Investigating Fractional Damping Effect on Euler-Bernoulli Beam Subjected to a Moving Load

In this work, the dynamic response of Euler-Bernoulli beams of four different boundary conditions with fractional order internal damping under a traversing moving load is investigated. The load is assumed to be moving with different values of constant velocity. A proposed approach to obtain the closed-form solution of the problem based on Green's functions combined with a decomposition technique in the Laplace transform domain is introduced. Several cases are studied and compared to the literature; for instance, if simply supported beam is considered, the following three cases are to be explored: the case of elastic (or undamped) beam, the damped (or viscously damped) beam, and finally the fractionally damped beam modeled by the fractional Kelvin-Voigt model. The effects to the beam dynamic response induced by magnitude of moving load velocity, damping ratio, and fractional damping order are explored. The results expressed sufficient agreement with similar problems found in literature and evidenced that the dynamic response of beams is significantly affected by varying the fractional order of beam damping as well as the moving load velocity. Accordingly, using fractionally damped materials exhibits better realistic behavior of beams and intermediate between elastic and viscous beam behaviors.