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Advances in Nano Research
  Volume 5, Number 2, June 2017 , pages 113-126

A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams
Ismail Bensaid

    This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.
Key Words
    nlocal theory; nanosize beam; hyperbolic shear deformation theory; bending; vibration
IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University of Tlemcen, Tlemcen, Algeria.

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