This study investigates the dynamic behavior of simply-supported beams connected to a fractional vibration damping system under moving loads at a constant speed. The dynamic vibration absorber damping is described by the fractional derivatives. An optimization procedure is elaborated for optimal fractional parameters. The Newmark’s approach is combined with a discrete fractional derivative scheme combined with an optimization process to solve the resulting coupled second-order fractional differential equations. The obtained numerical results demonstrate that the fractional damping coefficient, the number of absorbers and absorber locations are the parameters that heavily affect the dynamic response. Furthermore, there exists a specific fractional derivative order at which the beam exhibits reduced dynamic response compared to the case where classical integer-order derivatives are used. Moreover, the obtained results demonstrate excellent concurrence with specific cases reported in the literature.
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