Elastic waves in random-fibre networks

The propagation of the first displacement maximum of a semi-infinite wavetrain in a two-dimensional random-fibre network is analysed. Model calculations and numerical simulations are used for demonstrating that two qualitatively different wavefront velocities appear in the network. A transient wave, which travels fast and whose amplitude decreases exponentially, dominates the short-time behaviour when the bending stiffness of the fibres is small and the driving frequency is high. This mode can be described by a one-dimensional model. The transient-wave mode propagates even if the bending stiffness of the fibres vanishes, in which case the normal sound velocity is zero. The usual, and slower, effective medium mode always dominates at late times. It also dominates at short times if the driving frequency is low and/or the bending stiffness of the fibres is relatively high.