Higher-order WKB analysis of reflection from tapered elastic wedges

The reflection coefficient for a one-dimensional elastic wedge driven from an adjacent uniform plate is analysed using higher-order WKB-method matrix analysis and the results are compared with numerical simulations using Finite Elements. The numerical results are correctly predicted by the WKB analysis above a certain frequency. In general, this frequency is shown to fall as the order of the WKB analysis approximation is increased, but at least a second-order WKB approximation is required in the working frequency range. The total reflection coefficient depends not only on the practical truncation of the wedge but also on the discontinuity between the wedge and the plate to which it is attached. Interference between these two sources of reflection causes ripples in the total reflection coefficient. Apart from the usual power-law profile, alternative thickness variations are also considered. Limitations on the applicability of the analytical method are illustrated through a wedge whose thickness varies predominantly away from the junction between the wedge and the uniform plate.