Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load

This paper studies the vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving concentrated load. The volume fraction of constituent materials is assumed to vary in both the thickness and longitudinal directions by power-law functions. The governing equations of motion based on Timoshenko beam theory are constructed from Hamilton's principle. A finite element formulation is derived and used in combination with the Newmark method in computing the vibration response. A parametric study is carried out to highlight the effect of the material distribution and moving load speed on the vibration characteristics of the beams. The numerical results show that the two grading indexes which govern the variation of the effective material properties have opposite effect on the natural frequencies, dynamic magnification factor and mid-span axial stress. The influence of the aspect ratio on the dynamic behavior of the beams is also examined and discussed.