Structural Engineering and Mechanics

  • 제61권1호
  • /
  • Pages.65-76
  • /
  • 2017
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

In-plane and out-of-plane waves in nanoplates immersed in bidirectional magnetic fields

  • Kiani, Keivan (Department of Civil Engineering, K.N. Toosi University of Technology) ;
  • Gharebaghi, Saeed Asil (Department of Civil Engineering, K.N. Toosi University of Technology) ;
  • Mehri, Bahman (Department of Mathematical Sciences, Sharif University of Technology)
  • 투고 : 2016.04.04
  • 심사 : 2016.09.07
  • 발행 : 2017.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

Prediction of the characteristics of both in-plane and out-of-plane elastic waves within conducting nanoplates in the presence of bidirectionally in-plane magnetic fields is of interest. Using Lorentz's formulas and nonlocal continuum theory of Eringen, the nonlocal elastic version of the equations of motion is obtained. The frequencies as well as the corresponding phase and group velocities pertinent to the in-plane and out-of-plane waves are analytically evaluated. The roles of the strength of in-plane magnetic field, wavenumber, wave direction, nanoplate's thickness, and small-scale parameter on characteristics of waves are discussed. The obtained results show that the in-plane frequencies commonly grow with the in-plane magnetic field. However, the transmissibility of the out-of-plane waves rigorously depends on the magnetic field strength, direction of the propagated transverse waves, small-scale parameter, and thickness of the nanoplate. The criterion for safe transferring of the out-of-plane waves through the conducting nanoplate immersed in a bidirectional magnetic field is also explained and discussed.

