Steel and Composite Structures

  • 제25권3호
  • /
  • Pages.361-374
  • /
  • 2017
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effects of triaxial magnetic field on the anisotropic nanoplates

  • Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Janghorban, Maziar (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • 투고 : 2017.06.04
  • 심사 : 2017.07.31
  • 발행 : 2017.10.30
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, the influences of triaxial magnetic field on the wave propagation behavior of anisotropic nanoplates are studied. In order to include small scale effects, nonlocal strain gradient theory has been implemented. To study the nanoplate as a continuum model, the three-dimensional elasticity theory is adopted in Cartesian coordinate. In our study, all the elastic constants are considered and assumed to be the functions of (x, y, z), so all kind of anisotropic structures such as hexagonal and trigonal materials can be modeled, too. Moreover, all types of functionally graded structures can be investigated. eigenvalue method is employed and analytical solutions for the wave propagation are obtained. To justify our methodology, our results for the wave propagation of isotropic nanoplates are compared with the results available in the literature and great agreement is achieved. Five different types of anisotropic structures are investigated in present paper and then the influences of wave number, material properties, nonlocal and gradient parameter and uniaxial, biaxial and triaxial magnetic field on the wave propagation analysis of anisotropic nanoplates are presented. From the best knowledge of authors, it is the first time that three-dimensional elasticity theory and nonlocal strain gradient theory are used together with no approximation to derive the governing equations. Moreover, up to now, the effects of triaxial magnetic field have not been studied with considering size effects in nanoplates. According to the lack of any common approximations in the displacement field or in elastic constant, present theory has the potential to be used as a bench mark for future works.

