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Steel and Composite Structures
  Volume 25, Number 1, September20 2017 , pages 67-78

Vibration analysis of FG nanobeams based on third-order shear deformation theory under various boundary conditions
Ali Akbar Jandaghian and Omid Rahmani

    In this study, free vibration of functionally graded (FG) micro/nanobeams based on nonlocal third-order shear deformation theory and under different boundary conditions is investigated by applying the differential quadrature method. Third-order shear deformation theory can consider the both small-scale effects and quadratic variation of shear strain and hence shear stress along the FG nanobeam thickness. The governing equations are obtained by using the Hamilton's principle, based on third-order shear deformation beam theory. The differential quadrature (DQ) method is used to discretize the model and attain the natural frequencies and mode shapes. The properties of FG micro/nanobeam are assumed to be chanfged along the thickness direction based on the simple power law distribution. The effects of various parameters such as the nonlocal parameter, gradient index, boundary conditions and mode number on the vibration characteristics of FG micro/nanobeams are discussed in detail.
Key Words
    nanobeam; free vibration; nonlocal elasticity; third-order shear deformation theory; functionally gradient materials
Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran.

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