Advances in materials Research

  • 제8권4호
  • /
  • Pages.259-274
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  • 2019
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  • 2234-0912(pISSN)
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  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Flexoelectric effects on dynamic response characteristics of nonlocal piezoelectric material beam

  • Kunbar, Laith A. Hassan (Al-Mustansiriah University, Engineering Collage P.O. Box 46049) ;
  • Alkadhimi, Basim Mohamed (Wasit University, College of Engineering, Electrical Engineering Department) ;
  • Radhi, Hussein Sultan (University of Diyala, College of Engineering, Computer Engineering Department) ;
  • Faleh, Nadhim M. (Al-Mustansiriah University, Engineering Collage P.O. Box 46049)
  • 투고 : 2019.11.12
  • 심사 : 2019.12.30
  • 발행 : 2019.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

Flexoelectric effect has a major role on mechanical responses of piezoelectric materials when their dimensions become submicron. Applying differential quadrature (DQ) method, the present article studies dynamic characteristics of a small scale beam made of piezoelectric material considering flexoelectric effect. In order to capture scale-dependency of such piezoelectric beams, nonlocal elasticity theory is utilized and also surface effects are included for better structural modeling. Governing equations have been derived by utilizing Hamilton's rule with the assumption that the scale-dependent beam is subjected to thermal environment leading to uniform temperature variation across the thickness. Obtained results based on DQ method are in good agreement with previous data on pizo-flexoelectric beams. Finally, it would be indicated that dynamic response characteristics and vibration frequencies of the nano-size beam depends on the existence of flexoelectric influence and the magnitude of scale factors.

키워드

과제정보

The authors would like to thank Mustansiriyah university (www.uomustansiriyah.edu.iq) Baghdad-Iraq, Wasit university and university of Diyala for their support in the present work.