키워드

참고문헌

  1. Aifantis, E.C. (1992), "On the role of gradients in the localization of deformation and fracture", Int. J. Eng. Sci., 30, 1279-1299. https://doi.org/10.1016/0020-7225(92)90141-3
  2. Abouzar, M.H., Poghossian, A., Pedraza, A.M., Gandhi, D., Ingebrandt, S., Moritz, W. and Schoning, M.J. (2011), "An array of field-effect nanoplate SOI capacitors for (bio-)chemical sensing", Biosens. Bioelectron., 26, 3023-3028. https://doi.org/10.1016/j.bios.2010.12.006
  3. Aksencer, T. and Aydogdu, M. (2012), "Forced transverse vibration of nanoplates using nonlocal elasticity", Phys. E, 44, 1752-1759. https://doi.org/10.1016/j.physe.2011.12.004
  4. Ansari, R., Arash, B. and Rouhi, H. (2011), "Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity", Compos. Struct., 93, 2419-2429. https://doi.org/10.1016/j.compstruct.2011.04.006
  5. Ansari, R. and Gholami, R. (2016), "Size-dependent nonlinear vibrations of first-order shear deformable magneto-electrothermo elastic nanoplates based on the nonlocal elasticity theory", Int. J. Appl. Mech., 8, 1650053. https://doi.org/10.1142/S1758825116500538
  6. Ansari, R., Rajabiehfard, R. and Arash, B. (2010), "Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets", Comput. Mater. Sci., 49, 831-838. https://doi.org/10.1016/j.commatsci.2010.06.032
  7. Ansari, R., Sahmani, S. and Arash, B. (2010), "Nonlocal plate model for free vibrations of single-layered graphene sheets", Phys. Lett. A, 375, 53-62. https://doi.org/10.1016/j.physleta.2010.10.028
  8. Ansari, R., Shahabodini, A. and Rouhi, H. (2015), "A nonlocal plate model incorporating interatomic potentials for vibrations of graphene with arbitrary edge conditions", Curr. Appl. Phys., 15, 1062-1069. https://doi.org/10.1016/j.cap.2015.06.012
  9. Arash, B. and Wang, Q. (2012), "A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes", Comp. Mater. Sci., 51, 303-313. https://doi.org/10.1016/j.commatsci.2011.07.040
  10. Arash, B., Wang, Q. and Liew, K.M. (2012), "Wave propagation in graphene sheets with nonlocal elastic theory using finite element formulation", Comput. Meth. Appl. M., 223, 1-9.
  11. Assadi, A. (2013), "Size dependent forced vibration of nanoplates with consideration of surface effects", Appl. Math. Model., 37, 3575-3588. https://doi.org/10.1016/j.apm.2012.07.049
  12. Assadi, A. and Farshi, B. (2010), "Vibration characteristics of circular nanoplates", J. Appl. Phys., 108, 074312. https://doi.org/10.1063/1.3486514
  13. Chen, J., Lim, B., Lee, E.P. and Xia Y. (2009), "Shape-controlled synthesis of platinum nanocrystals for catalytic and electrocatalytic applications", Nano Today, 4, 81-95. https://doi.org/10.1016/j.nantod.2008.09.002
  14. Clark, D., Wood, D. and Erb, U. (1997), "Industrial applications of electrodeposited nanocrystals", Nanostruct. Mater., 9, 755-758. https://doi.org/10.1016/S0965-9773(97)00163-3
  15. Cosserat, E. and Cosserat, F. (1909), Theorie des Corps Deformables, Hermann et Fils, Paris.
  16. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10, 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  17. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  18. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  19. Fatemi, H., Khodadadi, A.A., Firooz, A.A., Mortazavi, Y. (2012), "Apple-biomorphic synthesis of porous ZnO nanostructures for glucose direct electrochemical biosensor", Curr. Appl. Phys., 2, 1033-1038.
  20. Grzelczak, M., Perez-Juste, J., Mulvaney, P. and Liz-Marzan, L.M. (2008), "Shape control in gold nanoparticle synthesis", Chem. Soc. Rev., 37, 1783-1791. https://doi.org/10.1039/b711490g
  21. Huang, H., Chen, H., Sun, D. and Wang, X. (2012), "Graphene nanoplate-Pt composite as a high performance electrocatalyst for direct methanol fuel cells", J. Power Sour., 204, 46-52. https://doi.org/10.1016/j.jpowsour.2012.01.023
  22. Huang, H. and Wang, X. (2011), "Graphene nanoplate-$MnO_2$ composites for supercapacitors: a controllable oxidation approach", Nanoscale, 3, 3185-3191. https://doi.org/10.1039/c1nr10229j
  23. Jomehzadeh, E. and Saidi, A.R. (2011), "Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates", Compos. Struct., 93, 1015-1020. https://doi.org/10.1016/j.compstruct.2010.06.017
  24. Karlicic, D., Murmu, T., Cajic, M., Kozic, P. and Adhikari, S. (2014), "Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field", J. Appl. Phys., 115, 234303. https://doi.org/10.1063/1.4883194
  25. Ke, L. L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory", Acta Mech. Sinica, 30, 516-525. https://doi.org/10.1007/s10409-014-0072-3
  26. Kiani, K. (2011a), "Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory", J. Sound Vib., 330, 4896-4914. https://doi.org/10.1016/j.jsv.2011.03.033
  27. Kiani, K. (2011b), "Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part I: Theoretical formulations", Phys. E, 44, 229-248. https://doi.org/10.1016/j.physe.2011.08.020
  28. Kiani, K. (2012a), "Transverse wave propagation in elastically confined single-walled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models", Phys. E, 45, 86-96. https://doi.org/10.1016/j.physe.2012.07.015
  29. Kiani, K. (2012b), "Magneto-elasto-dynamic analysis of an elastically confined conducting nanowire due to an axial magnetic shock", Phys. Lett. A, 376, 1679-1685. https://doi.org/10.1016/j.physleta.2012.03.051
