The effect of magnetic field on buckling and nonlinear vibrations of Graphene nanosheets based on nonlocal elasticity theory

International Journal of Nano Dimension

مقاله 4، دوره 13، شماره 1، فروردین 2022، صفحه 54-70   

نوع مقاله: Reasearch Paper

شناسه دیجیتال (DOI): 10.22034/ijnd.2022.683988

نویسندگان

Tayyeb Pourreza¹؛ Ali Alijani^{* 1}؛ Vahid Arab Maleki^{1، 2}؛ Admin Kazemi¹

¹Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran.

²Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran.

چکیده

In this paper, the buckling behavior and nonlinear vibrations of graphene nanosheets in the magnetic field are studied analytically. By considering mechanical and magnetic interactions, new relationships have been proposed for the forces exerted by the magnetic field. The nonlinear governing equation is derived using Kirchhoff's thin plate theory in conjunction with the nonlocal strain gradient theory of elasticity and von Karman's nonlinear strain-displacement relation. The nonlinear governing equation is discretized using the Galerkin method. According to the method of multiple scales, the approximate analytical solutions are extracted. For the three considered boundary conditions, nonlinear natural frequencies and amplitude-frequency curves are computed for different values ​​of magnetic field and nonlocal parameters. The results show that increasing the nonlocal parameter and applying a magnetic field reduces the flexural stiffness and increases the in-plate compressive force which results in reducing the natural frequency. In addition, excessive magnification of the magnetic field causes static buckling. The value of the critical magnetic field is highly dependent on the type of boundary conditions.

کلیدواژه‌ها

Buckling؛ Graphene Nanosheets؛ Magnetic Field؛ Natural Frequency؛ Nonlinear Vibrations

مراجع

[1] Nabavi M., Nazarpour V., Alibak A. H., Bagherzadeh A., Alizadeh S. M., (2021), Smart tracking of the influence of alumina nanoparticles on the thermal coefficient of nanosuspensions: Application of LS-SVM methodology. App. Nano. 34: 1-16.

[2] Kaabipour S., Hemmati S., (2021), A review on the green and sustainable synthesis of silver nanoparticles and one-dimensional silver nanostructures. Beilstein J. Nanotechnol. 12: 102-136.

[3] Seaberg J., Kaabipour S., Hemmati S., Ramsey J. D., (2020), A rapid millifluidic synthesis of tunable polymer-protein nanoparticles. Eur. J. Pharm. Biopharm. 154: 127-135.

[4] Biswas N., Sarkar U. K., Chamkha A. J.. Manna N. K., (2021), Magneto-hydrodynamic thermal convection of Cu–Al₂O₃/water hybrid nanofluid saturated with porous media subjected to half-sinusoidal nonuniform heating. J. Therm. Anal. Calorim.  143: 1727-1753.

[5] Biswas N., Manna N. K., Chamkha A. J., (2021), Effects of half-sinusoidal nonuniform heating during MHD thermal convection in Cu–Al₂O₃/water hybrid nanofluid saturated with porous media. J. Therm. Anal. Calorim. 143: 1665-1688.

[6] Farzaneh A., Mohammadi M., Ahmad Z., Ahmad I., (2013), Aluminium alloys in solar power− Benefits and Limitations.Chapter 13.

[7] Farzaneh A., Esrafili M. D., Mermer Ö., (2020), Development of TiO₂ nanofibers based semiconducting humidity sensor: Adsorption kinetics and DFT computations. Mater. Chem. Phys. 239: 56-78.

[8] Farzaneh A., Mohammadzadeh A., Esrafili M.D., Mermer O., (2019), Experimental and theoretical study of TiO₂ based nanostructured semiconducting humidity sensor. Ceram. Int. 45: 8362-8369.

[9] Biswas N., Manna N. K., Datta P., Mahapatra P. S., (2018), Analysis of heat transfer and pumping power for bottom-heated porous cavity saturated with Cu-water nanofluid. Powder Technol. 326: 356-369.

[10] Nabavi M., Elveny M., Danshina S. D., Behroyan I., Babanezhad M., (2021), Velocity prediction of Cu/water nanofluid convective flow in a circular tube: Learning CFD data by differential evolution algorithm based fuzzy inference system (DEFIS). Int. Commun. Heat Mass Transf. 126: 34-56.