키워드

참고문헌

  1. Ahouel, M., Houari, M.S.A., Bedia, E. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  2. Amara, K., Tounsi, A. and Mechab, I. (2010), "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field", Appl. Math. Model., 34(12), 3933-3942. https://doi.org/10.1016/j.apm.2010.03.029
  3. Askes, H. and Aifantis, E.C. (2009), "Gradient elasticity and flexural wave dispersion in carbon nanotubes", Phys. Rev. B, 80, 195412. https://doi.org/10.1103/PhysRevB.80.195412
  4. Azimi, M., Mirjavadi, S.S., Shafiei N. and Hamouda, A. (2017), "Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam", Appl. Phys. A, 123, 104.
  5. Batra, R., Qian, L. and Chen, L. (2004), "Natural frequencies of thick square plates made of orthotropic, trigonal, monoclinic, hexagonal and triclinic materials", J. Sound Vib., 270, 1074-1086. https://doi.org/10.1016/S0022-460X(03)00625-4
  6. Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E. and Mahmoud, S. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  7. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  8. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi A., Beg, O.A. and Mahmoud, S. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  9. Daneshmehr, A. and Rajabpoor, A. (2014), "Stability of size dependent functionally graded nanoplate based on nonlocal elasticity and higher order plate theories and different boundary conditions", Int. J. Eng. Sci., 82, 84-100. https://doi.org/10.1016/j.ijengsci.2014.04.017
  10. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  11. Eringen, A. (1976), Nonlocal polar field models, Academic, New York.
  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. Heireche, H., Tounsi, A., Benhassaini, H., Benzair, A., Bendahmane, M., Missouri, M. and Mokadem, S. (2010), "Nonlocal elasticity effect on vibration characteristics of protein microtubules", Physica E: Low-Dimensional Syst. Nanostruct., 42, 2375-2379. https://doi.org/10.1016/j.physe.2010.05.017
  14. Janghorban, M. and Nami, M. (2015), "Wave propagation in rectangular nanoplates based on a new strain gradient elasticity theory with considering in-plane magnetic field", Iranian J. Mater. Form., 2(2), 35-43.
  15. Janghorban, M. and Nami, M.R. (2016), "Wave propagation in functionally graded nanocomposites reinforced with carbon nanotubes based on second order shear deformation theory", Mech. Adv. Mater. Struct., 24(6), 458-468.
  16. Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36), 1650421. https://doi.org/10.1142/S0217984916504212
  17. Karami, B., Shahsavari, D. and Janghorban, M. (2017), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 1-11.
  18. Kraus, J.D. (1984), Electromagnetic, McGrawHill.
  19. Lei, J., He, Y., Zhang, B., Gan, Z. and Zeng, P. (2013), "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", Int. J. Eng. Sci., 72, 36-52. https://doi.org/10.1016/j.ijengsci.2013.06.012
  20. Li, L. and Hu, Y. (2016), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Comput. Mater. Sci., 112(1), 282-288. https://doi.org/10.1016/j.commatsci.2015.10.044
  21. Li, L., Hu, Y. and Ling, L. (2016a), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028
  22. Li, L., Li, X. and Hu, Y. (2016b), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  23. 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
  24. Mahmoud, S., Abd-alla A., Tounsi, A. and Marin, M. (2015), "The problem of wave propagation in magneto-rotating orthotropic non-homogeneous medium", J. Vib. Control, 21, 3281-3291. https://doi.org/10.1177/1077546314521443
  25. Mahmoud, S., Tounsi, A., Marin, M., Ali, S. and Ali, A. (2014), "Effect of magnetic field and initial stress on radial vibrations in rotating orthotropic homogeneous hollow sphere", J. Comput. Theor. Nanosci., 11(6), 1524-1529. https://doi.org/10.1166/jctn.2014.3529
  26. Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017), "Calibration of nonlocal strain gradient shell model for buckling analysis of nanotubes using molecular dynamics simulations", Physica B: Condensed Matter., 521, 102-111. https://doi.org/10.1016/j.physb.2017.06.058
  27. Murmu, T., Adhikari, S. and Mccarthy, M. (2014), "Axial vibration of embedded nanorods under transverse magnetic field effects via nonlocal elastic continuum theory", J. Comput. Theor. Nanosci., 11, 1230-1236. https://doi.org/10.1166/jctn.2014.3487
  28. Murmu, T., Mccarthy, M. 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(23), 5069-5086. https://doi.org/10.1016/j.jsv.2012.06.005
  29. Murmu, T., Mccarthy, M. 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
  30. Nami, M.R. and Janghorban, M. (2014a), "Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory", Iranian J. Mater. Form., 1(2), 1-13.
  31. Nami, M.R. and Janghorban, M. (2014b), "Wave propagation in rectangular nanoplates based on strain gradient theory with one gradient parameter with considering initial stress", Mod. Phy. Lett. B, 28(3), 1450021. https://doi.org/10.1142/S0217984914500213
  32. Nami, M.R. and Janghorban, M. (2015), "Free vibration analysis of rectangular nanoplates based on two-variable refined plate theory using a new strain gradient elasticity theory", J. Braz. Soc. Mech. Sci. Eng., 37(1), 313-324. https://doi.org/10.1007/s40430-014-0169-4
  33. Nami, M.R., Janghorban, M. and Damadam, M. (2015), "Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory", Aerosp. Sci. Technol., 41, 7-15. https://doi.org/10.1016/j.ast.2014.12.001
  34. Papargyri-beskou, S. and Beskos, D. (2008), "Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates", Arch. Appl. Mech., 78(8), 625-635. https://doi.org/10.1007/s00419-007-0166-5
  35. Peddieson, J., Buchanan, G.R. and Mcnitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41, 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  36. Prince, E., Finger, L. and Konnert, J. (2006), "Constraints and restraints in refinement. International Tables for Crystallography Volume C: Mathematical, physical and chemical tables. Springer.
  37. Sadd, M.H. (2009), Elasticity: theory, applications, and numerics, Academic Press.
  38. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Braz. Soc. Mech. Sci. Eng.. 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0
  39. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Express, 4(8).
  40. Sharma, P., Ganti, S. and Bhate, N. (2003), "Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities", Appl. Phys. Lett., 82(4), 535-537. https://doi.org/10.1063/1.1539929
  41. Sheehan, P.E. and Lieber, C.M. (1996), "Nanotribology and nanofabrication of MoO3 structures by atomic force microscopy", Science, 272(5265), 1158. https://doi.org/10.1126/science.272.5265.1158
  42. Shen, L., Shen, H.S. and Zhang, C.L. (2010), "Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments", Comput. Mater. Sci., 48(3), 680-685. https://doi.org/10.1016/j.commatsci.2010.03.006
  43. Simsek, M. (2016), "Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach", Int. J. Eng. Sci., 105, 12-27. https://doi.org/10.1016/j.ijengsci.2016.04.013
  44. Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010a), "Scale effects on flexural wave propagation in nanoplate embedded in elastic matrix with initial stress", Appl. Phys. A: Mater. Sci. Process., 99(4), 907-911. https://doi.org/10.1007/s00339-010-5666-4
  45. Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010b), "Scale effects on the longitudinal wave propagation in nanoplates", Physica E: Low-dimensional Syst. Nanostruct., 42(5), 1356-1360. https://doi.org/10.1016/j.physe.2009.11.036
  46. 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, 388. https://doi.org/10.1007/s00339-017-1007-1
  47. Yakobson, B.I. and Smalley, R.E. (1997), "Fullerene nanotubes: C 1,000,000 and beyond: Some unusual new molecules-long, hollow fibers with tantalizing electronic and mechanical properties-have joined diamonds and graphite in the carbon family", American Scientist, 85(4), 324-337.
  48. Zang J., Fang, B., Zhang, Y.W., Yang, T.Z. and Li, D.H. (2014), "Longitudinal wave propagation in a piezoelectric nanoplate considering surface effects and nonlocal elasticity theory", Physica E: Low-dimensional Syst. Nanostruct., 63, 147-150. https://doi.org/10.1016/j.physe.2014.05.019
  49. Zeighampour, H., Beni, Y.T. and Karimipour, I. (2017), "Wave propagation in double-walled carbon nanotube conveying fluid considering slip boundary condition and shell model based on nonlocal strain gradient theory", Microfluidics and Nanofluidics, 21, 85. https://doi.org/10.1007/s10404-017-1918-3
  50. Zhang, L., Liu, J., Fang, X. and Nie, G. (2014a), "Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates", Eur. J. Mech. -A/Solids, 46, 22-29. https://doi.org/10.1016/j.euromechsol.2014.01.005
  51. Zhang, L., Liu, J., Fang, X. and Nie, G. (2014b), "Surface effect on size-dependent wave propagation in nanoplates via nonlocal elasticity", Philos. Mag., 94(18), 2009-2020. https://doi.org/10.1080/14786435.2014.904057
  52. Zhu, X. and Li, L. (2017), "Closed form solution for a nonlocal strain gradient rod in tension", Int. J. Eng. Sci., 119, 16-28. https://doi.org/10.1016/j.ijengsci.2017.06.019

