Free flexural vibration of functionally graded size-dependent nanoplates

TL;DR

This study investigates the free flexural vibration of functionally graded size-dependent nanoplates using finite element analysis with nonlocal elasticity and B-spline approximation, highlighting effects of material gradation and size parameters.

Contribution

It introduces a finite element formulation for FG nanoplates considering size effects via nonlocal elasticity and B-spline approximation, providing detailed numerical insights.

Findings

Material gradient index significantly affects vibration response.

Size-dependent effects alter natural frequencies and mode shapes.

Boundary conditions influence vibrational characteristics.

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.