Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Dynamic modeling of smart magneto-electro-elastic curved nanobeams

  • Ebrahimi, Farzad (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University) ;
  • Barati, Mohammad Reza (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University) ;
  • Mahesh, Vinyas (Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology)
  • Received : 2018.10.06
  • Accepted : 2019.04.13
  • Published : 2019.05.25
⟨ Previous Next ⟩

Abstract

In this article, the influence of small scale effects on the free vibration response of curved magneto-electro-elastic functionally graded (MEE-FG) nanobeams has been investigated considering nonlocal elasticity theory. Power-law is used to judge the through thickness material property distribution of MEE nanobeams. The Euler-Bernoulli beam model has been adopted and through Hamilton's principle the Nonlocal governing equations of curved MEE-FG nanobeam are obtained. The analytical solutions are obtained and validated with the results reported in the literature. Several parametric studies are performed to assess the influence of nonlocal parameter, magnetic potential, electric voltage, opening angle, material composition and slenderness ratio on the dynamic behaviour of MEE curved nanobeams. It is believed that the results presented in this article may serve as benchmark results in accurate analysis and design of smart nanostructures.

Keywords

References

  1. Assadi, A. and Farshi, B. (2011), "Size dependent vibration of curved nanobeams and rings including surface energies", Physica E: Low-dimens. Syst. Nanostruct., 43(4), 975-978. https://doi.org/10.1016/j.physe.2010.11.031
  2. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  3. Barati, M.R., Zenkour, A.M. and Shahverdi, H. (2016), "Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory", Compos. Struct., 141, 203-212. https://doi.org/10.1016/j.compstruct.2016.01.056
  4. Beni, Y.T. (2016), "Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams", J. Intell. Mater. Syst. Struct., 1045389X15624798.
  5. Ebrahimi, F. and Barati, M.R. (2016), "Hygrothermal buckling analysis of magnetically actuated embedded higher order functionally graded nanoscale beams considering the neutral surface position", J. Thermal Stress., 39(10), 1210-1229. https://doi.org/10.1080/01495739.2016.1215726
  6. Ebrahimi, F. and Barati, M.R. (2017a), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams", J. Mech., 33(1), 23-33 https://doi.org/10.1017/jmech.2016.46
  7. Ebrahimi, F. and Barati, M.R. (2017b), "Through-the-length temperature distribution effects on thermal vibration analysis of nonlocal strain-gradient axially graded nanobeams subjected to nonuniform magnetic field", J. Thermal Stress., 40(5), 548-563. https://doi.org/10.1080/01495739.2016.1254076
  8. Ebrahimi, F. and Barati, M.R. (2017c), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intel. Mater. Syst. Struct., 28(11), 1472-1490. https://doi.org/10.1177/1045389X16672569
  9. Ebrahimi, F. and Barati, M.R. (2018a), "Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory", Microsyst. Technol., 24(3), 1643-1658. https://doi.org/10.1007/s00542-017-3529-z
  10. Ebrahimi, F. and Barati, M.R. (2018b), "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", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(13), pp. 2469-2481. https://doi.org/10.1177/0954406217720232
  11. Ebrahimi, F. and Dabbagh, A. (2017a), "Nonlocal strain gradient based wave dispersion behavior of smart rotating magneto-electro-elastic nanoplates", Mater. Res. Express, 4(2), 025003. https://doi.org/10.1088/2053-1591/aa55b5
  12. Ebrahimi, F. and Dabbagh, A. (2017b), "On flexural wave propagation responses of smart fg magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293. https://doi.org/10.1016/j.compstruct.2016.11.058
  13. Ebrahimi, F. and Dabbagh, A. (2017c), "Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory", Eur. Phys. J. Plus, 132(11), 449. https://doi.org/10.1140/epjp/i2017-11694-2
  14. Ebrahimi, F. and Dabbagh, A. (2017d), "Wave propagation analysis of smart rotating porous heterogeneous piezo-electric nanobeams", Eur. Phys. J. Plus, 132(4), 153. https://doi.org/10.1140/epjp/i2017-11366-3
