Application of Fractional Calculus for Modeling the Dynamic Behavior of Structures Under Moving Loads: A Review

This review presents a state-of-the-art analysis in the field of application of fractional calculus to dynamic problems in solid mechanics with moving loads. It includes papers devoted to the study of the dynamic behavior of structures carrying moving loads and made of a viscoelastic material and/or resting on viscoelastic foundations, the damping properties of which are described by models with fractional derivatives. A large number of numerical and experimental studies in this field gives grounds for using fractional-derivative models in dynamic contact problems. Issues on the action of moving oscillating loads in the form of systems with one or several degrees of freedom are also considered.