Abnormal dispersion of flexural Lamb waves in functionally graded plates

Abstract

A closed-form dispersion equation for Lamb waves is obtained for analyzing dispersion in functionally graded (FG) plates with arbitrary anisotropy and arbitrary transverse inhomogeneity. The dispersion equation is derived and analyzed by a variant of the sextic formalism, previously developed for Lamb waves propagating in anisotropic layered plates with homogeneous layers. For the case of FG plates with transverse asymmetric inhomogeneity, some peculiarities in dispersion of the fundamental flexural Lamb mode are observed, revealing discrepancy in asymptotic behavior at high frequencies between homogeneous and FG isotropic plates.