Advances in nano research

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Elastic wave dispersion modelling within rotating functionally graded nanobeams in thermal environment

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Haghi, Parisa (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • Received : 2017.12.22
  • Accepted : 2018.07.12
  • Published : 2018.09.25
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Abstract

In the present research, wave propagation characteristics of a rotating FG nanobeam undergoing rotation is studied based on nonlocal strain gradient theory. Material properties of nanobeam are assumed to change gradually across the thickness of nanobeam according to Mori-Tanaka distribution model. The governing partial differential equations are derived for the rotating FG nanobeam by applying the Hamilton's principle in the framework of Euler-Bernoulli beam model. An analytical solution is applied to obtain wave frequencies, phase velocities and escape frequencies. It is observed that wave dispersion characteristics of rotating FG nanobeams are extremely influenced by angular velocity, wave number, nonlocal parameter, length scale parameter, temperature change and material graduation.

Keywords

References

  1. Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  2. Alizada, A.N. and Sofiyev, A.H. (2011), "Modified Young's moduli of nano-materials taking into account the scale effects and vacancies", Meccanica, 46(5), 915-920. https://doi.org/10.1007/s11012-010-9349-1
  3. Aranda-Ruiz, J., Loya, J. and Fernandez-Saez, J. (2012), "Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory", Compos. Struct., 94(9), 2990-3001. https://doi.org/10.1016/j.compstruct.2012.03.033
  4. Aydogdu, M. (2014), "Longitudinal wave propagation in multiwalled carbon nanotubes", Compos. Struct., 107, 578-584. https://doi.org/10.1016/j.compstruct.2013.08.031
  5. Ebrahimi, F. and Barati, M.R. (2016a), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  6. Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 24(3), 549-564.
  7. Ebrahimi, F. and Barati, M.R. (2016c), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  8. Ebrahimi, F. and Barati, M.R. (2016d), "An exact solution for buckling analysis of embedded piezoelectromagnetically actuated nanoscale beams", Adv. Nano Res., Int. J., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  9. Ebrahimi, F. and Barati, M.R. (2016e), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 42(5), 1715-1726.
  10. Ebrahimi, F. and Barati, M.R. (2016f), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Smart Nano Mater., 7(3), 119-143. https://doi.org/10.1080/19475411.2016.1223203
  11. Ebrahimi, F. and Barati, M.R. (2016g), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9
  12. Ebrahimi, F. and Barati, M.R. (2016h), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  13. Ebrahimi, F. and Barati, M.R. (2016i), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intel. Mater. Syst. Struct., 28(11), 1472-1490.
  14. Ebrahimi, F. and Barati, M.R. (2016j), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y
  15. Ebrahimi, F. and Barati, M.R. (2016k), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  16. Ebrahimi, F. and Barati, M.R. (2016l), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2
  17. Ebrahimi, F. and Barati, M.R. (2016m), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  18. Ebrahimi, F. and Barati, M.R. (2016o), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 39(3), 937-952.
  19. Ebrahimi, F. and Barati, M.R. (2016p), "Buckling analysis of smart size-dependent higher order magnetoelectro-thermo-elastic functionally graded nanosize beams", J. Mech., 33(1), 23-33.
  20. Ebrahimi, F. and Barati, M.R. (2017a), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058
  21. Ebrahimi, F. and Barati, M.R. (2017b), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  22. Ebrahimi, F. and Boreiry, M. (2015), "Investigating various surface effects on nonlocal vibrational behavior of nanobeams", Appl. Phys. A, 121(3), 1305-1316. https://doi.org/10.1007/s00339-015-9512-6
  23. Ebrahimi, F. and Dabbagh, A. (2016), "On flexural wave propagation responses of smart FG magnetoelectro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293.
  24. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stress., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  25. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16001-3
  26. Ebrahimi, F. and Salari, E. (2015a), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent FG nanobeams", Mech. Adv. Mater. Struct., (justaccepted), 23(12), 1379-1397.
  27. Ebrahimi, F. and Salari, E. (2015b), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronautica, 113, 29-50. https://doi.org/10.1016/j.actaastro.2015.03.031
  28. Ebrahimi, F. and Salari, E. (2015c), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. Part B: Eng., 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  29. Ebrahimi, F. and Salari, E. (2015d), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007
  30. Ebrahimi, F. and Salari, E. (2015e), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
  31. Ebrahimi, F. and Salari, E. (2015f), "Thermo-mechanical vibration analysis of nonlocal temperaturedependent FG nanobeams with various boundary conditions", Compos. Part B: Eng., 78, 272-290. https://doi.org/10.1016/j.compositesb.2015.03.068
