Application of a general expression for the group velocity vector of elastodynamic guided waves

Abstract

In the field of elastodynamic guided waves, the calculation of the group velocity vector is closely tied with the numerical techniques used to calculate the waveguide's dispersion curves. These techniques often require mode sorting – which can be difficult for densely packed dispersion curves – or access to large matrices. In this paper, we implement Biot's general energy expression in order to derive the group velocity vector of elastodynamic guided waves. We demonstrate the flexibility and applicability of the expression by using it to calculate the group velocity of partial waves, Rayleigh waves, and Lamb waves. We also use it to calculate the skew angle of a guided wave in a transversely-isotropic plate and suggest how it may be used for 2D-arbitrary cross-sections. Explicit expressions for the group velocity are provided for each of these applications, thereby allowing insightful comparison between them. In particular, we compare the group velocity of Lamb waves and the partial waves of which they are composed. The primary benefit of the proposed expressions is that they enable the group velocity to be accurately calculated at a specific frequency and a specific wavenumber by using only the material parameters and the wave's displacement profile. More generally though, they give analysts more options for calculating group velocity and skew angle.