  15. Ebrahimi, F. and Dabbagh, A. (2018a), "Effect of humid-thermal environment on wave dispersion characteristics of single-layered graphene sheets", Appl. Phys. A, 124(4), 301. https://doi.org/10.1007/s00339-018-1734-y
  16. Ebrahimi, F. and Dabbagh, A. (2018b), "On modeling wave dispersion characteristics of protein lipid nanotubules", J. Biomech., 77, 1-7. https://doi.org/10.1016/j.jbiomech.2018.05.038
  17. Ebrahimi, F. and Dabbagh, A. (2018c), "On wave dispersion characteristics of double-layered graphene sheets in thermal environments", J. Electromag. Waves Appl., 32(15), 1869-1888. https://doi.org/10.1080/09205071.2017.1417918
  18. Ebrahimi, F. and Dabbagh, A. (2018d), "Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates", Eur. Phys. J. Plus, 133(3), 97. https://doi.org/10.1140/epjp/i2018-11910-7
  19. Ebrahimi, F. and Dabbagh, A. (2018e), "Wave dispersion characteristics of orthotropic double-nanoplate-system subjected to a longitudinal magnetic field", Microsyst. Technol., 24(7), 2929-2939. https://doi.org/10.1007/s00542-018-3738-0
  20. Ebrahimi, F. and Dabbagh, A. (2018f), "Wave dispersion characteristics of rotating heterogeneous magneto-electro-elastic nanobeams based on nonlocal strain gradient elasticity theory", J. Electromag. Waves Appl., 32(2), 138-169. https://doi.org/10.1080/09205071.2017.1369903
  21. Ebrahimi, F. and Dabbagh, A. (2018g), "Wave propagation analysis of magnetostrictive sandwich composite nanoplates via nonlocal strain gradient theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(22), 4180-4192. https://doi.org/10.1177/0954406217748687
  22. Ebrahimi, F. and Haghi, P. (2018), "Wave dispersion analysis of rotating heterogeneous nanobeams in thermal environment", Adv. Nano Res., Int. J., 6(1), 21-37. https://doi.org/10.21474/IJAR01/7640
  23. Ebrahimi, F. and Hosseini, S. (2016), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Thermal Stress., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  24. Ebrahimi, F. and Salari, E. (2015a), "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.
  25. Ebrahimi, F. and Salari, E. (2015b), "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
  26. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015), "Thermomechanical vibration behavior of fg nanobeams subjected to linear and non-linear temperature distributions", J. Thermal Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  27. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016a), "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
  28. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016b), "Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams", Appl. Phys. A, 122(11), 949. https://doi.org/10.1007/s00339-016-0465-1
  29. Ebrahimi, F., Dabbagh, A. and Barati, M.R. (2016c), "Wave propagation analysis of a size-dependent magneto-electro-elastic heterogeneous nanoplate", Eur. Phys. J. Plus, 131(12), 433. https://doi.org/10.1140/epjp/i2016-16433-7
  30. 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. Thermal Stress., 40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483
  31. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2018a), "Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects", Waves Random Complex Media, 28(2), 215-235. https://doi.org/10.1080/17455030.2017.1337281
  32. Ebrahimi, F., Haghi, P. and Dabbagh, A. (2018b), "Analytical wave dispersion modeling in advanced piezoelectric double-layered nanobeam systems", Struct. Eng. Mech., Int. J., 67(2), 175-183.
  33. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  34. 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
  35. Hosseini, S.A.H. and Rahmani, O. (2016), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phys. A, 122(3), 1-11.
  36. Hosseini-Hashemi, S., Nahas, I., Fakher, M. and Nazemnezhad, R. (2014), "Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity", Acta Mechanica, 225(6), 1555-1564. https://doi.org/10.1007/s00707-013-1014-z
  37. Kananipour, H., Ahmadi, M. and Chavoshi, H. (2014), "Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams", Latin Am. J. Solids Struct., 11(5), 848-853. https://doi.org/10.1590/S1679-78252014000500007
  38. Li, L. and Hu, Y. (2017), "Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory", Compos. Struct., 172, 242-250. https://doi.org/10.1016/j.compstruct.2017.03.097