  30. Kiani, K. (2012c), "Magneto-thermo-elastic fields caused by an unsteady longitudinal magnetic field in a conducting nanowire accounting for eddy-current loss", Mater. Chem. Phys., 136, 589-598. https://doi.org/10.1016/j.matchemphys.2012.07.031
  31. Kiani, K. (2014a), "Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field", J. Phys. Chem. Solid., 75, 15-22. https://doi.org/10.1016/j.jpcs.2013.07.022
  32. Kiani, K. (2014b), "Elastic wave propagation in magnetically affected double-walled carbon nanotubes", Meccanica, 50, 1003-1026.
  33. Kiani, K. (2014c), "Longitudinally varying magnetic field influenced transverse vibration of embedded double-walled carbon nanotubes", Int. J. Mech. Sci., 87, 179-199. https://doi.org/10.1016/j.ijmecsci.2014.04.018
  34. Kiani, K. (2014d), "Revisiting free transverse vibration of embedded single-layer graphene sheets acted upon by an inplane magnetic field", J. Mech. Sci. Tech., 28, 3511-3516. https://doi.org/10.1007/s12206-014-0811-1
  35. Kiani, K. (2014e), "Free vibration of conducting nanoplates exposed to unidirectional in-plane magnetic fields using nonlocal shear deformable plate theories", Phys. E, 57C, 179-192.
  36. Lee, C.L., Chiou, H.P., Syu, C.M., Liu, C.R., Yang, C.C. and Syu, C.C. (2011), "Displacement triangular Ag/Pd nanoplate as methanol-tolerant electrocatalyst in oxygen reduction reaction", Int. J. Hydrogen Energ., 36, 12706-12714. https://doi.org/10.1016/j.ijhydene.2011.07.064
  37. Li, Y.S., Cai, Z.Y. and Shi, S.Y. (2014), "Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory", Compos. Struct., 111, 522-529. https://doi.org/10.1016/j.compstruct.2014.01.033
  38. Malekzadeh, P. and Farajpour, A. (2012), "Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium", Acta Mech., 223, 2311-2330. https://doi.org/10.1007/s00707-012-0706-0
  39. Malekzadeh, P., Setoodeh, A.R. and Alibeygi Beni, A. (2011), "Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates", Compos. Struct., 93, 1631-1639. https://doi.org/10.1016/j.compstruct.2011.01.008
  40. Mandal, U. and Pradhan, S.C. (2014), "Transverse vibration analysis of single-layered graphene sheet under magnetothermal environment based on nonlocal plate theory", J. Appl. Phys., 116, 164303. https://doi.org/10.1063/1.4898759
  41. Mindlin, R.D. (1964), "Micro-structure in linear elasticity", Arch. Ration. Mech. An., 16, 51-78. https://doi.org/10.1007/BF00248490
  42. Murmu, T., McCarthy, M.A. and Adhikari, S. (2012), "Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach", J. Sound Vib., 331, 5069-5086. https://doi.org/10.1016/j.jsv.2012.06.005
  43. Murmu, T., McCarthy, M.A. and Adhikari, S. (2013), "In-plane magnetic field affected transverse vibration of embedded singlelayer graphene sheets using equivalent nonlocal elasticity approach", Compos. Struct., 96, 57-63. https://doi.org/10.1016/j.compstruct.2012.09.005
  44. Murmu, T. and Pradhan, S.C. (2009), "Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model", Phys. E, 41, 1628-1633. https://doi.org/10.1016/j.physe.2009.05.013
  45. Narendar, S. and Gopalakrishnan, S. (2012), "Temperature effects on wave propagation in nanoplates", Compos. Part B-Eng., 43, 1275-1281. https://doi.org/10.1016/j.compositesb.2011.11.029
  46. Narendar, S., Gupta, S.S. and Gopalakrishnan, S. (2012), "Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory", Appl. Math. Modell., 36, 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073
  47. Pradhan, S.C. and Phadikar, J.K. (2009), "Nonlocal elasticity theory for vibration of nanoplates", J. Sound Vib., 325, 206-223. https://doi.org/10.1016/j.jsv.2009.03.007
  48. Sewell, H. (2008), "Method for making a computer hard drive platen using a nano-plate", U.S. Patent No. 7, 409, 759.
  49. Toupin, R.A. (1964), "Elastic materials with couple stresses", Arch. Ration. Mech. An., 11, 385-414.
  50. Wang, H., Dong, K., Men, F., Yan, Y.J. and Wang, X. (2010), "Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix", Appl. Math. Model., 34, 878-889. https://doi.org/10.1016/j.apm.2009.07.005
  51. Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010), "Scale effects on the longitudinal wave propagation in nanoplates", Phys. E, 42, 1356-1360. https://doi.org/10.1016/j.physe.2009.11.036
  52. Wang, X., Shen, J.X., Liu, Y., Shen, G.G. and Lu, G. (2012), "Rigorous van der Waals effect on vibration characteristics of multi-walled carbon nanotubes under a transverse magnetic field", Appl. Math. Model., 36, 648-656. https://doi.org/10.1016/j.apm.2011.07.017
  53. Xie, H.J., Wang, X. and Li, Z. (2012), "Dynamic characteristics of multi-walled carbon nanotubes under longitudinal magnetic fields", Mech. Adv. Mater. Struct., 19, 568-575. https://doi.org/10.1080/15376494.2011.563410
  54. Zhong, L., Gan, S., Fu, X., Li, F., Han, D., Guo, L. and Niu, L. (2013), "Electrochemically controlled growth of silver nanocrystals on graphene thin film and applications for efficient nonenzymatic $H_2O_2$ biosensor", Electrochim. Acta, 89, 222-228. https://doi.org/10.1016/j.electacta.2012.10.161
  55. Zhu, Y., Zhao, Q., Zhang, Y.H. and Wu, G. (2012), "Hydrothermal synthesis of protective coating on magnesium alloy using de-ionized water", Surf. Coat. Tech., 206, 2961-2966. https://doi.org/10.1016/j.surfcoat.2011.12.029

피인용 문헌

  1. Instability of functionally graded micro-beams via micro-structure-dependent beam theory vol.39, pp.7, 2018, https://doi.org/10.1007/s10483-018-2343-8
  2. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2017, https://doi.org/10.12989/sem.2019.70.4.407