Dynamic characteristics of non-uniform multi-span functionally graded 3D graphene foams reinforced beams with elastic restraints

This paper investigates the dynamic characteristics of non-uniform multi-span functionally graded (FG) 3D graphene foams (3D-GFs) reinforced beams with elastic boundary conditions. It is assumed that the foams are distributed according to four porosity distributions along the thickness direction and the beams sections varies in height and width along the length with the power-law distribution. Based on Timoshenko beam theory and Hamilton's principle, the equations of motion for multi-span beams are derived and the discrete singular convolution (DSC) method is adopted to solve them numerically. The present analysis is rigorously validated through direct comparisons against the results by those available in open literatures. A comprehensive parametric study is conducted to study the effects of porosity distribution, slenderness ratio, taper ratio and different combination types of multi-span beams with non-uniform sections. This study provides a new conception of multi-span beam composition, providing designers with choices of beam forms under vibration response.