Free flexural vibration of functionally graded size-dependent nanoplates

Abstract

In this paper, the linear free flexural vibration behaviour of functionally graded (FG) size-dependent nanoplates are investigated using the finite element method. The field variables are approximated by non-uniform rational B-splines. The size-dependent FG nanoplate is investigated by using Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for FG nanoplate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is tested considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of FG nanoplate.