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Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory

  • Besseghier, Abderrahmane (Faculty of Technology, Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Houari, Mohammed Sid Ahmed (Faculty of Technology, Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Faculty of Technology, Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2016.09.15
  • Accepted : 2017.01.17
  • Published : 2017.06.25
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Abstract

In this work, free vibration analysis of size-dependent functionally graded (FG) nanoplates resting on two-parameter elastic foundation is investigated based on a novel nonlocal refined trigonometric shear deformation theory for the first time. This theory includes undetermined integral variables and contains only four unknowns, with is even less than the conventional first shear deformation theory (FSDT). Mori-Tanaka model is employed to describe gradually distribution of material properties along the plate thickness. Size-dependency of nanosize FG plate is captured via the nonlocal elasticity theory of Eringen. By implementing Hamilton's principle the equations of motion are obtained for a refined four-variable shear deformation plate theory and then solved analytically. To show the accuracy of the present theory, our research results in specific cases are compared with available results in the literature and a good agreement will be demonstrated. Finally, the influence of various parameters such as nonlocal parameter, power law indexes, elastic foundation parameters, aspect ratio, and the thickness ratio on the non-dimensional frequency of rectangular FG nanoscale plates are presented and discussed in detail.

Keywords

References

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  2. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment pp.1539-7742, 2019, https://doi.org/10.1080/15397734.2018.1557529
  3. Nonlinear Performance of Concrete Beam Reinforced with Prestressed Hybrid Cfrp/Gfrp Composite Sheet vol.27, pp.5, 2017, https://doi.org/10.1177/096369351802700505
  4. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2017, https://doi.org/10.12989/sem.2019.70.4.407
  5. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2017, https://doi.org/10.12989/scs.2019.31.5.503
  6. Fracture problems, vibration, buckling, and bending analyses of functionally graded materials: A state-of-the-art review including smart FGMS vol.37, pp.5, 2017, https://doi.org/10.1080/02726351.2017.1410265
  7. Buckling analysis of porous FGM sandwich nanoplates due to heat conduction via nonlocal strain gradient theory vol.1, pp.1, 2017, https://doi.org/10.1088/2631-8695/ab38f9
  8. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  9. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2017, https://doi.org/10.12989/was.2019.29.6.371
  10. Bending, Buckling and Free Vibration Analysis of Size-Dependent Nanoscale FG Beams Using Refined Models and Eringen’s Nonlocal Theory vol.12, pp.1, 2020, https://doi.org/10.1142/s1758825120500076
  11. Buckling response of smart plates reinforced by nanoparticles utilizing analytical method vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.001
  12. 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