Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Modeling the size effect on vibration characteristics of functionally graded piezoelectric nanobeams based on Reddy's shear deformation beam theory

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Fardshad, Ramin Ebrahimi (Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University)
  • Received : 2017.06.23
  • Accepted : 2018.02.02
  • Published : 2018.06.25
⟨ Previous Next ⟩

Abstract

In this work, free vibration characteristics of functionally graded piezoelectric (FGP) nanobeams based on third order parabolic shear deformation beam theory are studied by presenting a Navier type solution as the first attempt. Electro-mechanical properties of FGP nanobeam are supposed to change continuously throughout the thickness based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for third order shear deformable piezoelectric FG nanobeams are obtained and they are solved applying analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of the FGP nanobeams. The influences of several parameters including, external electric voltage, power-law exponent, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams is discussed in detail.

Keywords

References

  1. Ansari, R., Pourashraf, T. and Gholami, R. (2015), "An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory", Thin-Wall. Struct., 93, 169-176. https://doi.org/10.1016/j.tws.2015.03.013
  2. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimen. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  3. Dehrouyeh-Semnani, A.M. and Nikkhah-Bahrami, M. (2015), "The influence of size-dependent shear deformation on mechanical behavior of microstructures-dependent beam based on modified couple stress theory", Compos. Struct., 123, 325-336. https://doi.org/10.1016/j.compstruct.2014.12.038
  4. Doroushi, A., Eslami, M.R. and Komeili, A. (2011), "Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory", J. Intel. Mater. Syst. Struct., 22(3), 231-243. https://doi.org/10.1177/1045389X11398162
  5. Ebrahimi, F. and Salari, E. (2015a), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES: Comput. Model. Eng. Sci., 105(2), 151-181
  6. Ebrahimi, F. and Salari, E. (2015b), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. Part B: Eng., 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  7. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Technol., 29(3), 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  8. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  9. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013a), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Composite Structures, 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039
  10. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013b), "Static and stability analysis of nonlocal functionally graded nanobeams", Composite Structures, 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030
  11. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  12. 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
  13. 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
  14. Filippi, M., Carrera, E. and Zenkour, A.M. (2015), "Static analyses of FGM beams by various theories and finite elements", Compos. Part B: Eng., 72, 1-9.
  15. Hosseini-Hashemi, S., Nahas, I., Fakher, M. and Nazemnezhad, R. (2014), "Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity", Acta Mechanica, 225(6), 1555-1564. https://doi.org/10.1007/s00707-013-1014-z
  16. Kiani, Y., Rezaei, M., Taheri, S. and Eslami, M.R. (2011), "Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams", Int. J. Mech. Mater. Des., 7(3), 185-197. https://doi.org/10.1007/s10999-011-9158-2
  17. Komijani, M., Kiani, Y., Esfahani, S.E. and Eslami, M.R. (2013), "Vibration of thermo-electrically postbuckled rectangular functionally graded piezoelectric beams", Compos. Struct., 98, 143-152. https://doi.org/10.1016/j.compstruct.2012.10.047
  18. Lezgy-Nazargah, M. (2015), "A three-dimensional exact state-space solution for cylindrical bending of continuously non-homogenous piezoelectric laminated plates with arbitrary gradient composition", Arch. Mech., 67(1), 25-51.
  19. Lezgy-Nazargah, M. (2016), "A three-dimensional Peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending", Scientia Iranica A, 23(3), 788-801. https://doi.org/10.24200/sci.2016.2159
  20. Lezgy-Nazargah, M., Vidal, P. and Polit, O. (2013), "An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams", Compos. Struct., 104, 71-84. https://doi.org/10.1016/j.compstruct.2013.04.010
  21. 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
  22. 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
  23. Li, Y.S., Feng, W.J. and Cai, Z.Y. (2014), "Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory", Compos. Struct., 115, 41-50. https://doi.org/10.1016/j.compstruct.2014.04.005
  24. Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. https://doi.org/10.1016/j.compstruct.2013.12.006
  25. Rahmani, O. and Jandaghian, A.A. (2015), "Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory", Appl. Phys. A, 119(3), 1019-1032. https://doi.org/10.1007/s00339-015-9061-z
  26. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  27. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  28. Sharabiani, P.A. and Yazdi, M.R.H. (2013), "Nonlinear free vibrations of functionally graded nanobeams with surface effects", Compos. Part B: Eng., 45(1), 581-586. https://doi.org/10.1016/j.compositesb.2012.04.064
  29. Shegokar, N.L. and Lal, A. (2014), "Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties", Meccanica, 49(5), 1039-1068. https://doi.org/10.1007/s11012-013-9852-2
  30. Shi, Z.F. and Chen, Y. (2004), "Functionally graded piezoelectric cantilever beam under load", Arch. Appl. Mech., 74(3-4), 237-247. https://doi.org/10.1007/s00419-004-0346-5
  31. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  32. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mechanica, 94(3-4), 195-220. https://doi.org/10.1007/BF01176650
  33. Su, Z., Jin, G. and Ye, T. (2016), "Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions", Smart Mater. Struct., 25(6), 065003. https://doi.org/10.1088/0964-1726/25/6/065003
  34. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  35. Uymaz, B. (2013), "Forced vibration analysis of functionally graded beams using nonlocal elasticity", Compos. Struct., 105, 227-239. https://doi.org/10.1016/j.compstruct.2013.05.006
  36. Yang, J. and Xiang, H.J. (2007), "Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators", Smart Mater. Struct., 16(3), 784. https://doi.org/10.1088/0964-1726/16/3/028
  37. Zhu, X. and Li, L. (2017), "Twisting statics of functionally graded nanotubes using Eringen's nonlocal integral model", Compos. Struct., 178, 87-96. https://doi.org/10.1016/j.compstruct.2017.06.067

Cited by

  1. Instability analysis of bi-axial micro-scanner under electromagnetic actuation including small scale and damping effects vol.26, pp.8, 2020, https://doi.org/10.1007/s00542-020-04802-z