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The dynamic behaviour of an Euler–Bernoulli beam resting on the fractionally damped viscoelastic foundation subjected to a moving point load is investigated. The fractional-order derivative-based Kelvin–Voigt model describes the rheological properties of the viscoelastic foundation. The Riemann–Liouville fractional derivative model is applied for a fractional derivative order. The modal superposition method and Triangular strip matrix approach are applied to solve the fractional differential equation of motion. The dependence of the modal convergence on the system parameters is studied. The influences of (a) the fractional order of derivative, (b) the speed of the moving point load and (c) the foundation parameters on the dynamic response of the system are studied and conclusions are drawn. The damping of the beam-foundation system increases with increasing the order of derivative, leading to a decrease in the dynamic amplification factor. The results are compared with those using the classical integer-order derivative-based foundation model. The classical foundation model over-predicts the damping and under-predicts the dynamic deflections and stresses. The results of the classical (integer-order) foundation model are verified with literature.

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