A structural mechanics approach for the phonon dispersion analysis of graphene |
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| Institution: | 1. Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran;2. Department of Solid State Physics, Yerevan State University, Alex Manoogian 1, 0025 Yerevan, Armenia;1. Department of Physics, Middle East Technical University, 06800 Ankara, Turkey;2. Department of Physics, Muş Alparslan University, 49250 Muş, Turkey;1. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, 100081, PR China;2. School of Civil Engineering, The University of Queensland, St Lucia, Queensland, 4072, Australia;3. Université Bretagne Sud, IRDL (CNRS UMR 6027), Centre de Recherche, Rue de Saint Maudé, BP92116, 56321, Lorient Cedex, France;4. School of Mechanical and Mining Engineering, University of Queensland, St Lucia, Queensland 4067, Australia |
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| Abstract: | A molecular structural mechanics model for the numerical simulation of phonon dispersion relations of graphene is developed by relating the C-C bond molecular potential energy to the strain energy of the equivalent beam-truss space frame. With the stiffness matrix known and further based on the periodic structure characteristics, the Bloch theorem is introduced to develop the dispersion relation of graphene sheet. Being different from the existing structural mechanics model, interactions between the fourth-nearest neighbor atoms are further simulated with beam elements to compensate the reduced stretching stiffness, where as a result not only the dispersion relations in the low frequency field are accurately achieved, but results in the high frequency field are also reasonably obtained. This work is expected to provide new opportunities for the dynamic properties analysis of graphene and future application in the engineering sector. |
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| Keywords: | Graphene sheet Energy equivalence Beam-truss space frame Phonon dispersion relation Low-dimensional nanostructure |
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