참고문헌

  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. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, Int. J., 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489
  3. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and Alhodaly, M.S. (2019), "A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175
  4. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, Int. J., 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347
  5. 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
  6. Aissani, K., Bouiadjra, M.B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., Int. J., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743
  7. 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
  8. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., Int. J., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195
  9. Alasadi, A.A., Ahmed, R.A. and Faleh, N.M. (2019), "Analyzing nonlinear vibrations of metal foam nanobeams with symmetric and non-symmetric porosities", Adv. Aircr. Spacecr. Sci., 6(4), 273-282. https://doi.org/10.12989/aas.2019.6.4.273
  10. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic microcomposite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., Int. J., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  11. 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
  12. 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
  13. 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
  14. Bensaid, I. and Guenanou, A. (2017), "Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities", Adv. Mater. Res., Int. J., 6(1), 45-63. https://doi.org/10.12989/amr.2017.6.1.045
  15. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., Int. J., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351
  16. 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
  17. 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
  18. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  19. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503
  20. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., Int. J., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161
  21. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 191-208. https://doi.org/10.12989/anr.2019.7.3.191
  22. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., Int. J., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
  23. Civalek, O and Demir, C (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Mathe. Computat., 289, 335-352. https://doi.org/10.1016/j.amc.2016.05.034
  24. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, Int. J., 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369
  25. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubesreinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117
  26. Ebrahimi, F. and Barati, M.R. (2017), "Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory", Eur. Phys. J. Plus, 132(1), 19. https://doi.org/10.1140/epjp/i2017-11320-5
  27. 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
  28. Fernandez-Saez, J., Zaera, R., Loya, J.A. and Reddy, J.N. (2016), "Bending of Euler-Bernoulli beams using Eringen's integral formulation: a paradox resolved", Int. J. Eng. Sci., 99, 107-116. https://doi.org/10.1016/j.ijengsci.2015.10.013
  29. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Rational Mech. Anal., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  30. Jiang, X., Huang, W. and Zhang, S. (2013), "Flexoelectric nano-generator: Materials, structures and devices", Nano Energy, 2(6), 1079-1092. https://doi.org/10.1016/j.nanoen.2013.09.001
  31. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "On pre-stressed functionally graded anisotropic nanoshell in magnetic feld", J. Brazil. Soc. Mech. Sci. Eng., 41, 495. https://doi.org/10.1007/s40430-019-1996-0
  32. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9
  33. Ke, L.L. and Wang, Y.S. (2012), "Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory", Smart Mater. Struct., 21(2), 025018. https://doi.org/10.1088/0964-1726/21/2/025018
  34. Ke, L.L., Liu, C. and Wang, Y.S. (2015), "Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions", Physica E: Low-dimens. Syst. Nanostruct., 66, 93-106. https://doi.org/10.1016/j.physe.2014.10.002
  35. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-019-00732-1
  36. Kocaturk, T. and Akbas, S.D. (2013), "Wave propagation in a microbeam based on the modified couple stress theory", Struct. Eng. Mech., Int. J., 46(3), 417-431. https://doi.org/10.12989/sem.2013.46.3.417
  37. Li, Y.S. and Pan, E. (2016), "Bending of a sinusoidal piezoelectric nanoplate with surface effect", Compos. Struct., 136, 45-55. https://doi.org/10.1016/j.compstruct.2015.09.047
  38. Liang, X., Hu, S. and Shen, S. (2014), "Effects of surface and flexoelectricity on a piezoelectric nanobeam", Smart Mater. Struct., 23(3), 035020. https://doi.org/10.1088/0964-1726/23/3/035020
  39. Liang, X., Hu, S. and Shen, S. (2015), "Size-dependent buckling and vibration behaviors of piezoelectric nanostructures due to flexoelectricity", Smart Mater. Struct., 24(10), 105012. https://doi.org/10.1088/0964-1726/24/10/105012
  40. Liu, C., Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2013), "Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory", Compos. Struct., 106, 167-174. https://doi.org/10.1016/j.compstruct.2013.05.031
  41. Liu, C., Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Buckling and post-buckling of sizedependent piezoelectric Timoshenko nanobeams subject to thermo-electro-mechanical loadings", Int. J. Struct. Stabil. Dyn., 14(3), 1350067. https://doi.org/10.1142/S0219455413500673
  42. Liu, C., Ke, L.L., Wang, Y.S. and Yang, J. (2015), "Nonlinear vibration of nonlocal piezoelectric nanoplates", Int. J. Struct. Stabil. Dyn., 15(8), 1540013. https://doi.org/10.1142/S0219455415400131
  43. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177/1099636217727577
  44. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., Int. J., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595
  45. 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
  46. 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
  47. 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
  48. 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
  49. 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
  50. 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
  51. 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
  52. 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
  53. 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
  54. 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
  55. 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
  56. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G. and Azimzadeh, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method. Struct. Eng. Mech., Int. J., 54(6), 1061-1073. https://doi.org/10.12989/sem.2015.54.6.1061
  57. 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
  58. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
  59. Shafiei, N., Mirjavadi, S.S., Afshari, B.M., Rabby, S. and Hamouda, A.M.S. (2017), "Nonlinear thermal buckling of axially functionally graded micro and nanobeams", Compos. Struct., 168, 428-439. https://doi.org/10.1016/j.compstruct.2017.02.048
  60. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., Int. J., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637
  61. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., Int. J., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  62. Wang, K.F. and Wang, B.L. (2011), "Vibration of nanoscale plates with surface energy via nonlocal elasticity. Physica E: Low-dimens. Syst. Nanostruct., 44(2), 448-453. https://doi.org/10.1016/j.physe.2011.09.019
  63. Wang, K.F. and Wang, B.L. (2012), "The electromechanical coupling behavior of piezoelectric nanowires: surface and small-scale effects", EPL (Europhysics Letters), 97(6), 66005. https://doi.org/10.1209/0295-5075/97/66005
  64. Yan, Z. and Jiang, L.Y. (2011), "The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects", Nanotechnology, 22(24), 245703. https://doi.org/10.1088/0957-4484/22/24/245703
  65. Yang, W., Liang, X. and Shen, S. (2015), "Electromechanical responses of piezoelectric nanoplates with flexoelectricity", Acta Mechanica, 226(9), 3097-3110. https://doi.org/10.1007/s00707-015-1373-8
  66. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
  67. 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
  68. Zhang, C., Chen, W. and Zhang, C. (2013), "Two-dimensional theory of piezoelectric plates considering surface effect", Eur. J. Mech.-A/Solids, 41, 50-57. https://doi.org/10.1016/j.euromechsol.2013.02.005
  69. Zhang, Z., Yan, Z. and Jiang, L. (2014a), "Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoplate", J. Appl. Phys., 116(1), 014307. https://doi.org/10.1063/1.4886315
  70. Zhang, L.L., Liu, J.X., Fang, X.Q. and Nie, G.Q. (2014b), "Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects", Physica E: Low-dimens. Syst. Nanostruct., 57, 169-174. https://doi.org/10.1016/j.physe.2013.11.007