694
Views
49
CrossRef citations to date
0
Altmetric
Original Articles

Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory

, , , &
Pages 1252-1264 | Received 25 Aug 2015, Accepted 29 Jan 2016, Published online: 09 Sep 2016

References

  • Z.W. Pan, Z.R. Dai, and Z.L. Wang, Nanobelts of semiconducting oxides, Science, vol. 291, no. 5510, pp. 1947–1949, 2001.
  • Z.L. Wang, ZnO nanowire and nanobelt platform for nanotechnology, Mater. Sci. Eng. R., vol. 64, no. 3–4, pp. 33–71, 2009.
  • U. Galan, Y.R. Lin, G.J. Ehlert, and H.A. Sodano, Effect of ZnO nanowire morphology on the interfacial strength of nanowire coated carbon fibers, Compos. Sci. Technol., vol. 71, no. 7, pp. 946–954, 2011.
  • S. Xu and Z.L. Wang, One-dimensional ZnO nanostructures: Solution growth and functional properties (invited review), Nano Res., vol. 4, no. 11, pp. 1013–1098, 2011.
  • S.M. Tanner, J.M. Gray, C.T. Rogers, K.A. Bertness, and N.A. Sanford, High-Q GaN nanowire resonators and oscillators, Appl. Phys. Lett., vol. 91, art. 203117, 2007.
  • J.H. He, C.L. Hsin, J. Liu, L.J. Chen, and Z.L. Wang, Piezoelectric gated diode of a single ZnO nanowire, Adv. Mater., vol. 19, no. 6, pp. 781–784, 2007.
  • C.Q. Chen, Y. Shi, Y.S. Zhang, J. Zhu, and Y.J. Yan, Size dependence of Young's modulus in ZnO nanowires, Phys. Rev. Lett., vol. 96, no. 7, art. 075505, 2006.
  • G. Stan, C.V. Ciobanu, P.M. Parthangal, and R.F. Cook, Diameter-dependent radial and tangential elastic moduli of ZnO nanowires, Nano Lett., vol. 7, no. 12, pp. 3691–3697, 2007.
  • A.C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci., vol. 10, no. 1, pp. 1–16, 1972.
  • A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., vol. 54, pp. 4703–4710, 1983.
  • A.C. Eringen, Nonlocal Continuum Field Theories, Springer, NewYork, 2002.
  • J.N. Reddy, Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates, Int. J. Eng. Sci., vol. 48, no. 11, pp. 1507–1518, 2010.
  • Y.M. Xu, H.S. Shen, and C.L. Zhang, Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments, Compos. Struct., vol. 98, pp. 294–302, 2013.
  • M.E. Golmakani and J. Rezatalab, Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics, Compos. Struct., vol. 111, pp. 85–97, 2014.
  • M. Sobhy, Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium, Physica E, vol. 56, pp. 400–409, 2014.
  • S.C. Pradhan and T. Murmu, Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory, Physica E, vol. 42, no. 5, pp. 1293–1301, 2010.
  • H.S. Shen and C.L. Zhang, Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model, Compos. Struct., vol. 92, no. 5, pp. 1073–1084, 2010.
  • A.M. Zenkour and M. Sobhy, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler-Pasternak elastic substrate medium, Physica E, vol. 53, pp. 251–259, 2013.
  • H.S. Shen, Nonlocal shear deformable shell model for torsional buckling and postbuckling of microtubules in thermal environments, Mech. Res. Commun., vol. 54, pp. 83–95, 2013.
  • S.C. Pradhan and A. Kumar, Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method, Compos. Struct., vol. 93, no. 2, pp. 774–779, 2011.
  • R. Ansari, B. Arash, and H. Rouhi, Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity, Compos. Struct., vol. 93, no. 9, pp. 2419–2429, 2011.
  • S. Hosseini-Hashemi, M. Zare, and R. Nazemnezhad, An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity, Compos. Struct., vol. 100, pp. 290–299, 2013.
  • L.L. Ke, Y. Xiang, J. Yang, and S. Kitipornchai, Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Comput. Mater. Sci., vol. 47, no. 2, pp. 409–417, 2009.
  • J. Yang, L.L. Ke, and S. Kitipornchai, Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E, vol. 42, no. 5, pp. 1727–1735, 2010.
