Structural differences in wave propagation in discrete and continuous systems (Q1904944)

The authors show analytically for the one-dimensional case that the replacement of the (exact) continuous model of an elastic bar by ordinary, mechanically motivated discrete ones (cascades) leads to structural differences in the dynamic response with respect to harmonic and transient behavior (impedances, transmission factors, phase- and group velocities). The solution, based on a mesh refinement of the considered discrete models, turns out not to converge uniformly towards the response of the underlying continuous model. Further, a symmetric mass distribution along an element does not necessarily result in a better convergence when compared with a nonsymmetric mass distribution.