Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analyzing large-amplitude vibration of nonlocal beams made of different piezo-electric materials in thermal environment

  • Muhammad, Ahmed K. (Al-Mustansiriah University, Engineering Collage) ;
  • Hamad, Luay Badr (Al-Mustansiriah University, Engineering Collage) ;
  • Fenjan, Raad M. (Al-Mustansiriah University, Engineering Collage) ;
  • Faleh, Nadhim M. (Al-Mustansiriah University, Engineering Collage)
  • Received : 2019.09.06
  • Accepted : 2019.12.30
  • Published : 2019.09.25
⟨ Previous Next ⟩

Abstract

The present article researches large-amplitude thermal free vibration characteristics of nonlocal two-phase piezo-magnetic nano-size beams having geometric imperfections by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All previous studies on vibrations of piezoelectric-magnetic nano-size beams ignore the influences of geometric imperfections which are crucial since a nanobeam is not always ideal or perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtain nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic imperfection amplitude and substrate constants.

Keywords

Acknowledgement

Supported by : Mustansiriyah university

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. Alzahrani, E.O., Zenkour, A.M. and Sobhy, M. (2013), "Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium", Compos. Struct., 105, 163-172. https://doi.org/10.1016/j.compstruct.2013.04.045
  4. 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
  5. Ansari, R., Ramezannezhad, H. and Gholami, R. (2012), "Nonlocal beam theory for nonlinear vibrations of embedded multiwalled carbon nanotubes in thermal environment", Nonlinear Dyn., 67(3), 2241-2254. https://doi.org/10.1007/s11071-011-0142-z
  6. Ansari, R., Gholami, R and Rouhi, H. (2015), "Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory", Compos. Struct., 126, 216-226. https://doi.org/10.1016/j.compstruct.2015.02.068
  7. Arefi, M and Zenkour, A.M. (2016), "Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face-sheets", Smart Mater. Struct., 25(11), 115040. https://doi.org/10.1088/0964-1726/25/11/115040
  8. 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.
  9. 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
  10. Barati, M. R and Zenkour, A. (2017), "A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate", Compos. Struct., 168, 885-892. https://doi.org/10.1016/j.compstruct.2017.02.090
  11. Berrabah, H.M., Tounsi, A., Semmah, A. and Adda, B. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., Int. J., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
  12. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  13. Besseghier, A., Houari, M.S.A., Tounsi, A and Mahmoud, S.R. (2017), "Free vibration analysis of mbedded 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
  14. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  15. 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
  16. Chen, C., Li, S., Dai, L. and Qian, C. (2014), "Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces", Commun. Nonlinear Sci. Numer. Simul., 19(5), 1626-1637. https://doi.org/10.1016/j.cnsns.2013.09.017
  17. Ebrahimi, F. and Barati, M.R. (2016), "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. (2017), "Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates", J. Brazil. Soc. Mech. Sci. Eng., 39(6), 2203-2223. https://doi.org/10.1007/s40430-016-0646-z
  19. Ebrahimi, F., Mahmoodi, F. and Barati, M.R. (2017), "Thermo-mechanical vibration analysis of functionally graded micro/nanoscale beams with porosities based on modified couple stress theory", Adv. Mater. Res., Int. J., 6(3), 279-301. https://doi.org/10.12989/amr.2017.6.3.279
  20. 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
  21. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano. Res., Int. J., 4(1), 51-64. https://doi.org/10.12989/anr.2016.4.1.051
  22. 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
  23. Fang, B., Zhen, Y.X., Zhang, C.P. and Tang, Y. (2013), "Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory", Appl. Math. Model., 37(3), 1096-1107. https://doi.org/10.1016/j.apm.2012.03.032
  24. 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
  25. 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