  • L. Shen, H.S. Shen, and C.L. Zhang, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Comput. Mater. Sci., vol. 48, no. 3, pp. 680–685, 2010.
  • Q. Wang and V.K. Varadan, Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes, Smart Mater. Struct., vol. 16, pp. 178–190, 2007.
  • A.L. Chen, Y.S. Wang, L.L. Ke, Y.F. Guo, and Z.D. Wang, Wave propagation in nanoscaled periodic layered structures, J. Comput. Theor. Nanosci., vol. 10, no. 10, pp. 2427–2437, 2013.
  • C. Liu, L.L. Ke, Y.S. Wang, J. Yang, and S. Kitipornchai, Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Compos. Struct., vol. 106, pp. 167–174, 2013.
  • L.L. Ke, C. Liu, and Y.S. Wang, Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions, Physica E, vol. 66, pp. 93–106, 2015.
  • S.R. Asemi and A. Farajpour, Thermo-electro-mechanical vibration of coupled piezoelectric nanoplate systems under non-uniform voltage distribution embedded in Pasternak elastic medium, Curr. Appl. Phys., vol. 14, no. 5, pp. 814–832, 2014.
  • S.R. Asemi, A. Farajpour, H.R. Asemi, and M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E, vol. 63, pp. 169–179, 2014.
  • A.G. Arani, M.A. Roudbari, and S. Amir, Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle, Physica B, vol. 407, no. 17, pp. 3646–3653, 2012.
  • A.G. Arani, V. Atabakhshian, A. Loghman, A.R. Shajari, and S. Amir, Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Physica B, vol. 407, no. 17, pp. 2549–2555, 2012.
  • A.G. Arani, S. Amir, A.R. Shajari, and M.R. Mozdianfard, Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory, Composites Part B, vol. 43, no. 2, pp. 195–203, 2012.
  • A.G. Arani, M. Abdollahian, R. Kolahchi, and A.H. Rahmati, Electro-thermo-torsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composites Part B, vol. 51, pp. 291–299, 2013.
  • K.F. Wang and B.L. Wang, The electromechanical coupling behavior of piezoelectric nanowires: Surface and small-scale effects, Europhys. Lett., vol. 97, art. 66005, 2012.
  • L.L. Zhang, J.X. Liu, X.Q. Fang, and G.Q. Nie, Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates, Eur. J. Mech. A. Solids, vol. 46, pp. 22–29, 2014.
  • L.L. Ke, Y.S. Wang, and Z.D. Wang, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Compos. Struct., vol. 94, no. 6, pp. 2038–2047, 2012.
  • C. Liu, L.L. Ke, Y.S. Wang, J. Yang, and S. Kitipornchai, Buckling and post-buckling of size-dependent piezoelectric Timoshenko nanobeams subject to thermo-electro-mechanical loadings, Int. J. Struct. Stab. Dyn., vol. 14, no. 3, art. 1350067, 2014.
  • S.R. Asemi, A. Farajpour, and M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Compos. Struct., vol. 116, pp. 703–712, 2014.
  • C. Liu, L.L. Ke, Y.S. Wang, and J. Yang, Nonlinear vibration of nonlocal piezoelectric nanoplates, Int. J. Struct. Stab. Dyn., vol. 15, no. 8, art. 1540013, 2015.
  • M.H. Zhao, C.F. Qian, S.W.R. Lee, P. Tong, H. Suemasu, and T.Y. Zhang, Electro-elastic analysis of piezoelectric laminated plates, Adv. Compos. Mater., vol. 16, no. 1, pp. 63–81, 2006.
  • M. Pietrzakowski, Piezoelectric control of composite plate vibration: Effect of electric potential distribution, Compos. Struct., vol. 86, no. 9, pp. 948–954, 2008.
  • Q. Wang, Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer, Int. J. Solid Struct., vol. 39, no. 11, pp. 3023–3037, 2002.
  • C. Shu, Differential Quadrature and its Application in Engineering, Springer, London, 2002.
  • H.N. Chu and G. Herrmann, Influence of large amplitudes on free flexural vibrations of rectangular plates, J. Appl. Mech., vol. 23, no. 5–6, pp. 532–540, 1956.
  • N. Sundararajan, T. Prakash, and M. Ganapathi, Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments, Finite Elem. Anal. Des., vol. 42, no. 2, pp. 152–168, 2005.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.