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Nonlinear stability of smart nonlocal magneto-electro-thermo-elastic beams with geometric imperfection and piezoelectric phase effects

  • Faleh, Nadhim M. (Al-Mustansiriah University, Engineering Collage) ;
  • Abboud, Izz Kadhum (Al-Mustansiriah University, Engineering Collage) ;
  • Nori, Amer Fadhel (Al-Mustansiriah University, Engineering Collage)
  • Received : 2019.09.22
  • Accepted : 2020.01.15
  • Published : 2020.06.25
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Abstract

In this paper, analysis of thermal post-buckling behaviors of sandwich nanobeams with two layers of multi-phase magneto-electro-thermo-elastic (METE) composites have been presented considering geometric imperfection effects. Multi-phase METE material is composed form piezoelectric and piezo-magnetic constituents for which the material properties can be controlled based on the percentages of the constituents. Nonlinear governing equations of sandwich nanobeam are derived based on nonlocal elasticity theory together with classic thin beam model and an analytical solution is provided. It will be shown that post-buckling behaviors of sandwich nanobeam in thermo-electro-magnetic field depend on the constituent's percentages. Buckling temperature of sandwich nanobeam is also affected by nonlocal scale factor, magnetic field intensity and electrical voltage.

Keywords

Acknowledgement

The authors would like to thank Mustansiriyah university (www.uomustansiriyah.edu.iq) Baghdad-Iraq for its support in the present work.

