Abstract
In this paper, the propagation of elastic waves in a single-layered graphene sheet supported by an elastic medium is studied via the nonlocal continuum model. The graphene sheet is modeled as an isotropic plate which contains small scale effects. The elastic medium is treated as a two-parameter elastic foundation. The governing equations accounting for coupled longitudinal and vertically polarized shear waves are obtained and dispersion relations are given. The effects of small-scale and foundation stiffnesses on the phase velocities of the lowest-order two modes are presented. From the numerical results, it can be observed that the phase velocities decrease with increase of the scale coefficient. With including the small-scale effect, the phase velocities may escape and stop propagating above certain frequencies. Larger values of the scale coefficient cause lower escape frequencies. The results also reveal that the elastic foundation plays an important role in the phase velocities of the lowest-order two modes. The elastic foundation may lead to the occurrence of cut-off frequencies. The phase velocities increase as the foundation stiffnesses increase.
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