عنوان مقاله [English]
نویسندگان [English]چکیده [English]
In this paper, governing equations of transverse vibration of single-layer graphene sheet with different boundary conditions under 2D in-plane magnetic field action, considering its consequent forces and moments, are investigated for the first time using differential quadrature method (DQM). Governing equations of motion are obtained using non-local theory and considering Lorentz's force. The partial differential equations of system are changed to the ordinary differential equations using separation of variables method. Using differential quadrature method, the obtained governing equations are solved for different boundary conditions. The effects of elastic foundation stiffness, non-local parameter, plate aspect ratio and 2D magnetic field effects on the natural frequency of graphene sheet are evaluated. The results show that increase of foundation stiffness, non-local parameter and aspect ratio result in increase of fundamental frequency, in all boundary conditions. But, action of in-plane magnetic field results in decrease of fundamental frequency, because of decreasing flexural stiffness and increasing in-plane pressure loading.
 T. Monetta, A. Acquesta, F. Bellucci, Graphene/Epoxy coating as multifunctional material for aircraft structures, Aerospace, Vol. 2, pp. 423-434, 2015.
 S. Bellucci, J. Gonzalez, F. Guinea, P. Onorato, E. Perfetto, Magnetic field effects in carbon nanotubes, Journal of Physics: Condens Matter. Vol. 19, No. 39, 2007.
 S. Li, H. Xie, X. Wang, Dynamic characteristics of multi-walled carbon nanotubes under a transverse magnetic field, Bulletin of Materials Science, Vol. 34, pp. 45–52, 2011.
 M. Kibalchenko, M. Payne, J. Yates, Magnetic response of single-walled carbon nanotubes induced by an external magnetic field, American chemical society Nano, Vol. 5, No. 1, pp. 537-545, 2011.
 Z. Fu, Z. Wang, S. Li, P. Zhang, Magnetic quantum oscillations in a monolayer graphene under a perpendicular magnetic field, Chinese Physics B, Vol. 20, No. 5, 2011.
 F. Lopez-Urias, J. Rodriguez-Manzo, E. Munoz-Sandoval, M. Terrones, H. Terrones, Magnetic response in finite carbon graphene sheets and nanotubes, Optical Materials, Vol. 29, No. 1, pp. 110-115, 2006.
 K. Shizuya, Electromagnetic response and effective gauge theory of graphene in a magnetic field, Physical Review B, Vol. 75 , 2007.
 Y. Wang, Y. Huang, Y. Song, X. Zhang, Y. Ma, J. Liang, Room-temperature ferromagnetism of graphene, Nano Letters, Vol. 9, No. 1, pp. 220-224, 2009.
 T. Murmu, S. Adhikari, Axial instability of double-nano bea-systems, Physics Letters A, Vol. 375, pp. 601-608, 2011.
 T. Murmu, S. Adhikari, Nonlocal vibration of bonded double-nanoplate-systems, Composites: Part B, Vol. 42, pp. 1901- 1911, 2011.
 T. Murmu, S. C. Pradhan, Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity, Journal of Applied Physics, Vol. 106, 2009.
 K. Kiani, Vibration analysis of elastically restrained double-walled carbon nanotubes on elastic foundation subjected to axial load using nonlocal shear deformable beam theories, International Journal of Mechanical Sciences, Vol. 68, pp. 16-34, 2012.
 H. Ajiki, T. Ando, Energy bands of carbon nanotubes in magnetic fields, Journal of Physical Society of Japan, Vol. 65, pp. 505-514, 1996.
 R. Saito, G. Dresselhaus, M. S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998.
 A. Ghorbanpour Arani, S. Amir, Magneto-thermo-elastic stresses and perturbation of magnetic field vector in a thin functionally graded rotating disk, Journal of Solid Mechanics, Vol. 3, No. 4, pp. 392-407, 2011.
 K. Kiani, Transverse wave propagation in elastically confined single-walled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models, Physica E, Vol. 45, pp. 86-96, 2012.
 T. Murmu, M. A. McCarthy, S. Adhikari, In-plane magnetic field affected transverse vibration of embedded single-layer graphene sheets using equivalent nonlocal elasticity approach, Composite Structures, Vol. 96, pp. 57-63, 2013.
 K. Kiani, Free vibration of conducting nanoplates exposed to unidirectional in-plane magnetic fields using nonlocal shear deformable plate theories, Physica E, Vol. 57, pp. 179-192, 2014.
 K. Kiani, Revisiting the free transverse vibration of embedded single-layer graphene sheets acted upon by an in-plane magnetic field, Journal of mechanical science and Technology, Vol. 28, No. 9, pp. 3511-3516, 2014.
 T. Murmu, S. Adhikari, M. A. McCarthy, Axial vibration of embedded nanorods under transverse magnetic field effects via nonlocal elastic continuum theory, Journal of Computational and Theoretical Nanoscience, Vol. 11, No. 5, pp. 1230–1236, 2014.
 P. Malekzadeh, A. R. Setoodeh, A. Alibeygi Beni, Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates, Composite Structures, Vol. 93, pp. 1631-1639, 2011.
 A. Eringen, On differential-equations of nonlocal elasticity and solutions of screw dislocation and surface-waves, Journal of Applied Physics, Vol. 54, pp. 4703, 1983.
 S. Narendar, S. Gopalakrishnan, Spectral finite element formulation for nanorods via nonlocal continuum mechanics, Journal of Applied Mechanics-Trans ASME, Vol. 78, No. 6, 2011.
 S. C. Pradhan, A. Kumar, Vibration analysis of ortho-tropic graphene sheets using nonlocal elasticity theory and differential quadrature method, Composite Structures, Vol. 93, No. 2, pp. 774-779, 2011.
 S. Rajasekaran, Structural Dynamics of Earthquake Engineering, Woodhead Publishing Series in Civil and Structural Engineering, 2009.
 Chang Shu, Differential Quadrature and its Application in Engineering, Springer Verlag London Berlin Heidelberg, 1999.
 R. Kolahchi, H. Hosseini, M. Esmailpour, Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories, Composite Structures, Vol. 157, pp. 174-186, 2016.
 R. Ansari, M. Faghih Shojaei, A. Shahabodini, M. Bazdid-Vahdati, Three-dimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach, Composite Structures, Vol. 131, pp. 753-764, 2015.
 S. C. Pradhan, R. Raj, Vibration analysis of nanoplate with various boundary conditions using DQ method, Journal of Computational and Theoretical Nanoscience, Vol. 8, No. 8, pp. 1432-1436, 2011.
 M. Ghadiri, N. Shafiei, H. Alavi, Thermo-mechanical vibration of orthotropic cantilever and propped cantilever nanoplate using generalized differential quadrature method, Mechanics of Advanced Materials and Structures, 2016.