References

  1. Aboudi, J. (2001), "Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites", Smart Mater. Struct., 10(5), 867. https://doi.org/10.1088/0964-1726/10/5/303
  2. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., Int. J., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175
  3. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., Int. J., 18(6), 1125-1143. http://dx.doi.org/10.12989/sss.2016.18.6.1125
  4. Allam, M.N.M., Tantawy, R. and Zenkour, A.M. (2018), "Magneto-thermo-elastic response of exponentially graded piezoelectric hollow spheres", Adv. Computat. Des., Int. J., 3(3), 303-318. https://doi.org/10.12989/acd.2018.3.3.303
  5. Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monitor. Mainten., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147
  6. Annigeri, A.R., Ganesan, N. and Swarnamani, S. (2007), "Free vibration behaviour of multiphase and layered magneto-electro-elastic beam", J. Sound Vib., 299(1-2), 44-63. https://doi.org/10.1016/j.jsv.2006.06.044
  7. Azimi, M., Mirjavadi, S.S., Shafiei, N. and Hamouda, A.M.S. (2017), "Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam", Appl. Phys. A, 123(1), 104. https://doi.org/10.1007/s00339-016-0712-5
  8. Azimi, M., Mirjavadi, S.S., Shafiei, N., Hamouda, A.M.S. and Davari, E. (2018), "Vibration of rotating functionally graded Timoshenko nano-beams with nonlinear thermal distribution", Mech. Adv. Mater. Struct., 25(6), 467-480. https://doi.org/10.1080/15376494.2017.1285455
  9. Barati, M.R. (2017), "Coupled effects of electrical polarization-strain gradient on vibration behavior of double-layered flexoelectric nanoplates", Smart Struct. Syst., Int. J., 20(5), 573-581. https://doi.org/10.12989/sss.2017.20.5.573
  10. Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Computat. Des., Int. J., 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213
  11. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2018), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., Int. J., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163
  12. Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., Int. J., 19(6), 601-614. https://doi.org/10.12989/sss.2017.19.6.601
  13. 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., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  14. Chaudhary, S., Sahu, S.A. and Singhal, A. (2017), "Analytic model for Rayleigh wave propagation in piezoelectric layer overlaid orthotropic substratum", Acta Mechanica, 228(2), 495-529. https://doi.org/10.1007/s00707-016-1708-0
  15. Chaudhary, S., Sahu, S.A. and Singhal, A. (2018), "On secular equation of SH waves propagating in pre-stressed and rotating piezo-composite structure with imperfect interface", J. Intel. Mater. Syst. Struct., 29(10), 2223-2235. https://doi.org/10.1177%2F1045389X18758192 https://doi.org/10.1177/1045389X18758192
  16. Chaudhary, S., Sahu, S.A., Dewangan, N. and Singhal, A. (2019a), "Stresses produced due to moving load in a prestressed piezoelectric substrate", Mech. Adv. Mater. Struct., 26(12), 1028-1041. https://doi.org/10.1080/15376494.2018.1430265
  17. Chaudhary, S., Sahu, S., Singhal, A. and Nirwal, S. (2019b), "Interfacial imperfection study in pres-stressed rotating multiferroic cylindrical tube with wave vibration analytical approach", Mater. Res. Express, 6(10), 105704. https://doi.org/10.1088/2053-1591/ab3880
  18. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Mathe. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  19. Eshraghi, I., Jalali, S.K. and Pugno, N.M. (2016), "Imperfection sensitivity of nonlinear vibration of curved single-walled carbon nanotubes based on nonlocal timoshenko beam theory", Materials, 9(9), 786. https://doi.org/10.3390/ma9090786
  20. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  21. Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities", Coupl. Syst. Mech., Int. J., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247
  22. Guo, J., Chen, J. and Pan, E. (2016), "Static deformation of anisotropic layered magnetoelectroelastic plates based on modified couple-stress theory", Compos. Part B: Eng., 107, 84-96. https://doi.org/10.1016/j.compositesb.2016.09.044
  23. Jandaghian, A.A. and Rahmani, O. (2016), "Free vibration analysis of magneto-electro-thermo-elastic nanobeams resting on a Pasternak foundation", Smart Mater. Struct., 25(3), 035023. https://doi.org/10.1088/0964-1726/25/3/035023
  24. Ke, L.L. and Wang, Y.S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Physica E: Low-Dimens. Syst. Nanostruct., 63, 52-61. https://doi.org/10.1016/j.physe.2014.05.002
  25. Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidiscipl. Model. Mater. Struct., 3(4), 461-476. https://doi.org/10.1163/157361107782106401
  26. Li, Y. and Shi, Z. (2009), "Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature", Compos. Struct., 87(3), 257-264. https://doi.org/10.1016/j.compstruct.2008.01.012
  27. Li, Y.S., Ma, P. and Wang, W. (2016), "Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory", J. Intel. Mater. Syst. Struct., 27(9), 1139-1149. https://doi.org/10.1177%2F1045389X15585899 https://doi.org/10.1177/1045389X15585899
  28. Li, L., Tang, H. and Hu, Y. (2018), "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
  29. Mirjavadi, S.S., Rabby, S., Shafiei, N., Afshari, B.M. and Kazemi, M. (2017a), "On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment", Appl. Phys. A, 123(5), 315. https://doi.org/10.1007/s00339-017-0918-1
  30. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017b), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams. Steel Compos. Struct., Int. J., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415
