Wave propagation in nonlocal elastic continua modelled by a fractional calculus approach

In the present paper, the wave propagation in one-dimensional elastic continua, characterized by nonlocal interactions modeled by fractional calculus, is investigated. Spatial derivatives of non-integer order 1 < α < 2 are involved in the governing equation, which is solved by fractional finite differences. The influence of long-range interactions is then analyzed as α varies: the resonant frequencies and the standing waves of a nonlocal bar are evaluated and the deviations from the classical (local) ones, recovered by imposing α = 2, are discussed.

► One-dimensional nonlocal elastic continua modelled by a fractional approach.
► We investigate the wave propagation.
► Fractional spatial derivatives are discretized by fractional finite differences.
► Resonant frequencies show a non-linear behavior.
► Standing waves deviate from the classical local ones.