Finite element analysis of multi-span functionally graded beams under a moving harmonic load

A finite element procedure for vibration analysis of multi-span functionally graded material (FGM) beams subjected to a moving harmonic load is presented. The material properties of the beam are assumed to vary continuously in the thickness direction by a power-law distribution. The finite element formulation is derived by using the exact solution of the governing differential equations of an FGM Timoshenko beam segment to interpolate the displacements and rotation. The shift in the neutral axis position is taken into account in the formulation. The dynamic response of the beam is computed with the aid of the Newmark method. The numerical results show that the proposed formulation is capable to give accurate dynamic characteristics of the beams. A parametric study is carried out to highlight the effect of the material heterogeneity, number of spans and loading parameters on the dynamic response of the beams. The influence of the aspect ratio is also studied and highlighted.