피인용 문헌

  1. A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law vol.15, pp.5, 2017, https://doi.org/10.1108/wje-11-2017-0357
  2. Multiscale modelling approach to determine the specific heat of cementitious materials vol.23, pp.5, 2017, https://doi.org/10.1080/19648189.2018.1443157
  3. 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
  4. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2017, https://doi.org/10.12989/scs.2019.31.5.503
  5. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2017, https://doi.org/10.12989/scs.2019.33.5.699
  6. Using IGA and trimming approaches for vibrational analysis of L-shape graphene sheets via nonlocal elasticity theory vol.33, pp.5, 2019, https://doi.org/10.12989/scs.2019.33.5.717
  7. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  8. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2017, https://doi.org/10.12989/was.2019.29.6.371
  9. Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches vol.34, pp.2, 2020, https://doi.org/10.12989/scs.2020.34.2.261
  10. Flow of casson nanofluid along permeable exponentially stretching cylinder: Variation of mass concentration profile vol.38, pp.1, 2017, https://doi.org/10.12989/scs.2021.38.1.033
  11. Thermal stress effects on microtubules based on orthotropic model: Vibrational analysis vol.11, pp.3, 2017, https://doi.org/10.12989/acc.2021.11.3.255
  12. Effect of suction on flow of dusty fluid along exponentially stretching cylinder vol.10, pp.3, 2017, https://doi.org/10.12989/anr.2021.10.3.263
  13. Elastic wave phenomenon of nanobeams including thickness stretching effect vol.10, pp.3, 2017, https://doi.org/10.12989/anr.2021.10.3.271
  14. On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations vol.40, pp.3, 2021, https://doi.org/10.12989/scs.2021.40.3.389