Smart Structures and Systems

  • 제20권5호
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  • Pages.573-581
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  • 2017
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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Coupled effects of electrical polarization-strain gradient on vibration behavior of double-layered flexoelectric nanoplates

  • Barati, Mohammad Reza (Aerospace Engineering Department & Center of Excellence in Computational Aerospace, Amirkabir University of Technology)
  • 투고 : 2017.06.23
  • 심사 : 2017.09.05
  • 발행 : 2017.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

A vibrating double-layered nanoscale piezoelectric plate is developed accounting for the flexoelectricity and surface effects. The flexoelectricity is due to the coupling between electrical polarization and strain gradient. Applying Hamilton's principle, the governing equations and related boundary conditions are derived. Assuming suitable approximate functions, the governing equations are numerically solved for simply-supported and clamped boundary conditions. Obtained results indicate that both the flexoelectricity and surface effects possess notable impact on the vibration frequencies of the system. Only flexoelectricity yields a considerable difference between the present model and previous investigations on conventional piezoelectric nanoplates. Generally, a parametric study has been performed to examine the effects of surface elasticity, flexoelectricity, applied electric voltage, interlayer stiffness, geometrical parameters and boundary conditions on vibration frequencies of piezoelectric nanoplates.

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참고문헌

  1. 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., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  2. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125
  3. Arani, A.G., Kolahchi, R. and Zarei, M.S. (2015), "Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory", Compos. Struct., 132, 506-526. https://doi.org/10.1016/j.compstruct.2015.05.065
  4. Asemi, S.R., Farajpour, A. and Mohammadi, M. (2014), "Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory", Compos. Struct., 116, 703-712. https://doi.org/10.1016/j.compstruct.2014.05.015
  5. Asemi, S.R., Farajpour, A., Asemi, H.R. and Mohammadi, M. (2014), "Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM", Physica E: Low-dimensional Syst. Nanostruct., 63, 169-179. https://doi.org/10.1016/j.physe.2014.05.009
  6. Barati, M.R. and Shahverdi, H. (2017), "Small-scale effects on the dynamic response of inhomogeneous nanobeams on elastic substrate under uniform dynamic load", The European Physical Journal Plus, 132(4), 167. https://doi.org/10.1140/epjp/i2017-11441-9
  7. 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., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  8. 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
  9. Ebrahimi, F. and Barati, M.R. (2017a), "Damping vibration analysis of smart piezoelectric polymeric nanoplates on viscoelastic substrate based on nonlocal strain gradient theory", Smart Mater. Struct., 26(6), 065018. https://doi.org/10.1088/1361-665X/aa6eec
  10. Ebrahimi, F. and Barati, M.R. (2017b), "Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory", The European Physical Journal Plus, 132(1), 19. https://doi.org/10.1140/epjp/i2017-11320-5
  11. Ebrahimi, F. and Barati, M.R. (2017c), "Vibration analysis of sizedependent flexoelectric nanoplates incorporating surface and thermal effects", Mech. Adv. Mater. Struct., 1-11.
  12. Ebrahimi, F. and Salari, E. (2017), "Semi-analytical vibration analysis of functionally graded size-dependent nanobeams with various boundary conditions", Smart Struct. Syst., 19(3), 243-257. https://doi.org/10.12989/sss.2017.19.3.243
  13. Elmerabet, A.H., Heireche, H., Tounsi, A. and Semmah, A. (2017), "Buckling temperature of a single-walled boron nitride nanotubes using a novel nonlocal beam model", Adv. Nano Res., 5(1), 1-12. https://doi.org/10.12989/anr.2017.5.1.001
  14. 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
  15. Gholami, R. and Ansari, R. (2017), "A unified nonlocal nonlinear higher-order shear deformable plate model for postbuckling analysis of piezoelectric-piezomagnetic rectangular nanoplates with various edge supports", Compos. Struct., 166, 202-218. https://doi.org/10.1016/j.compstruct.2017.01.045
  16. Gurtin, M.E. and Ian Murdoch, A. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. An., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  17. Karimi, M. and Shahidi, A.R. (2017), "Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loadings", Appl. Phys. A, 123(5), 304. https://doi.org/10.1007/s00339-017-0828-2
  18. 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
  19. Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  20. 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
  21. 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
  22. Liang, X., Yang, W., Hu, S. and Shen, S. (2016), "Buckling and vibration of flexoelectric nanofilms subjected to mechanical loads", J. Phys. D: Appl. Phys., 49(11), 115307. https://doi.org/10.1088/0022-3727/49/11/115307
  23. Ray, M.C. (2016), "Analysis of smart nanobeams integrated with a flexoelectric nano actuator layer", Smart Mater. Struct., 25(5), 055011. https://doi.org/10.1088/0964-1726/25/5/055011
  24. Shen, J.P., Li, C., Fan, X.L. and Jung, C.M. (2017), "Dynamics of silicon nanobeams with axial motion subjected to transverse and longitudinal loads considering nonlocal and surface effects", Smart Struct. Syst., 19(1), 105-113. https://doi.org/10.12989/sss.2017.19.1.105
  25. Wang, W., Li, P., Jin, F. and Wang, J. (2016), "Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects", Compos. Struct., 140, 758-775. https://doi.org/10.1016/j.compstruct.2016.01.035
  26. Yan, Z. (2016), "Size-dependent bending and vibration behaviors of piezoelectric circular nanoplates", Smart Mater. Struct., 25(3), 035017. https://doi.org/10.1088/0964-1726/25/3/035017
  27. Yan, Z. and Jiang, L. (2013), "Size-dependent bending and vibration behaviour of piezoelectric nanobeams due to flexoelectricity", J. Phys. D: Appl. Phys., 46(35), 355502. https://doi.org/10.1088/0022-3727/46/35/355502
  28. 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
  29. Zang, J., Fang, B., Zhang, Y.W., Yang, T.Z. and Li, D.H. (2014), "Longitudinal wave propagation in a piezoelectric nanoplate considering surface effects and nonlocal elasticity theory", Physica E: Low-dimensional Syst. Nanostruct., 63, 147-150. https://doi.org/10.1016/j.physe.2014.05.019
  30. Zhang, L.L., Liu, J.X., Fang, X.Q. and Nie, G.Q. (2014), "Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates", Eur. J. Mech.-A-Solid., 46, 22-29. https://doi.org/10.1016/j.euromechsol.2014.01.005
  31. Zhang, Y., Hong, J., Liu, B. and Fang, D. (2009), "Strain effect on ferroelectric behaviors of BaTiO3 nanowires: a molecular dynamics study", Nanotechnology, 21(1), 015701. https://doi.org/10.1088/0957-4484/21/1/015701
  32. Zhang, Z. and Jiang, L. (2014), "Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity", J. Appl. Phys., 116(13), 134308. https://doi.org/10.1063/1.4897367

피인용 문헌

  1. Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading vol.78, pp.1, 2017, https://doi.org/10.12989/sem.2021.78.1.015