Evaluation of nonlocal higher order shear deformation models for the vibrational analysis of functionally graded nanostructures

ABSTRACT

Small scale effects in the functionally graded beam are investigated by using various nonlocal higher-order shear deformation beam theories. The material properties of a beam are supposed to vary according to power law distribution of the volume fraction of the constituents. The nonlocal equilibrium equations are obtained and an exact solution is presented for vibration analysis of functionally graded (FG) nanobeams. The accuracy of the present model is discussed by comparing the results with previous studies and a parametric investigation is presented to study the effects of power law index, small-scale parameter, and aspect ratio on the vibrational behavior of FG nanostructures.

KEYWORDS:

• Nanobeam
• vibration
• nonlocal elasticity theory
• functionally graded material
• higher-order shear deformation beam theory