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 < alpha < 2 are involved in the governing equation, which is solved by fractional finite differences. The influence of long-range interactions is then analyzed as alpha 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 alpha = 2, are discussed. (c) 2012 Elsevier B.V. All rights reserved.