THE VARIATION, WITH THE POISSON RATIO, OF LAMB MODES IN A FREE PLATE .2. AT TRANSITIONS AND COINCIDENCE VALUES

A set of spectra of real- and imaginary-valued Lamb modes has been presented in a companion paper, each spectrum being for a fixed value of the Poisson ratio, σ, and the set covering the full range of σ. The analysis is extended in this paper by examining in more detail situations in which transitions need to be interpreted or in which coincidences of modes of like symmetry lead to discontinuities requiring explanation. This includes studies of the upper end of the range of σ, where the complicated Lamb mode spectra of an elastic plate must change to the much simpler spectrum of a fluid plate, and of the transition from positive to negative σ, the special behaviour of the real Lamb mode branches at σ = 0 being explained in terms of Mindlin's rules of bounds. For negative σ, discontinuous changes of slope of individual real modes are shown to occur under certain conditions and, for both positive and negative σ, a different type of slope discontinuity is demonstrated in association with occurrences of phase and group velocities in opposite directions. © 1990.