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Nonlinear force driven coupled vertical and torsional vibrations of suspension bridges, when the frequency of an external force is approaching one of the natural frequencies of the suspension system, which, in its turn, undergoes the conditions of the one-to-one internal resonance, are investigated. The method of multiple time scales is used as the method of solution. The damping features are described by the fractional derivative, which is interpreted as the fractional power of thedoi:10.22337/2587-9618-2020-16-2-113-131 fatcat:jbafh3ztj5e6vc7lsi4whdxw2m