Approximations of the dispersion relation for an elastic plate composed ofstrongly anisotropic elastic material

In this paper approximations of the dispersion relation associated with har monic waves propagating along the axis of transverse isotropy, parallel to the traction free surfaces, in a fibre-reinforced elastic plate are derived . High and low wave number expansions are derived which have potential appl ications to impact problems within plates and shells and acoustic scatterin g and radiation respectively. Plots of the associated group velocity curves are presented and a wave front travelling with a speed of the same order o f magnitude as the Young's modulus along the fibre direction is observed. A particularly interesting feature of this front is that its formation arise s through the cumulative effect of various harmonics in adjacent wave numbe r regimes. The paper concludes with both a conjecture concerning the proper ties of this wave as the Young's modulus increases and the derivation of ap proximate solutions for the dispersion relation in the neighbourhood of the associated wave front. (C) 1999 Academic Press.