  32. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., Int. J., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  33. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015a), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Technol., 29(3), 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  34. Ebrahimi, F., Shaghaghi, G.R. and Boreiry, M. (2015b), "A semi-analytical evaluation of surface and nonlocal effects on buckling and vibrational characteristics of nanotubes with various boundary conditions", Int. J. Struct. Stabil. Dyn., 16(6), 1550023.
  35. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015c), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and nonlinear temperature distributions", J. Therm. Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  36. Ebrahimi, F., Shaghaghi, G.R. and Boreiry, M. (2016a), "An investigation into the influence of thermal loading and surface effects on mechanical characteristics of nanotubes", Struct. Eng. Mech., Int. J., 57(1), 179-200. https://doi.org/10.12989/sem.2016.57.1.179
  37. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016b), "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
  38. Ebrahimi, F., Barati, M.R. and Haghi, P. (2016c), "Nonlocal thermo-elastic wave propagation in temperature-dependent embedded small-scaled nonhomogeneous beams", Eur. Phys. J. Plus, 131(11), 383. https://doi.org/10.1140/epjp/i2016-16383-0
  39. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017a), "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
  40. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017b), "Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory", J. Vib. Control, 1077546317711537.
  41. Ehyaei, J., Ebrahimi, F. and Salari, E. (2016), "Nonlocal vibration analysis of FG nano beams with different boundary conditions", Adv. Nano Res., Int. J., 4(2), 85-111.
  42. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  43. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026
  44. 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
  45. Filiz, S. and Aydogdu, M. (2015), "Wave propagation analysis of embedded (coupled) functionally graded nanotubes conveying fluid", Compos. Struct., 132, 1260-1273. https://doi.org/10.1016/j.compstruct.2015.07.043
  46. Ghadiri, M. and Shafiei, N. (2015), "Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen's theory using differential quadrature method", Microsyst. Technol., 22(12), 2853-2867.
  47. Ghadiri, M., Shafiei, N. and Safarpour, H. (2016), "Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen's nonlocal elasticity", Microsyst. Technol., 23(4), 1045-1065.
  48. Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014
  49. Li, L., Li, X. and Hu, Y. (2016), "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
  50. Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91. https://doi.org/10.1016/j.ijengsci.2017.11.021
  51. Mohammadi, M., Safarabadi, M., Rastgoo, A. and Farajpour, A. (2016), "Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment", Acta Mechanica, 227(8), 2207-2232. https://doi.org/10.1007/s00707-016-1623-4
  52. Narendar, S. (2016), "Wave dispersion in functionally graded magneto-electro-elastic nonlocal rod", Aerosp. Sci. Technol., 51, 42-51. https://doi.org/10.1016/j.ast.2016.01.012
  53. Narendar, S. and Gopalakrishnan, S. (2009), "Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes", Computat. Mater. Sci., 47(2), 526-538. https://doi.org/10.1016/j.commatsci.2009.09.021
  54. Narendar, S. and Gopalakrishnan, S. (2011), "Nonlocal wave propagation in rotating nanotube", Results in Physics 1, 17-25. https://doi.org/10.1016/j.rinp.2011.06.002
  55. 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. Model., 36(9), 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073
  56. Pradhan, S.C. and Murmu, T. (2010), "Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever", Phys. E: Low-dimensional Syst. Nanostruct., 42(7), 1944-1949. https://doi.org/10.1016/j.physe.2010.03.004
  57. 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
  58. Srivastava, D. (1997), "A phenomenological model of the rotation dynamics of carbon nanotube gears with laser electric fields", Nanotechnology, 8(4), 186. https://doi.org/10.1088/0957-4484/8/4/005
  59. Syahmazgi, M.G., Falamaki, C. and Lotfi, A.S. (2014), "A novel method for the synthesis of nano-magnetite particles", Adv. Nano Res., Int. J., 2(2), 89-98. https://doi.org/10.12989/anr.2014.2.2.089
  60. Wang, L. (2010), "Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory", Computat. Mater. Sci., 49(4), 761-766. https://doi.org/10.1016/j.commatsci.2010.06.019
  61. Wang, J. and Chan, K.S. (2015), "Generation of valley polarized current in graphene using quantum adiabatic pumping", Adv. Nano Res., Int. J., 3(1), 39-47. https://doi.org/10.12989/anr.2015.3.1.039
  62. Yang, Y., Zhang, L. and Lim, C.W. (2011), "Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model", J. Sound Vib., 330(8), 1704-1717. https://doi.org/10.1016/j.jsv.2010.10.028
  63. Zhang, S., Liu, W.K. and Ruoff, R.S. (2004), "Atomistic simulations of double-walled carbon nanotubes (DWCNTs) as rotational bearings", Nano Lett., 4(2), 293-297. https://doi.org/10.1021/nl0350276
  64. 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

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