Abstract
In this study, an investigation of “the free vibrations of hollow circular plates’’ is reported. The study is based on elastic foundation and the results depicted are further extended to study the special case of “graphene sheets.’’ The first-order shear deformation theory is applied to study the elastic properties of the material. A hollow circular sheet is modeled and the vibrations are simulated with the aid of finite element method. The results obtained are in good agreement with the theoretical findings. After the validation, a model of graphene is presented. Graphene contains a layer of honeycomb carbon atoms. Inside a layer, each carbon atom C is attached to three other carbon atoms and produces a sheet of hexagonal array. A 25 nm × 25 nm graphene sheet is modeled and simulated using the validated technique, that is, via the first-order shear deformation theory. The key findings of this study are the vibrational frequencies and vibrational mode shapes.
Highlights
The importance of the graphene, which is a sheet of a single layer of carbon atoms, cannot be denied due to its novel applications, in the field of engineering and in the field of biology
Free vibrations of hollow circular plates based on elastic foundation are investigated and the results are extended to graphene sheets
The effect of the foundation elastic coefficient on the first three frequencies of the sheet with the specification given by numerical method is investigated by finite element method, the slopes of the analytical and numerical results were in close agreement (Figure 3)
Summary
The importance of the graphene, which is a sheet of a single layer (monolayer) of carbon atoms, cannot be denied due to its novel applications, in the field of engineering and in the field of biology. Keywords Graphene, vibrational behavior, first-order shear deformation theory, hollow circular plates Free vibrations of thick hollow circular plates based on elastic substrates are investigated. Yalcin et al.[5] presented a semi-analytic solution for vibrations of circular plates with free, simple, and clamped boundary conditions, using the differential transform method (DTM).
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