Structural Engineering and Mechanics

  • 제72권3호
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  • Pages.329-338
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  • 2019
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Modeling wave propagation in graphene sheets influenced by magnetic field via a refined trigonometric two-variable plate theory

  • Fardshad, R. Ebrahimi (Department of Mechanical Engineering, Faculty of Industrial and Mechanical Engineering, Islamic Azad University) ;
  • Mohammadi, Y. (Department of Mechanical Engineering, Faculty of Industrial and Mechanical Engineering, Islamic Azad University) ;
  • Ebrahimi, F. (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2018.08.18
  • 심사 : 2019.06.04
  • 발행 : 2019.11.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the magnetic field influence on the wave propagation characteristics of graphene nanosheets is examined within the frame work of a two-variable plate theory. The small-scale effect is taken into consideration based on the nonlocal strain gradient theory. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. A derivation of the differential equation is conducted, employing extended principle of Hamilton and solved my means of analytical solution. A refined trigonometric two-variable plate theory is employed in Kinematic relations. The scattering relation of wave propagation in solid bodies which captures the relation of wave number and the resultant frequency is also investigated. According to the numerical results, it is revealed that the proposed modeling can provide accurate wave dispersion results of the graphene nanosheets as compared to some cases in the literature. It is shown that the wave dispersion characteristics of graphene sheets are influenced by magnetic field, elastic foundation and nonlocal parameters. Numerical results are presented to serve as benchmarks for future analyses of graphene nanosheets.

