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On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model

  • Belkorissat, Ismahene ;
  • Houari, Mohammed Sid Ahmed ;
  • Tounsi, Abdelouahed ;
  • Bedia, E.A. Adda ;
  • Mahmoud, S.R.
  • Received : 2014.07.17
  • Accepted : 2014.11.06
  • Published : 2015.04.25

Abstract

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

Keywords

nonlocal elasticity theory;nano-plates;free vibration;refined plate theory;functionally graded materials

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  53. Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods vol.229, pp.1, 2018, https://doi.org/10.1007/s00707-017-1952-y
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  58. A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates vol.22, pp.2, 2016, https://doi.org/10.12989/scs.2016.22.2.257
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  61. Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory vol.10, pp.3, 2016, https://doi.org/10.12989/gae.2016.10.3.357
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  71. Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors vol.131, pp.6, 2017, https://doi.org/10.12693/APhysPolA.131.1439
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  77. Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0922-5
  78. Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory vol.57, pp.4, 2016, https://doi.org/10.12989/sem.2016.57.4.617
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  81. Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method 2017, https://doi.org/10.1016/j.aej.2017.06.001
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  83. Parametric excitation analysis of a piezoelectric-nanotube conveying fluid under multi-physics field 2017, https://doi.org/10.1007/s00542-017-3670-8
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  85. Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept vol.20, pp.5, 2016, https://doi.org/10.12989/scs.2016.20.5.963
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