Modares Mechanical Engineering

Modares Mechanical Engineering

Vibration analysis of circular single layer graphene sheet under temperature changes in thermal environment

Authors
Seyyed Mohammad Miri 1
Hamid Reza Jashnani 2
1 Graduated master / Saze San'at Samar consultant engineering
2 Shahid Sattari Aeronautical University of Science and Technology
Abstract
Considering broad applications of sheets, specially circular sheets in the industry and the widespread use of nanotechnology to pass from limitations of each branches of science, particularly mechanics of materials and also importance of vibration (or buckling) due to temperature changes or thermal loads, in this thesis, development of relative relations of circular single layer nanographene sheets’ vibrations due to temperature changes, were studied. Nonlocal thin plate theory of Eringen is employed to investigate effects of thermal environment on the behavior of circular single-layer graphene sheet freely vibration containing a circular perforation of arbitrary size and location. In order to analytically solve the equation of motion, the separation of variables method in conjunction with the translational addition theorem for Bessel functions is used. The results of changing various geometric and physical parameters and different kinds of restrains and boundary conditions on the natural frequency of a single layer circular graphene sheet were examined and discussed. In some cases, thermal buckling phenomenon was observed.
Keywords
Graphene sheet
Nonlocal elasticity
thermal effects
translational addition theorem
eccentric perforation

Subjects

[1] C. Soldano, A. Mahmood, E. Dujardin, Production, properties and potential of graphene, Carbon, Vol. 48, pp. 2127–2150, 2010.
[2] R.Aghababaei, J.N. Reddy, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, journal of sound and vibration, Vol. 326, pp 277-289, 2009.
[3] T. Murmu, S.C.Pradhan; Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory, journal of applied physics, Vol. 105, 2009.
[4] M. Mohammadi et all, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, pp. 659-682, 2014.
[5] T.J. Prasanna Kumar et all, Thermal vibration analysis of monolayer graphene embedded in elastic medium based on nonlocal continuum mechanics, Composite Structures, Vol. 100, pp. 332–342, 2013.
[6] L. Shen, et all, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Computational Materials Science, Vol. 48, pp. 680–685, 2010
[7] S.A. Fazelzadeh, S. Pouresmaeeli, Thermo-mechanical vibration of double-orthotropic nanoplates surrounded by elastic medium, Journal of Thermal Stresses, Vol. 36, pp. 225–238, 2013.
[8] A. Zenkour, M. Sobhy, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E, Vol. 53, pp. 251-259, 2013.
[9] M. Sobhy, Levy-type solution for bending of single-layered graphene sheets in thermal environment using the two-variable plate theory, International Journal of Mechanical Sciences, Vol. 90, pp. 171–178, 2015.
[10] L. Wang, H. Hu, Thermal vibration of a rectangular single-layered graphene sheet with quantum effects, Journal of Applied Physics, Vol. 115, 2014.
[11] S.R. Asemi, A. Farajpour, Decoupling the nonlocal elasticity equations for thermo-mechanical vibration of circular graphene sheets including surface effects, Physica E, Vol. 60, pp. 80-90, 2014
[12] M. Fadaee, M.R. Ilkhani, Study on the effect of an eccentric hole on the vibrational behavior of a graphene sheet using an analytical approach, Acta Mechanica, Vol. 226, pp. 1-13, 2015.
[13] A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface wave, J. Appl. Phys Vol. 54, pp. 4703-4710, 1983.
[14] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge university press, 1995.
[15] Y.Y. Zhang, Q.X. Pei, Y.W. Mai, Y.T. Gu, Temperature and strain-rate dependent fracture strength of graphynes, Journal of Physics D: Applied Physics Vol. 47, 2014
[16] J.W. Jiang, J.S. Wang, B. Li, Young’s modulus of graphene: A molecular dynamics study, Physical review Vol. 80, 2009
[17] J.W. Jiang, B.S. Wang, J.S. Wang, H.S. Park, A review on the flexural mode of graphene: lattice dynamics, thermal conduction, thermal expansion, elasticity and nanomechanical resonance, Journal of Physics: Condensed Matter Vol. 27, 2015
[18] K.M. Liew, X.Q. He, S. Kitipornchai, Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix, Acta Materialia. Vol. 54, pp. 4229–4236, 2006.
Modares Mechanical Engineering
Volume 18, Issue 8
December 2018
Pages 133-141