키워드

참고문헌

  1. Arash, B., Wang, Q. and Liew, K.M. (2012), "Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation", Comput. Methods Appl. Mech. Eng., 223-224, 1-9. https://doi.org/10.1016/j.cma.2012.02.002.
  2. Aydogdu, M. (2009), "A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration", Physica E, 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014.
  3. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38, 265-275. https://doi.org/10.1007/s40430-015-0354-0.
  4. Ebrahimi, F. and Barati, M.R. (2018), "Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium", Proceedings of the Institution of Mech. Eng., Part C: J. Mech. Eng. Sci., 232(11), 2067-2078. https://doi.org/10.1177/0954406217713518
  5. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016a), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", J. Eng. Sci.,107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008.
  6. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stresses,40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483.
  7. Ebrahimi, F. and Salari, E. (2015), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES: Comput. Model. Eng. Sci, 105(2), 151-181.
  8. Ebrahimi, F. and Barati, M.R. (2017), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intelligent Mater. Syst. Struct., 28(11), 1472-1490. https://doi.org/10.1177/1045389X16672569.
  9. Ebrahimi, F. and Dabbagh, A. (2017c), "Nonlocal strain gradient based wave dispersion behavior of smart rotating magneto-electro-elastic nanoplates", Mater. Res. Exp., 4(2), 025003. https://doi.org/10.1088/2053-1591/aa55b5.
  10. Eltaher, M., Alshorbagy, A.E. and Mahmoud, F. (2013), "Vibration analysis of euler-bernoulli nanobeams by using finite element method", Appl Math. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016.
  11. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", J. Eng. Sci.,10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X.
  12. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys.,54(9), 4703-4710. https://doi.org/10.1063/1.332803.
  13. Farajpour, A., Yazdi, M.H., Rastgoo, A. and Mohammadi, M. (2016), "A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment", Acta Mechanica, 227(7), 1849-1867. https://doi.org/10.1007/s00707-016-1605-6.
  14. Fleck, N. and Hutchinson, J. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solids,41(12), 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-N.
  15. Arani, A.G., Haghparast, E. and Zarei, H.B. (2016), "Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-pasternak foundation under longitudinal magnetic field", Physica B, 495, 35-49. https://doi.org/10.1016/j.physb.2016.04.039.
  16. Arani, A.G. and M. Jalaei (2016), "Nonlocal dynamic response of embedded single-layered graphene sheet via analytical approach", J. Eng. Math., 98(1), 129-144. https://doi.org/10.1007/s10665-015-9814-x.
  17. Hadji, L. (2017a), "Analysis of functionally graded plates using a sinusoidal shear deformation theory", Smart Struct. Syst., 19(4), 441-448. https://doi.org/10.12989/sss.2017.19.4.441.
  18. Hadji, L., Zouatnia, N. and Kassoul, A. (2017b), "Wave propagation in functionally graded beams using various higher-order shear deformation beams theories", Struct. Eng. Mech., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143.
  19. Hadji, L., Ait Amar Meziane, M., and Safa, A., (2018), "A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 66(6), 771-781. https://doi.org/10.12989/sem.2018.66.6.771.
  20. Khelifa, Z., Hadji, L., Hassaine Daouadji, T., and Bourada, M., (2018), "Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 67(2), 125-130. https://doi.org/10.12989/sem.2018.67.2.125.
  21. Lam, D. Yang, C.F., Chong, A., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids,51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  22. Lee, C., Wei, X., Kysar, J.W. and Hone, J. (2008), "Measurement of the elastic properties and intrinsic strength of monolayer graphene", Science, 321(5887), 385-388. https://doi.org/10.1126/science.1157996
  23. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", J. Eng. Sci.,97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013
  24. Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids,78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  25. Liu, H. and Yang, J.L. (2012), "Elastic wave propagation in a single-layered graphene sheet on two-parameter elastic foundation via nonlocal elasticity", Physica E, 44(7), 1236-1240. https://doi.org/10.1016/j.physe.2012.01.018.
  26. Malekzadeh, P., Setoodeh, A. and Beni, A. A. (2011), "Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates", Composite Structures, 93(7), 1631-1639. https://doi.org/10.1016/j.compstruct.2011.01.008.
  27. Murmu, T., McCarthy, M.A. and 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. https://doi.org/10.1016/j.compstruct.2012.09.005.
  28. Murmu, T. and Pradhan, S. (2009), "Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory", J. Appl. Phys., 105(6), https://doi.org/10.1063/1.3091292.
  29. Narendar S. and Gopalakrishnan, S. (2012a), "Study of terahertz wave propagation properties in nanoplates with surface and small-scale effects", J. Mech. Sci., 64(1), 221-231. https://doi.org/10.1016/j.ijmecsci.2012.06.012.
  30. Narendar S. and Gopalakrishnan, S. (2012b), "Temperature effects on wave propagation in nanoplates", Composites Part B, 43(3), 1275-1281. https://doi.org/10.1016/j.compositesb.2011.11.029.
  31. Natarajan S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci.,65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031.
  32. Larbi, L.O., Hadji, L., Meziane, M. A.A. and Adda Bedia, E.A. (2018), "An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory", Wind Struct., 27(4), 247-254. https://doi.org/10.12989/was.2018.27.4.247.
  33. Pradhan S. and T. Murmu (2010), "Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory", Physica E,42(5), 1293-1301. https://doi.org/10.1016/j.physe.2009.10.053.
  34. Pradhan, S.C. and Kumar, A. (2011), "Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method", Compos. Struct., 93(2), 774-779. https://doi.org/10.1016/j.compstruct.2010.08.004.
  35. Rouhi S. and Ansari, R. (2012), "Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets", Physica E, 44(4), 764-772. https://doi.org/10.1016/j.physe.2011.11.020.
  36. Seol J.H., Jo, I., Moore, A.L., Lindsay, L., Aitken, Z., Pettes, M., Li, X., Yao, Z., Huang, R., Broido, D., Mingo, N., Ruoff, R. and Shi, L. (2010), "Two-dimensional phonon transport in supported graphene", Science, 328(5975), 213-216. https://doi.org/10.1126/science.1184014.
  37. Wang, Q. and Varadan, V. (2007), "Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes", Smart Mater. Struct.,16(1), 178. https://doi.org/10.1088/0964-1726/16/1/022.
  38. Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010), "Scale effects on the longitudinal wave propagation in nanoplates", Physica E,42(5),1356-1360. ttps://doi.org/10.1016/j.physe.2009.11.036.
  39. Xiao, W., Li, L. and Wang, M. (2017), "Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory", Appl. Phys. A,123(6), 388. https://doi.org/10.1007/s00339-017-1007-1.
  40. Zouatnia, N., Hadji, L. and Kassoul, A. (2017), "An analytical solution for bending and vibration responses of functionally graded beams with porosities", Wind Struct., 25(4), 329-342. https://doi.org/10.12989/was.2017.25.4.329.
  41. Zenkour, A.M. (2016), "Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium", Physica E, 79, 87-97. https://doi.org/10.1016/j.physe.2015.12.003.

피인용 문헌

  1. Reflection of electro-magneto-thermoelastic plane waves in a rotating medium in context of three theories with two-temperature vol.78, pp.1, 2019, https://doi.org/10.12989/sem.2021.78.1.023