  39. 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
  40. 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
  41. Niknam, H. and Aghdam, M.M. (2015), "A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation", Compos. Struct., 119, 452-462. https://doi.org/10.1016/j.compstruct.2014.09.023
  42. Ochs, S., Li, S., Adams, C. and Melz, T. (2017), "Efficient Experimental Validation of Stochastic Sensitivity Analyses of Smart Systems", In: Smart Structures and Materials, Springer International Publishing, pp. 97-113.
  43. Rahmani, O. and Jandaghian, A.A. (2015), "Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory", Appl. Phys. A, 119(3), 1019-1032. https://doi.org/10.1007/s00339-015-9061-z
  44. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  45. Setoodeh, A., Derahaki, M. and Bavi, N. (2015), "DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory", Latin Am. J. Solids Struct., 12(10), 1901-1917. https://doi.org/10.1590/1679-78251894
  46. Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011
  47. Tufekci, E., Aya, S.A. and Oldac, O. (2016), "In-Plane Static Analysis of Nonlocal Curved Beams with Varying Curvature and Cross-Section", Int. J. Appl. Mech., 8(1), 1650010. https://doi.org/10.1142/S1758825116500101
  48. Vinyas, M. (2019a), "A higher order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods", Compos. Part B, 158, 286-301. https://doi.org/10.1016/j.compositesb.2018.09.086
  49. Vinyas, M. (2019b), "Vibration control of skew magneto-electro-elastic plates using active constrained layer damping", Compos. Struct., 208, 600-617. https://doi.org/10.1016/j.compstruct.2018.10.046
  50. Vinyas, M. and Kattimani, S.C. (2017a), "Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads", Composite Structures, 163, 216-237. https://doi.org/10.1016/j.compstruct.2016.12.040
  51. Vinyas, M. and Kattimani, S.C. (2017b), "A Finite element based assessment of static behavior of multiphase magneto-electro-elastic beams under different thermal loading", Structural Engineering and Mechanics, 62, 519-535. https://doi.org/10.12989/sem.2017.62.5.519
  52. Vinyas, M. and Kattimani, S.C. (2017c), "Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: A finite element study", Composite Structures, 178, 63-86. https://doi.org/10.1016/j.compstruct.2017.06.068
  53. Vinyas, M. and Kattimani, S.C. (2018a), "Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higher-order shear deformation theory", Composite Structures, 202, 1339-1352. https://doi.org/10.1016/j.compstruct.2018.06.069
  54. Vinyas, M. and Kattimani, S.C. (2018b), "Investigation of the effect of $BaTiO_3/CoFe_2O_4$ particle arrangement on the static response of magneto-electro-thermo-elastic plates", Composite Structures, 185(1), 51-64. https://doi.org/10.1016/j.compstruct.2017.10.073
  55. Vinyas, M., Kattimani, S.C., Loja, M.A.R. and Vishwas, M. (2018), "Effect of BaTiO3/CoFe2O4 micro-topological textures on the coupled static behaviour of magneto-electro-thermo-elastic beams in different thermal environment", Mater. Res. Express, 5, 125702. https://doi.org/10.1088/2053-1591/aae0c8
  56. Vinyas, M., Nischith, G., Loja, M.A.R., Ebrahimi, F. and Duc, N.D. (2019), "Numerical analysis of the vibration response of skew magneto-electro-elastic plates based on the higher-order shear deformation theory", Compos. Struct., 214, 132-142. https://doi.org/10.1016/j.compstruct.2019.02.010
  57. Yan, Z. and Jiang, L. (2011), "Electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects", Journal of Physics D: Applied Physics, 44(36), 365301. https://doi.org/10.1088/0022-3727/44/36/365301
  58. Zhu, X. and Li, L. (2017a), "Twisting statics of functionally graded nanotubes using Eringen's nonlocal integral model", Compos. Struct., 178, 87-96. https://doi.org/10.1016/j.compstruct.2017.06.067
  59. Zhu, X. and Li, L. (2017b), "Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity", Int. J. Mech. Sci., 133, 639-650. https://doi.org/10.1016/j.ijmecsci.2017.09.030

Cited by

  1. Nonlinear vibration behavior of hybrid multi-scale cylindrical panels via semi numerical method vol.28, pp.3, 2021, https://doi.org/10.12989/cac.2021.28.3.233