A study of Lamb waves in anisotropic plates

Abstract

This paper is concerned with the Lamb wave spectra for layered orthotropic elastic media. The spectra computed from three-dimensional elasticity theory for orthotropic layers are compared with those computed from simpler exact or approximate theories as follows: classical plate theory, plane stress (membrane mode), plane strain, and SV wave analogue. At low frequencies, it is found that there are seven roots of the generalized Rayleigh–Lamb equation for a single layer system. Three of the seven roots are close to the values predicted by the plane stress model for the symmetric mode and by the classical plate theory for the antisymmetric mode. The other three roots are identical to those predicted by the SV analogue and by the plane strain state, and these roots correspond to spurious modes. The spurious wave speeds also represent the limiting values of genuine wave speeds representing guided waves, such as when the frequency tends to infinity. The final root corresponds to a common point of different branches of slowness surfaces. Good agreement is also found between the three-dimensional elasticity analysis and simplified membrane and plate analyses for multilayered media.