Abstract:
This paper presents the transverse vibration of Bernoulli-Euler homogeneous isotropic damped beams. These beams are subjected to a harmonic load moving with constant velocity. The damping characteristics of the beams are described in terms of a fractional derivative of arbitrary orders. In the analysis where the initial conditions are assumed to be homogeneous, the Laplace transform cooperates with the decomposition method to find the analytical solution of the handled problems. Subsequently, curves are plotted to show the dynamic response of two beams under different sets of parameters including different orders of the fractional derivatives. The curves reveal that the dynamic response increases as the fractional derivative order becomes greater than unity. This yields that smaller the order of the fractional derivative, the more oscillations the beam suffers. Finally, the literature reviews had shown a good command of agreement with the results obtained in this paper.