Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load

In this paper, free vibration characteristics and the dynamic behavior of a functionally graded simply-supported beam under a concentrated moving harmonic load are investigated. The system of equations of motion is derived by using Lagrange’s equations under the assumptions of the Euler–Bernoulli beam theory. Trial functions denoting the transverse and the axial deflections of the beam are expressed in polynomial forms. The constraint conditions of supports are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the exponential law and the power-law form. In this study, the effects of the different material distribution, velocity of the moving harmonic load, the excitation frequency on the dynamic responses of the beam are discussed. Numerical results show that the above-mentioned effects play very important role on the dynamic deflections of the beam.