ИСТИНА

Propagation of harmonic Lamb waves in functionally graded (FG) plates with transverse inhomogeneity is analysed by applying the modified Cauchy six-dimensional formalism. For arbitrary transverse inhomogeneity and arbitrary elastic anisotropy a closed form implicit analytical solution for dispersion equation is derived. Dispersion relations for materials with exponential inhomogeneity are obtained revealing abnormal behaviour of both symmetric and asymmetric (flexural) fundamental modes. In particular, the asymptotic behaviour at high frequencies of the flexural and symmetric modes for a FG plate with the asymmetric inhomogeneity becomes different, in contrast to a homogeneous plate, for which both fundamental modes have common asymptotes at high frequencies. It should also be noted that for the considered inhomogeneities, the frequency values at which the symmetric fundamental Lamb mode cannot propagate were not found.