The variation, with the Poisson ratio, of Lamb modes in a free plate, III: Behaviour of individual modes

Abstract

The way individual, real-valued Lamb mode branches of a free, elastic plate vary with the Poisson ratio, σ, is studied, the coverage extending over the whole range, both positive and negative, of the latter parameter. After examining the zero order antisymmetric and symmetric branches, an investigation is made of the non-zero order branches of arbitrary order. The overall behaviour is shown to be largely influenced by two cylicities; the first of these applies over the full range of σ and occurs when the normal displacements within the plate are entirely dilatational, while the second cyclicity applies only over the negative range of σ and occurs when the normal displacements within the plate are entirely shear. Illustrations covering the full range of σ are presented for the first few non-zero order modes. Additionally, guidance supplementing Mindlin's rules of bounds is proffered for the easy sketching (without need for any computations) of sets of Lamb mode spectra, at any positive or negative value of σ, onto grids of Mindlin's bounds.