Veering of Rayleigh-Lamb waves in orthorhombic materials

Abstract

We analyse veering of Rayleigh-Lamb waves propagating in a plane of elastic symmetry for a thin orthotropic plate. We demonstrate that veering results from interference of partial waves in a similar manner as it occurs in systems composed of one-dimensional (1D) structures, such as beams or strings. Indeed, in the neighbourhood of a veering point, the system may be approximated by a pair of interacting tout strings, whose wave speed is the geometric average of the phase and group velocity of the relevant partial wave at the veering point. This complementary pair of partial waves provides the coupling terms in a form compatible with a action-reaction principle. We prove that veering of symmetric waves near the longitudinal bulk wave speed repeats itself indefinitely with the same structure. However, the dispersion behaviour of Rayleigh-Lamb waves are richer than that of 1D systems, and this reflects also on the veering pattern. In fact, the interacting tout string model fails whenever the dispersion branch is not guided by either partial wave. This often occurs when neighbouring veering points interact and partial waves no longer provide guiding curves.