  31. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2018a), "Strain gradient based dynamic response analysis of heterogeneous cylindrical microshells with porosities under a moving load", Mater. Res. Express, 6(3), 035029. https://doi.org/10.1088/2053-1591/aaf5a2
  32. Mirjavadi, S.S., Afshari, B.M., Khezel, M., Shafiei, N., Rabby, S. and Kordnejad, M. (2018b), "Nonlinear vibration and buckling of functionally graded porous nanoscaled beams", J. Brazil. Soc. Mech. Sci. Eng., 40(7), 352. https://doi.org/10.1007/s40430-018-1272-8
  33. Mirjavadi, S.S., Forsat, M., Hamouda, A.M.S. and Barati, M.R. (2019a), "Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads", Mater. Res. Express, 6(7), 075045. https://doi.org/10.1088/2053-1591/ab1552
  34. Mirjavadi, S.S., Forsat, M., Nikookar, M., Barati, M.R. and Hamouda, A.M.S. (2019b), "Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets", Eur. Phys. J. Plus, 134(10), 508. https://doi.org/10.1140/epjp/i2019-12806-8
  35. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M. S. (2019c), "Transient response of porous FG nanoplates subjected to various pulse loads based on nonlocal stress-strain gradient theory", Eur. J. Mech.-A/Solids, 74, 210-220. https://doi.org/10.1016/j.euromechsol.2018.11.004
  36. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019d), "Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection", Microsyst. Technol., 25, 3137-3150. https://doi.org/10.1007/s00542-018-4277-4
  37. Mirjavadi, SS., Forsat, M., Barati, M.R., Abdella, G.M., Hamouda, A.M.S., Afshari, B.M. and Rabby, S. (2019e), "Post-buckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents", Microsyst. Technol., 25(9), 3477-3488. https://doi.org/10.1007/s00542-018-4241-3
  38. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Afshari, B.M., Hamouda, A.M.S. and Rabby, S. (2019f), "Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency", Eur. Phys. J. Plus, 134(5), 214. https://doi.org/10.1140/epjp/i2019-12540-3
  39. Mohammadi, H., Mahzoon, M., Mohammadi, M. and Mohammadi, M. (2014), "Postbuckling instability of nonlinear nanobeam with geometric imperfection embedded in elastic foundation", Nonlinear Dyn., 76(4), 2005-2016. https://doi.org/10.1007/s11071-014-1264-x
  40. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454. http://dx.doi.org/10.12989/sem.2016.59.3.431
  41. 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. https://doi.org/10.12989/sss.2017.19.2.115
  42. Mu'tasim, S., Al-Qaisia, A.A. and Shatarat, N.K. (2017), "Nonlinear Vibrations of a SWCNT with Geometrical Imperfection Using Nonlocal Elasticity Theory", Modern Appl. Sci., 11(10), 91. https://doi.org/10.5539/mas.v11n10p91
  43. Nan, C.W. (1994), "Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases", Phys. Rev. B, 50(9), 6082. https://doi.org/10.1103/PhysRevB.50.6082
  44. Nirwal, S., Sahu, S.A., Singhal, A. and Baroi, J. (2019), "Analysis of different boundary types on wave velocity in bedded piezo-structure with flexoelectric effect", Compos. Part B: Eng., 167, 434-447. https://doi.org/10.1016/j.compositesb.2019.03.014
  45. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3-4), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006
  46. Sahu, S.A., Singhal, A. and Chaudhary, S. (2018), "Surface wave propagation in functionally graded piezoelectric material: an analytical solution", J. Intel. Mater. Syst. Struct., 29(3), 423-437. https://doi.org/10.1177%2F1045389X17708047 https://doi.org/10.1177/1045389X17708047
  47. Singh, M.K., Sahu, S.A., Singhal, A. and Chaudhary, S. (2018), "Approximation of surface wave velocity in smart composite structure using Wentzel-Kramers-Brillouin method", J. Intel. Mater. Syst. Struct., 29(18), 3582-3597. https://doi.org/10.1177%2F1045389X18786464 https://doi.org/10.1177/1045389x18786464
  48. Singhal, A. and Chaudhary, S. (2019), "Mechanics of 2D Elastic Stress Waves Propagation Impacted by Concentrated Point Source Disturbance in Composite Material Bars", J. Appl. Computat. Mech. https://doi.org/10.22055/JACM.2019.29666.1621
  49. Singhal, A. and Sahu, S.A. (2017), "Transference of rayleigh waves in corrugated orthotropic layer over a pre-stressed orthotropic half-space with self weight", Procedia Eng., 173, 972-979. https://doi.org/10.1016/j.proeng.2016.12.164
  50. Singhal, A., Sahu, S.A. and Chaudhary, S. (2018a), "Approximation of surface wave frequency in piezo-composite structure", Compos. Part B: Eng., 144, 19-28. https://doi.org/10.1016/j.compositesb.2018.01.017
  51. Singhal, A., Sahu, S.A. and Chaudhary, S. (2018b), "Liouville-Green approximation: An analytical approach to study the elastic waves vibrations in composite structure of piezo material", Compos. Struct., 184, 714-727. https://doi.org/10.1016/j.compstruct.2017.10.031
  52. Singhal, A., Sahu, S.A. and Chaudhary, S. (2019a), "Study of surface wave vibration in rotating human long bones of cylindrical shape under the magnetic field influence", Waves Random Complex Media, 1-17. https://doi.org/10.1080/17455030.2019.1686551
  53. Singhal, A., Sahu, S.A., Chaudhary, S. and Baroi, J. (2019b), "Initial and couple stress influence on the surface waves transmission in material layers with imperfect interface", Mater. Res. Express, 6(10), 105713. https://doi.org/10.1088/2053-1591/ab40e2
  54. Thai, H.T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009
  55. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693

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