The effect of length scale on the vibration response of a single-layer graphene sheet
embedded in an elastic medium is studied using nonlocal Mindlin plate theory. The elastic
medium is modeled using both Winkler-type and Pasternak-type elastic foundations.
An explicit solution is derived for the natural frequencies of the graphene sheet. Through the
analytical solution it is found that the vibration response of graphene sheet concerning the
length scale effects considerably different from the results obtained by the classical theories.
In comparison with the classical plate theory, the nonlocal model showed that the natural
frequency of the graphene sheet decreases for smaller lengths of graphene sheet, higher aspect
ratios, greater values of nonlocal parameter and stiffer elastic foundations.
Keywords: graphene sheets; frequency; nonlocal elasticity; elastic medium
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