Guided waves in anisotropic layers: the low-frequency limits

The low-frequency limiting velocities of guided waves propagating in homogeneous layers with the traction-free boundary conditions and arbitrary elastic anisotropy are analyzed by constructing the secular equation based on Cauchy sextic formalism coupled with the low-frequency asymptotic analysis. The combined method allows us constructing a closed form solution in terms of the eigenvalues of a three-dimensional auxiliary matrix (tensor) composed of convolutions of the elasticity tensor with the unit normal to the median plane and the wave vector. The performed analytical and numerical studies reveal (i) coinciding (up to a multiplier) the set of admissiblelimiting velocities with the spectral set of an auxiliary matrix; (ii) degeneracy of the constructed auxiliary matrix at any elastic anisotropy; and (iii) presence of no more than two low-frequency limiting velocities (not necessarily distinct) at any kind of elastic anisotropy.