DOI QR코드

DOI QR Code

Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading

  • Fenjan, Raad M. (Al-Mustansiriah University, Engineering Collage) ;
  • Ahmed, Ridha A. (Al-Mustansiriah University, Engineering Collage) ;
  • Faleh, Nadhim M. (Al-Mustansiriah University, Engineering Collage)
  • Received : 2019.09.29
  • Accepted : 2020.10.19
  • Published : 2021.04.10

Abstract

An investigation of the nonlinear thermal buckling behavior of a nano-sized beam constructed from intelligent materials called piezo-magnetic materials has been presented in this article. The nano-sized beam geometry has been considered based on two assumptions: an ideal straight beam and an imperfect beam. For incorporating nano-size impacts, the nano-sized beam formulation has been presented according to nonlocal elasticity. After establishing the governing equations based on classic beam theory and nonlocal elasticity, the nonlinear buckling path has been obtained via Galerkin's method together with an analytical trend. The dependency of buckling path to piezo-magnetic material composition, electro-magnetic fields and geometry imperfectness has been studied in detail.

Keywords

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. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. http://dx.doi.org/10.12989/sss.2016.18.6.1125.
  3. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  4. Ansari, R. and Gholami, R. (2016), "Size-dependent modeling of the free vibration characteristics of postbuckled third-order shear deformable rectangular nanoplates based on the surface stress elasticity theory", Compos. Part B: Eng., 95, 301-316. https://doi.org/10.1016/j.compositesb.2016.04.002.
  5. Barati, M.R. (2017), "Coupled effects of electrical polarization-strain gradient on vibration behavior of double-layered flexoelectric nanoplates", Smart Struct. Syst., 20(5), 573-581. https://doi.org/10.12989/sss.2017.20.5.573.
  6. 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., 19(6), 601-614. https://doi.org/10.12989/sss.2017.19.6.601.
  7. Bohlooly, M. and Malekzadeh Fard, K. (2019), "Buckling and postbuckling of concentrically stiffened piezo-composite plates on elastic foundations", J. Appl. Comput. Mech., 5(1), 128-140. https://doi.org/10.22055/jacm.2018.25539.1277.
  8. Bohlooly, M. and Mirzavand, B. (2018), "Postbuckling and deflection response of imperfect piezo-composite plates resting on elastic foundations under in-plane and lateral compression and electro-thermal loading", Mech. Adv. Mater. Struct., 25(3), 192-201. https://doi.org/10.1080/15376494.2016.1255818.
  9. 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.
  10. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  11. Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016), "Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039.
  12. Fard, K.M. and Bohlooly, M. (2017), "Postbuckling of piezolaminated cylindrical shells with eccentrically/concentrically stiffeners surrounded by nonlinear elastic foundations", Compos. Struct., 171, 360-369. https://doi.org/10.1016/j.compstruct.2017.03.058.
  13. Jia, X.L., Zhang, S.M., Yang, J. and Kitipornchai, S. (2013), "Pull-in instability of electrically actuated poly-SiGe graded micro-beams", Coupl. Syst. Mech., 2(3), 215-230. https://doi.org/10.12989/csm.2013.2.3.215.
  14. Kattimani, S.C. and Ray, M.C. (2015), "Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates", Int. J. Mech. Sci., 99, 154-167. https://doi.org/10.1016/j.ijmecsci.2015.05.012.
  15. 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.
  16. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory", Acta Mechanica Sinica, 30(4), 516-525. https://doi.org/10.1007/s10409-014-0072-3.
  17. Li, L and Hu, Y. (2017a), "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.
  18. Li, L and Hu, Y. (2017b), "Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects", Int. J. Mech. Sci., 120, 159-170. https://doi.org/10.1016/j.ijmecsci.2016.11.025.
  19. Li, Y.S., Cai, Z.Y. and Shi, S.Y. (2014), "Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory", Compos. Struct., 111, 522-529. https://doi.org/10.1016/j.compstruct.2014.01.033.
  20. 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%2F1045389X15585899
