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The Small Scale Effect on Nonlinear Vibration of Single Layer Graphene Sheets
Abstract:In the present article, nonlinear vibration analysis of single layer graphene sheets is presented and the effect of small length scale is investigated. Using the Hamilton's principle, the three coupled nonlinear equations of motion are obtained based on the von Karman geometrical model and Eringen theory of nonlocal continuum. The solutions of Free nonlinear vibration, based on a one term mode shape, are found for both simply supported and clamped graphene sheets. A complete analysis of graphene sheets with movable as well as immovable in-plane conditions is also carried out. The results obtained herein are compared with those available in the literature for classical isotropic rectangular plates and excellent agreement is seen. Also, the nonlinear effects are presented as functions of geometric properties and small scale parameter.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081215Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1951
 H. Chu, G. Herrmann, "Influence of large amplitudes on free flexural vibrations of rectangular elastic plates", Journal of Applied Mechanics, 23, 1956, pp. 532-540.
 N. Yamaki, "Influence of large amplitudes on flexural vibrations of elastic plates", ZAMM, 41, 1961, pp. 501-540.
 G. Singh, K. Raju, G.V. Rao, "Non-linear vibrations of simply supported rectangular cross-ply plates", Journal of Sound and Vibration, 142, 1990, pp. 213-226.
 A.Y.T. Leung, S.G. Mao, "A symplectic Galerkin method for non-linear vibration of beams and plates", Journal of Sound and Vibration, 183, 1995, pp. 475-491.
 M. Amabili, "Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments", Computers and Structures, 82, 2004, pp. 2587-2605.
 M. Haterbouch, R. Benamar, "Geometrically nonlinear free vibrations of simply supported isotropic thin circular plates", Journal of Sound and Vibration, 280, 2005, pp. 903-924.
 J. Woo, S.A. Meguid, L.S. Ong, "Nonlinear free vibration behavior of functionally graded plates", Journal of Sound and Vibration, 289, 2006, pp. 595-611
 M. Amabili, S. Farhadi, "Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates", Journal of Sound and Vibration, 320, 2009, pp. 649-667.
 C.W. Lima, L.H. He, "Size-dependent nonlinear response of thin elastic films with nano-scale thickness", International Journal of Mechanical Sciences, 46, 2004, pp. 1715-1726.
 S. Kitipornchai, X.Q. He, K.M. Liew, "Continuum model for the vibration of multilayered graphene sheets", Physical Review B, 72, 075443, 2005, 6 pages.
 Y.M. Fu, J.W. Hong, X.Q. Wang, "Analysis of nonlinear vibration for embedded carbon nanotubes", Journal of Sound and Vibration, 296, 2006, pp. 746-756
 S.C. Pradhan, J.K. Phadikar. "Nonlocal elasticity theory for vibration of nanoplates", Journal of Sound and Vibration, 325, 2009, pp. 206-223.
 L.L. Ke, Y. Xiang, J. Yang, S. Kitipornchai, "Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory", Computational Materials Science, 47, 2009, pp.409-417.
 Y.X. Dong, C.W. LIM, "Nonlinear vibrations of nano-beams accounting for nonlocal effect using a multiple scale method", Science in China Series E: Technological Sciences, 52, 2009, pp. 617-621.
 T. Murmu, S.C. Pradhan, "Thermo-mechanical vibration of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Computational Materials Science, 46, 2009, pp. 854-859.
 J. Yang, L.L. Ke, S. Kitipornchai, "Nonlinear free vibration of singlewalled carbon nanotubes using nonlocal Timoshenko beam theory", Physica E, 42, 2010, pp. 1727-1735.
 M.A. Hawwa, H.M. Al-Qahtani, "Nonlinear oscillations of a doublewalled carbon nanotube", Computational Materials Science, 48, 2010, pp. 140-143.
 C. Eringen, "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", Journal of Applied Physics, 54, 1983, pp. 4703-4710.
 I.S. Raju, G.V. Rao, K. Raju, "Effect of longitudinal or inplane deformation and inertia on the large amplitude flexural vibrations of slender beam and thin plates", Journal of Sound and Vibration, 49, 1976, pp. 415-422.
 A. Beléndez, D.I. Méndez, E. Fernandez, S. Marini, I. Pascual, "An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method", Physics Letters A, 373, 2009, pp. 2805-2809.
 J.J. Stoker, "Nonlinear vibrations in Mechanical and Electrical Systems", John Wiley & Sons, Inc., New York, 1950.