2D-Magnetic Field and Biaxiall In-Plane Pre-Load Effects on the Vibration of Double Bonded Orthotropic Graphene Sheets

Document Type: Research Paper

Authors

1 Faculty of Mechanical Engineering, University of Kashan, Kashan

2 Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan

3 Faculty of Mechanical Engineering, University of Kashan

Abstract

In this study, thermo-nonlocal vibration of double bonded graphene sheet (DBGS) subjected to 2D-magnetic field under biaxial in-plane pre-load are presented. The elastic forces between layers of graphene sheet (GS) are taken into account by Pasternak foundation and the classical plate theory (CLPT) and continuum orthotropic elastic plate are used. The nonlocal theory of Eringen and Maxwell’s relations are employed to incorporate the small-scale effect and magnetic field effects, respectively, into the governing equations of the GSs. The differential quadrature method (DQM) is used to solve the governing differential equations for simply supported edges. The detailed parametric study is conducted, focusing on the remarkable effects of the angle and magnitude of magnetic field, different type of loading condition for couple system, tensile and compressive in-plane pre-load, aspect ratio and nonlocal parameter on the vibration behavior of the GSs. The result of this study can be useful to design of micro electro mechanical systems and nano electro mechanical systems.

Keywords


[1] Pradhan S.C., Kumar A., 2010, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Materials Science 50: 239-245.

[2] Murmu T., Adhikari S., 2011, Axial instability of double-nanobeam-systems, Physics Letters A 375: 601-608.

[3] Murmu T., Adhikari S., 2011, Nonlocal vibration of bonded double-nanoplate-systems, Composites: Part B 42: 1901-1911.

[4] Singh J.P., Dey S.S., 1990, Transverse vibration of rectangular plates subjected to inplane forses by a difference based vibrational approach, International Journal of Mechanical Sciences 32: 591-599.

[5] Zhang Y., Liu G., Han X., 2005, Transverse vibrations of double-walled carbon nanotubes under compressive axial load, Physics Letters A 340: 258-266.

[6] Mustapha K.B., Zhong Z.W., 2010, Free transverse vibration of an axially loaded non-prismatic single-walled carbon nanotube embedded in a two-parameter elastic medium, Computational Materials Science 50: 742-751.

[7] Karami Khorramabadi M., 2009, Free vibration of functionally graded beams with piezoelectric layers subjected to axial load, Journal of Solid Mechanics 1: 22-28.

[8] Murmu T., Pradhan S.C., 2009, Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity, Journal of Applied Physics 106: 104301.

[9] Kiani K., 2012, 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 68: 16-34.

[10] Ajiki H., Ando T., 1993, Electronic states of carbon nanotubes, Journal of Physical Society of Japan 62: 1255-1266.

[11] Ajiki H., Ando T., 1994, Aharonov-bohm effect in carbon nanotubes, Physica B 201: 252-349.

[12] Ajiki H., Ando T., 1996, Energy bands of carbon nanotubes in magnetic fields, Journal of Physical Society of Japan 65: 505-514.

[13] Saito R., Dresselhaus G., Dresselhaus M.S., 1998, Physical Properties of Carbon Nanotubes, Imperial College Press, London.

[14] O´connell M.J., 2006, Carbon Nanotubes: Properties and Applications, CRC Press, Boca Raton.

[15] Ghorbanpour Arani A., Amir S., 2011, Magneto-thermo-elastic stresses and perturbation of magnetic field vector in a thin functionally graded rotating disk, Journal of Solid Mechanics 3: 392-407.

[16] Lu H., Gou J., Leng J., Du S., 2011, Magnetically aligned carbon nanotube in nanopaper enabled shape-memory nanocomposite for high speed electrical actuation, Applied Physics Letters 98: 174105.

[17] Camponeschi E., Vance R., Al-Haik M., Garmestani H., Tannenbaum R., 2007, Properties of carbon nanotube–polymer composites aligned in a magnetic field, Carbon 45: 2037-2046.

[18] Bubke K., Gnewuch H., Hempstead M., Hammer J., Green M.L.H., 1997, Optical anisotropy of dispersed carbon nanotubes induced by an electric field, Applied Physics Letters 71: 1906-1908.

[19] Liu T X., Spencer J.L., Kaiser A.B., Arnold W.M., 2004, Electric-field oriented carbon nanotubes in different dielectric solvents, Current Applied Physics 4: 125-128.

[20] Kiani K., 2012, Transverse wave propagation in elastically confined single-walled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models, Physica E 45: 86-96.

[21] Murmu T., McCarthy M.A., Adhikari S., 2013, In-plane magnetic field affected transverse vibration of embedded single-layer graphene sheets using equivalent nonlocal elasticity approach, Composite Structures 96: 57-63.

[22] Timoshenko S., Woinowsky-Krieger S., 1959, Theory of Plates and Shells, Second edition, MCGRAW-HILL, London.

[23] Eringen A.C. 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703-4710.

[24] John, K.D., 1984, Electromagnetics, McGraw-Hil1, Moscow.

[25] Reddy J.N., 1997, Mechanics of Laminated Composite Plates, Theory and Analysis, Chemical Rubber Company, Boca Raton, FL.

[26] Sherbourne A.N., Pandey M.D., 1991, Differential quadrature method in the buckling analysis of beams and composite plates, Computers and Structures 40: 903-913.

[27] Bert C.W., Malik M., 1996, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews 49: 1-28.

[28] Chen W., Shu C., He W., Zhong T., 2000, The applications of special matrix products to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates, Computers and Structures 74: 65-76.

[29] Lancaster P., Timenetsky M., 1985, The Theory of Matrices with Applications, second edition, Academic Press Orlando.

[30] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Mozdianfard M.R., Node S.M., 2013, Elastic foundation effect on nonlinear thermo-vibration of embedded double layered orthotropic graphene sheets using differential quadrature method, Journal of Mechanical Engineering Science: Part C 227:862-879.