[11] Esmaeili J., Andalibi H., (2013), Investigation of the effects of nano-silica on the properties of concrete in comparison with micro-silica. Int. J. Nano Dimens. 3: 321-328.

[12] Pashaki V., Milad Pouya P., Maleki V. A., (2018), High-speed cryogenic machining of the carbon nanotube reinforced nanocomposites: Finite element analysis and simulation. Proc. Inst. Mech. Eng. Mechan. 232: 1927-1936.

[13] Rezaee M., Maleki V. A., (2015), An analytical solution for vibration analysis of carbon nanotube conveying viscose fluid embedded in visco-elastic medium. Proc. Inst. Mech. Eng. Pt. Mechan. 229: 644-650.

[14] Mondal M. K., Biswas N., Manna N. K., (2019), MHD convection in a partially driven cavity with corner heating. SN App. Sci. 1: 1-19.

[15] Manna N. K., Mondal M. K., Biswas N., (2021), A novel multi-banding application of magnetic field to convective transport system filled with porous medium and hybrid nanofluid. Phy. Scripta. 96: 56-78.

[16] Manna N. K., Biswas N., (2021), Magnetic force vectors as a new visualization tool for magnetohydrodynamic convection. Int. J. Therm. Sci. 167: 45-67.

[17] Ajri M., Rastgoo A., Fakhrabadi M. M. S., (2019), Non-stationary vibration and super-harmonic resonances of nonlinear viscoelastic nano-resonators. Struc. Eng. Mech. 70: 623–637.

[18] Tourki S. A., Hosseini Hashemi S., (2012), Buckling analysis of graphene nanosheets based on nonlocal elasticity theory. Int. J. Nano Dimens. 2: 227-232.

[19] Kaabipour S., Hemmati S., (2021), A review on the green and sustainable synthesis of silver nanoparticles and one-dimensional silver nanostructures. Beilstein J. Nanotechnol. 12: 102-136.

[20] Gao K., Gao W., Chen D., Yang J., (2018), Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation. Comp. Struct. 204: 831–846.

[21] Beitollai H., Safaei M., Tajik S., (2019), Application of Graphene and Graphene Oxide for modification of electrochemical sensors and biosensors: A review. Int. J. Nano Dimens. 10: 125-140.

 [22] Aghababaei R., Reddy J. N., (2009), Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. J. Sound. Vib. 326: 277–289.

[23] Murmu T., Pradhan S. C., (2009), Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory. J. Appl. Phy. 105: 23-45.

[24] Ebrahimi F., Barati M. R., (2018), Vibration analysis of graphene sheets resting on the orthotropic elastic medium subjected to hygro-thermal and in-plane magnetic fields based on the nonlocal strain gradient theory. Proc. Inst. Mech. Eng. Mech. 232: 2469–2481.

[25] Jalaei M. H., Ghorbanpour-Arani A., (2018), Size-dependent static and dynamic responses of embedded double-layered graphene sheets under longitudinal magnetic field with arbitrary boundary conditions. Comp. B. Eng. 142: 117–130.

[26] 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. Compos. Struct. 96: 57–63.

[27] Biglari A. E. H., (2017), Transverse vibration of single-layer graphene sheet under 2D magnetic field action by differential quadrature method. Aerosp. Knwl. Sci. Technol. J. 6: 81–92.

[28] Farajpour A., Mohammadi M., Shahidi A. R., Mahzoon M., (2011), Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model. Phys. E. Low Dimens. Syst. Nanostruct. 43: 1820–1825.

[29] Samaei A. T., Abbasion S., Mirsayar M. M., (2011), Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory. Mech. Res. Commun. 38: 481–485.

[30] Pradhan S. C., (2009), Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys. Lett. A. 373: 4182–4188.

[31]  Allahyari E., Asgari M., Jafari A. A., (2020), Nonlinear size-dependent vibration behavior of graphene nanoplate considering surfaces effects using a multiple-scale technique. Mech. Adv. Mat. Struc. 27: 697-706.

