Dynamic Response of Beam with Multi-Attached Oscillators and Moving Mass: Fractional Calculus Approach

This paper presents the dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simplysupported beam. The beam is appendaged to single-degree-of-freedom (SDOF) fractionally-damped N-oscillators and subjected to a moving load with a uniform velocity. The damping characteristics of the beam and oscillators are formally described in terms of fractional derivative of an arbitrary order. In the analysis, the initial conditions are assumed to be homogeneous, and the Laplace transform is combined with the used decomposition method to find the solution of the handled problem. Subsequently, curves are plotted to show the vibration of the utilized beam under different sets of parameters including different orders of fractional derivatives for both of the beam and oscillators. The numerical results obtained in this paper show that the dynamic response decreases as the number of absorbers attached to the beam increases, as both the damping-ratios of absorbers and beam increase the dynamic response decreases, and there are some critical values of fractional derivatives which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivatives model. In addition, the obtained results show very good agreement with special case studies that were previously published in literature.