  26. Karlicic, D., Kozic, P., Pavlovic, R. and Nesic, N. (2017), "Dynamic stability of single-walled carbon nanotube embedded in a viscoelastic medium under the influence of the axially harmonic load", Compos. Struct., 162, 227-243. https:r//doi.org/10.1016/j.compstruct.2016.12.003
  27. Karlicic, D., Cajic, M. and Adhikari, S. (2018), "Dynamic stability of a nonlinear multiple-nanobeam system. Nonlinear Dynamics, 93(3), 1495-1517. https://doi.org/10.1007/s11071-018-4273-3
  28. 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
  29. 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
  30. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011
  31. 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
  32. 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
  33. Mashat, D.S., Zenkour, A.M. and Sobhy, M. (2016), "Investigation of vibration and thermal buckling of nanobeams embedded in an elastic medium under various boundary conditions", J. Mech., 32(3), 277-287. https://doi.org/10.1017/jmech.2015.83
  34. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. Mirjavadi, S.S., 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
  42. 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
  43. Nan, C.W. (1994), "Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases", Physical Review B, 50(9), 6082. https://doi.org/10.1103/physrevb.50.6082
  44. 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
  45. Semmah, A., Beg, O.A., Mahmoud, S.R., Heireche, H. and Tounsi, A. (2014), "Thermal buckling properties of zigzag single-walled carbon nanotubes using a refined nonlocal model", Adv. Mater. Res., Int. J., 3(2), 77-89. https://doi.org/10.12989/amr.2014.3.2.077
  46. Sobhy, M. (2014a), "Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions", Acta Mechanica, 225(9), 2521-2538. https://doi.org/10.1007/s00707-014-1093-5
  47. Sobhy, M. (2014b), "Natural frequency and buckling of orthotropic nanoplates resting on two-parameter elastic foundations with various boundary conditions", J. Mech., 30(5), 443-453. https://doi.org/10.1017/jmech.2014.46
  48. Sobhy, M. (2015), "Levy-type solution for bending of single-layered graphene sheets in thermal environment using the two-variable plate theory", Int. J. Mech. Sci., 90, 171-178. https://doi.org/10.1016/j.ijmecsci.2014.11.014
  49. Sobhy, M. (2019), "Levy solution for bending response of FG carbon nanotube reinforced plates under uniform, linear, sinusoidal and exponential distributed loadings", Eng. Struct., 182, 198-212. https://doi.org/10.1016/j.engstruct.2018.12.071
  50. Sobhy, M. and Abazid, M.A. (2019), "Dynamic and instability analyses of FG graphene-reinforced sandwich deep curved nanobeams with viscoelastic core under magnetic field effect", Compos. Part B: Eng., 106966. https://doi.org/10.1016/j.compositesb.2019.106966
  51. Sobhy, M. and Radwan, A.F. (2017), "A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates", Int. J. Appl. Mech., 9(1), 1750008. https://doi.org/10.1142/S1758825117500089
  52. Sobhy, M. and Zenkour, A.M. (2018a), "Magnetic field effect on thermomechanical buckling and vibration of viscoelastic sandwich nanobeams with CNT reinforced face sheets on a viscoelastic substrate", Compos. Part B: Eng., 154, 492-506. https://doi.org/10.1016/j.compositesb.2018.09.011
  53. Sobhy, M. and Zenkour, A.M. (2018b), "The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations", Mech. Adv. Mater. Struct., 1-14. https://doi.org/10.1080/15376494.2018.1482579
  54. Sobhy, M. and Zenkour, A.M. (2018c), "Nonlocal thermal and mechanical buckling of nonlinear orthotropic viscoelastic nanoplates embedded in a visco-pasternak medium", Int. J. Appl. Mech., 10(8), 1850086. https://doi.org/10.1142/S1758825118500862
  55. 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
  56. 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
  57. Zenkour, A.M. and Sobhy, M. (2013), "Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler-Pasternak elastic substrate medium", Physica E: Low-dimens. Syst. Nanostruct., 53, 251-259. https://doi.org/10.1016/j.physe.2013.04.022
  58. Zenkour, A.M. and Sobhy, M. (2015), "A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment", Phys. E: Low-Dimens. Syst. Nanostruct., 70, 121-128. https://doi.org/10.1016/j.physe.2015.02.022

Cited by

  1. Finite element simulation for investigation on thermal post-buckling of geometrically imperfect GOP-reinforced beam vol.12, pp.2, 2021, https://doi.org/10.12989/acc.2021.12.2.135
  2. 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