A new shear deformation micro-beam model based on a nonlocal elasticity theory

In this article, a nonlocal refined shear deformation beam theory is proposed to analyze the free vibration behavior of FG nanobeams. The formulation is based on the nonlocal differential constitutive equations of Eringen that accounts for small scale effects. Material properties vary continuously through thickness according to a power law distribution. The study is performed within the framework of a new parametric shear deformation theory which provides parabolic transverse shear strains across the thickness direction and hence, does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the nanobeam are satisfied rigorously. Equations of motion of FG nanobeam are derived from both the nonlocal differential constitutive relations of Eringen and Hamilton’s principle. The system of differential equations is solved using the Navier solution technique. The parametric study is conducted to examine the effects of volume fraction index, length scale parameter and length ratio on the free frequencies of vibration of FG thin and thick nanobeams.