Structural Engineering and Mechanics

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A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium

  • Aissani, Khadidja (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de Genie Cvil) ;
  • Bouiadjra, Mohamed Bachir (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de Genie Cvil) ;
  • Ahouel, Mama (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de Genie Cvil)
  • Received : 2015.05.12
  • Accepted : 2015.07.07
  • Published : 2015.08.25
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Abstract

This work presents a new nonlocal hyperbolic shear deformation beam theory for the static, buckling and vibration of nanoscale-beams embedded in an elastic medium. The present model is able to capture both the nonlocal parameter and the shear deformation effect without employing shear correction factor. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as nanobeams. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale-beam are obtained using Hamilton's principle. The effect of the surrounding elastic medium on the deflections, critical buckling loads and frequencies of the nanobeam is investigated. Both Winkler-type and Pasternak-type foundation models are used to simulate the interaction of the nanobeam with the surrounding elastic medium. Analytical solutions are presented for a simply supported nanoscale-beam, and the obtained results compare well with those predicted by the other nonlocal theories available in literature.

Keywords

Acknowledgement

Supported by : Algerian National Thematic Agency of Research in Science and Technology (ATRST), university of Sidi Bel Abbes (UDL SBA)

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  15. Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory vol.64, pp.6, 2015, https://doi.org/10.12989/sem.2017.64.6.683
  16. Forced vibration analysis of cracked functionally graded microbeams vol.6, pp.1, 2015, https://doi.org/10.12989/anr.2018.6.1.039
  17. Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments vol.65, pp.6, 2018, https://doi.org/10.12989/sem.2018.65.6.645
  18. A unified formulation for modeling of inhomogeneous nonlocal beams vol.66, pp.3, 2015, https://doi.org/10.12989/sem.2018.66.3.369
  19. Bending of a cracked functionally graded nanobeam vol.6, pp.3, 2015, https://doi.org/10.12989/anr.2018.6.3.219
  20. Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory vol.6, pp.3, 2018, https://doi.org/10.12989/anr.2018.6.3.279
  21. Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials vol.7, pp.1, 2015, https://doi.org/10.12989/anr.2019.7.1.051
  22. Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix vol.70, pp.3, 2019, https://doi.org/10.12989/sem.2019.70.3.269
  23. A review of mechanical analyses of rectangular nanobeams and single-, double-, and multi-walled carbon nanotubes using Eringen’s nonlocal elasticity theory vol.89, pp.9, 2015, https://doi.org/10.1007/s00419-019-01542-z
  24. Flexoelectric effects on dynamic response characteristics of nonlocal piezoelectric material beam vol.8, pp.4, 2015, https://doi.org/10.12989/amr.2019.8.4.259
  25. Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects vol.7, pp.2, 2015, https://doi.org/10.12989/aas.2020.7.2.169
  26. A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams vol.9, pp.1, 2015, https://doi.org/10.12989/amr.2020.9.1.033
  27. A comprehensive review on the modeling of smart piezoelectric nanostructures vol.74, pp.5, 2015, https://doi.org/10.12989/sem.2020.74.5.611
  28. Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.201
  29. Dynamic response of size-dependent porous functionally graded beams under thermal and moving load using a numerical approach vol.7, pp.2, 2015, https://doi.org/10.12989/smm.2020.7.2.069
  30. On scale-dependent stability analysis of functionally graded magneto-electro-thermo-elastic cylindrical nanoshells vol.75, pp.6, 2015, https://doi.org/10.12989/sem.2020.75.6.659
  31. Porosity effects on post-buckling behavior of geometrically imperfect metal foam doubly-curved shells with stiffeners vol.75, pp.6, 2015, https://doi.org/10.12989/sem.2020.75.6.701
  32. Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method vol.76, pp.3, 2015, https://doi.org/10.12989/sem.2020.76.3.413
  33. Wave propagation analysis of a rectangular sandwich composite plate with tunable magneto-rheological fluid core vol.27, pp.11, 2015, https://doi.org/10.1177/1077546320938189
  34. On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations vol.40, pp.3, 2021, https://doi.org/10.12989/scs.2021.40.3.389