  21. Mirjavadi, S.S., Forsat, M., Badnava, S. and Barati, M.R. (2020a), "Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme", J. Strain Anal. Eng. Des., 55(7-8), 258-270. https://doi.org/10.1177%2F0309324720917285. https://doi.org/10.1177%2F0309324720917285
  22. Mirjavadi, S.S., Forsat, M., Badnava, S., Barati, M.R. and Hamouda, A.M.S. (2020b), "Nonlinear dynamic characteristics of nonlocal multi-phase magneto-electro-elastic nano-tubes with different piezoelectric constituents", Appl. Phys. A, 126(8), 1-16. https://doi.org/10.1007/s00339-020-03743-8.
  23. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2020e), "Investigating nonlinear forced vibration behavior of multi-phase nanocomposite annular sector plates using Jacobi elliptic functions", Steel Compos. Struct., 36(1), 87-101. https://doi.org/10.12989/scs.2020.36.1.087.
  24. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2020f), "Nonlinear forced vibrations of multi-scale epoxy/CNT/fiberglass truncated conical shells and annular plates via 3D Mori-Tanaka scheme", Steel Compos. Struct., 35(6), 765-777. https://doi.org/10.12989/scs.2020.35.6.765.
  25. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2021), "Investigating nonlinear vibrations of multi-scale truncated conical shell segments with carbon nanotube/fiberglass reinforcement using a higher order conical shell theory", J. Strain Anal. Eng. Des., 56(3), 181-192. https://doi.org/10.1177%2F0309324720939811. https://doi.org/10.1177%2F0309324720939811
  26. Mirjavadi, S.S., Forsat, M., Yahya, Y.Z., Barati, M.R., Jayasimha, A.N. and Hamouda, A.M.S. (2020c), "Porosity effects on postbuckling behavior of geometrically imperfect metal foam doubly-curved shells with stiffeners", Struct. Eng. Mech., 75(6), 701-711. https://doi.org/10.12989/sem.2020.75.6.701.
  27. Mirjavadi, S.S., Nikookar, M., Mollaee, S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2020d), "Analyzing exact nonlinear forced vibrations of two-phase magneto-electro-elastic nanobeams under an elliptic-type force", Adv. Nano Res., 9(1), 47-58. https://doi.org/10.12989/anr.2020.9.1.047.
  28. Oh, I.K., Han, J.H. and Lee, I. (2000), "Postbuckling and vibration characteristics of piezolaminated composite plate subject to thermo-piezoelectric loads", J. Sound Vib., 233(1), 19-40. https://doi.org/10.1006/jsvi.1999.2788.
  29. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006.
  30. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates", Mech. Adv. Mater. Struct., 13(3), 249-266. https://doi.org/10.1080/15376490600582750.
  31. Shen, H.S. (2001), "Thermal postbuckling of shear-deformable laminated plates with piezoelectric actuators", Compos. Sci. Technol., 61(13), 1931-1943. https://doi.org/10.1016/S0266-3538(01)00099-9.
  32. Sobhy, M. (2015), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980. https://doi.org/10.1016/j.compstruct.2015.08.102.
  33. Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001.
  34. Varelis, D. and Saravanos, D.A. (2004), "Coupled buckling and postbuckling analysis of active laminated piezoelectric composite plates", Int. J. Solid. Struct., 41(5-6), 1519-1538. https://doi.org/10.1016/j.ijsolstr.2003.09.034.
  35. Wu, C.P., Chen, S.J. and Chiu, K.H. (2010), "Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method", Mech. Res. Commun., 37(1), 54-60. https://doi.org/10.1016/j.mechrescom.2009.10.003.
  36. Zenkour, A.M., Abouelregal, A.E., Alnefaie, K.A., Abu-Hamdeh, N.H. and Aifantis, E.C. (2014), "A refined nonlocal thermoelasticity theory for the vibration of nanobeams induced by ramp-type heating", Appl. Math. Comput., 248, 169-183. https://doi.org/10.1016/j.amc.2014.09.075.
  37. Zhang, Y.Q., Liu, G.R. and Xie, X.Y. (2005), "Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity", Phys. Rev. B, 71(19), 195404. https://doi.org/10.1103/PhysRevB.71.195404.
  38. Zhu, X. and Li, L. (2017a), "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.
  39. Zhu, X. and Li, L. (2017b), "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.

Cited by

  1. Analyzing dynamic response of nonlocal strain gradient porous beams under moving load and thermal environment vol.26, pp.1, 2021, https://doi.org/10.12989/gae.2021.26.1.089
  2. Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment vol.40, pp.6, 2021, https://doi.org/10.12989/scs.2021.40.6.893