMoS2) suspended over a concentric circular hole are investigated using a two-segment circular Kirchhoff plate (TSCKP) corresponding to different initial stresses and molecular dynamics (MD) simulations. An analytical solution is proposed to analyze the free vibrations of the TSCKP model. van der Waals (vdW) interaction coefficient between the single-layered MoS2 (SLMoS2) and the silicon substrate is derived theoretically. MD simulations show that the TSCKP model can give a good prediction to the vibrational behaviors of the CSLMoS2 suspended over a concentric circular hole. The effects of the overlapped width and radial initial stresses on the vibrational behaviors of the CSLMoS(2)s are investigated. The natural frequencies of the TSCKP model become much closer to those of a one-segment circular Kirchhoff plate with the clamped supported boundary (OSCKP-CC) as the radius of the inner-segment circular plate increases; however, the value predicted by the TSCKP model is always smaller than that predicted by the OSCKP-CC. The TSCKP model can also give a reasonable prediction to the vibrational behaviors of the square SLMoS2 suspended over a concentric circular hole when the overlapped widths between the circular and square SLMoS(2)s and elastic substrate along any radial direction are sufficiently large. Published under license by AIP Publishing.

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