Structural Engineering and Mechanics

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Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories

  • Rahmani, Omid (Structures and New Advanced Materials Laboratory Department of Mechanical Engineering, University of Zanjan) ;
  • Asemani, S. Samane (Department of Mechanical Engineering, University of Tarbiat Modares)
  • Received : 2017.10.02
  • Accepted : 2019.12.14
  • Published : 2020.04.25
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Abstract

The theories having been developed thus far account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A shear correction factor, therefore, is not required. In this paper, the effect of surface on the axial buckling and free vibration of nanobeams is studied using various refined higher-order shear deformation beam theories. Furthermore, these theories have strong similarities with Euler-Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and expressions of the resultant stress. The equations of motion and boundary conditions were derived from Hamilton's principle. The resultant system of ordinary differential equations was solved analytically. The effects of the nanobeam length-to-thickness ratio, thickness, and modes on the buckling and free vibration of the nanobeams were also investigated. Finally, it was found that the buckling and free vibration behavior of a nanobeam is size-dependent and that surface effects and surface energy produce significant effects by increasing the ratio of surface area to bulk at nano-scale. The results indicated that surface effects influence the buckling and free vibration performance of nanobeams and that increasing the length-to-thickness increases the buckling and free vibration in various higher-order shear deformation beam theories. This study can assist in measuring the mechanical properties of nanobeams accurately and designing nanobeam-based devices and systems.

Keywords

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