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Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Dabbagh, Ali (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Tornabene, Francesco (Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna) ;
  • Civalek, Omer (Akdeniz University, Engineering Faculty, Civil Engineering Department, Division of Mechanics)
  • Received : 2018.12.20
  • Accepted : 2019.04.19
  • Published : 2019.05.25

Abstract

In this paper, a classical plate model is utilized to formulate the wave propagation problem of magnetostrictive sandwich nanoplates (MSNPs) while subjected to hygrothermal loading with respect to the scale effects. Herein, magnetostriction effect is considered and controlled on the basis of a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations can be derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of presented model is verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

Keywords

wave propagation;magnetostrictive materials;nonlocal strain gradient theory (NSGT);sandwich nanoplates;hygro-thermal environments

References

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of fgm sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 25(6), 693-704.
  2. Abualnour, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel quasi-3d trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  3. 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
  4. Bayat, R., Jafari, A.A. and Rahmani, O. (2015), "Analytical solution for free vibration of laminated curved beam with magnetostrictive layers", Int. J. Appl. Mech., 7(3), p. 1550050. https://doi.org/10.1142/S1758825115500507
  5. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of s-fgm plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  6. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., Int. J., 62(6), 695-702.
  7. 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
  8. Ebrahimi, F. and Barati, M.R. (2017), "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
  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), 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), p. 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), p. 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), p. 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), p. 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, pp. 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), p. 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 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
  23. 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
  24. 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
  25. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016b), "Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams", Appl. Phys. A, 122(11), p. 949. https://doi.org/10.1007/s00339-016-0465-1
  26. 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), p. 433. https://doi.org/10.1140/epjp/i2016-16433-7
  27. 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
  28. 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
  29. 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.
  30. 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
  31. 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), pp. 1849-1867. https://doi.org/10.1007/s00707-016-1605-6
  32. Fleck, N.A. and Hutchinson, J.W. (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
  33. Ghorbanpour Arani, A., Jamali, M., Ghorbanpour-Arani, A.H., Kolahchi, R. and Mosayyebi, M. (2017), "Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(2), 387-403. https://doi.org/10.1177/0954406215627830
  34. Hamza-Cherif, R., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, S. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1
  35. Hong, C. (2009), "Transient responses of magnetostrictive plates without shear effects", Int. J. Eng. Sci., 47(3), 355-362. https://doi.org/10.1016/j.ijengsci.2008.11.004
  36. Hosseini-Hashemi, S., Zare, M. and Nazemnezhad, R. (2013), "An exact analytical approach for free vibration of mindlin rectangular nano-plates via nonlocal elasticity", Compos. Struct., 100, 290-299. https://doi.org/10.1016/j.compstruct.2012.11.035
  37. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., Int. J., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  38. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631.
  39. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  40. Karami, B., Shahsavari, D., Karami, M. and Li, L. (2019), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(6), 2149-2169. https://doi.org/10.1177/0954406218781680
  41. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013
  42. Li, L., Tang, H. and Hu, Y. (2018a), "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
  43. Li, L., Tang, H. and Hu, Y. (2018b), "Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature", Compos. Struct., 184, 1177-1188. https://doi.org/10.1016/j.compstruct.2017.10.052
  44. Lim, C.W., Zhang, G. and Reddy, J.N. (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
  45. Mouffoki, A., Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., Int. J., 20(3), 369-383.
  46. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Computat. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031
  47. Reddy, J.N. and Barbosa, J.I. (2000), "On vibration suppression of magnetostrictive beams", Smart Mater. Struct., 9(1), p. 49. https://doi.org/10.1088/0964-1726/9/1/305
  48. Stolken, J.S. and Evans, A.G. (1998), "A microbend test method for measuring the plasticity length scale", Acta Materialia, 46(14), 5109-5115. https://doi.org/10.1016/S1359-6454(98)00153-0
  49. Tang, H., Li, L., Hu, Y., Meng, W. and Duan, K. (2019), "Vibration of nonlocal strain gradient beams incorporating poisson's ratio and thickness effects", Thin-Wall. Struct., 137, 377-391. https://doi.org/10.1016/j.tws.2019.01.027
  50. 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), p. 388. https://doi.org/10.1007/s00339-017-1007-1
  51. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  52. Yan, J.W., Tong, L.H., Li, C., Zhu, Y. and Wang, Z.W. (2015), "Exact solutions of bending deflections for nano-beams and nano-plates based on nonlocal elasticity theory", Compos. Struct., 125, 304-313. https://doi.org/10.1016/j.compstruct.2015.02.017
  53. Yifeng, Z., Lei, C., Yu, W. and Xiaoping, Z. (2013), "Variational asymptotic micromechanics modeling of heterogeneous magnetostrictive composite materials", Compos. Struct., 106, 502-509. https://doi.org/10.1016/j.compstruct.2013.06.018
  54. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2d and quasi-3d shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B: Eng., 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051
  55. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., Int. J., 64(2), 145-153.