Dynamic Response of Non-Uniform Functionally Graded Beams Subjected to a Variable Speed Moving Load

Abstract

A finite element formulation based on the first-order shear deformable beam theory for dynamic analysis of multispan beams made of functionally graded material (FGM) subjected to a variable speed moving load is presented. The beam material is assumed to be graded in the thickness direction by a power-law distribution. Exact solution of static part of the governing differential equations of a FGM beam segment is employed to interpolate the displacements and rotation. The shift in the neutral axis position arose from the material inhomogeneity is taken into consideration in the formulation. The dynamic response of the beam is computed with the aid of the direct integration Newmark method. The numerical results show that the proposed formulation is capable to give accurate dynamic characteristics of the beam by using a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity and loading parameters on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic response is also examined and highlighted.