[32] Rong D., Fan J., Lim C. W., Xu X., Zhou Z., (2018), A new analytical approach for free vibration, buckling and forced vibration of rectangular nanoplates based on nonlocal elasticity theory. Int. J. Struct. Stab. Dyn. 18: 1850055.

[33] Saadatmand M., Shahabodini A., Ahmadi B., Chegini S. N., (2021), Nonlinear forced vibrations of initially curved rectangular single layer graphene sheets: An analytical approach. Phys. E: Low-Dimens. Syst. Nanostruc. 127: 34-56.

[34] Mortazavi B., Cuniberti G., Rabczuk T., (2015), Mechanical properties and thermal conductivity of graphitic carbon nitride: A molecular dynamics study. Comput. Mater. Sci. 99: 285–289.

[35] Huang J., Ma Z., Wu Z., Peng L., Su B., (2021), Magnetic sensitive Crack sensor with ultrahigh sensitivity at room temperature by depositing graphene nanosheets upon a flexible magnetic film. Adv. Elec. Mate. 34: 56-67.

[36] Dhakal U., Rai D., (2019), Magnetic field control of current through model graphene nanosheets. Phy. Lett. A. 383: 2193-2200.

[37] Terdalkar S. S., Huang S., Yuan H., Rencis J. J., Zhu T., Zhang S., (2010), Nanoscale fracture in graphene. Chem. Phys. Lett. 494: 218–222.

[38] Ismail R., Cartmell M. P., (2012), An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation. J. Sound. Vib. 331: 2929–2948.

[39] Joshi P. V., Jain N. K., Ramtekkar G. D., (2015), Analytical modelling for vibration analysis of partially cracked orthotropic rectangular plates. Eur. J. Mech. A-Solids. 50: 100–111. 

[40] Israr A., Cartmell M. P., Manoach E., Trendafilova I., Ostachowicz W., Krawczuk  M., Zak A., (2009), Analytical modeling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading. J. Appl. Mech. 76: 45-67.

[41] Pourreza T., Alijani A., Maleki V. A., Kazemi A., (2021), Nonlinear vibration of nanosheets subjected to electromagnetic fields and electrical current. Techno-Press. 10: 481–491.

[42] Ajri M., Rastgoo A.,  Fakhrabadi, M. M. S., (2020), How does flexoelectricity affect static bending and nonlinear dynamic response of nanoscale lipid bilayers?Phys. Scr. 95: 025001.

[43] Ghaderi M., Ghaffarzadeh H., A Maleki V., (2015), Investigation of the stability and vibration of cracked columns under compressive axial Load.J. Ferdowsi. Civ. Eng.26: 21-23.

[44] Jahanghiry R., Yahyazadeh R., Sharafkhani N., Maleki V. A., (2016), Stability analysis of FGM microgripper subjected to nonlinear electrostatic and temperature variation loadings. Sci. Eng. Compos. Mater. 23: 199–207.

[45] Leissa  A. W., (1969), Tabulated numerical results of theories of plate vibration. Vibration of plates . NASA SP. (patent No160).

[46] Nayfeh A. H., Mook  D. T.,  Holmes P., (1980), Nonlinear oscillations. J. Appl. Mech. 47: 692-693.

[47] Cao G., (2014), Atomistic studies of mechanical properties of Graphene. Polymers. 6: 2404-2432.

[48] Mousavi H., Bagheri M., Khodadadi J., (2015), Magnetic susceptibility and heat capacity of graphene in two-band Harrison model. Phys. E. Low Dimens. Syst. Nanostruct. 74: 135–139.

[49] Wang Y., Li F. M., Wang  Y. Z., (2015), Nonlinear vibration of double layered viscoelastic nanoplates based on nonlocal theory. Phys. E. Low Dimens. Syst. Nanostruct. 67: 65–76.

[50] Pradhan S. C., Phadikar J. K., (2009), Nonlocal elasticity theory for vibration of nanoplates. J. Sound. Vib. 325: 206–223.

[51] Kitipornchai S., He X. Q., Liew K. M., (2005), Continuum model for the vibration of multilayered graphene sheets. Phys. Rev. B. 72: 075443.