On the dispersion of wedge acoustic waves

Acoustic waves guided at the apex of an ideal infinite elastic wedge are non-dispersive. Weak dispersion arises due to a variety of factors. Three of them are investigated in detail: (i) Coating of one or both of the two surfaces of the infinite wedge, (ii) truncating the wedge at its apex or replacing the tip of the wedge by a different material, (iii) slight modification of the material constants of the wedge material in an extended spatial region of the wedge near its tip. These three cases have been analysed within the perturbation theory, and the third case, in addition, with the help of semi-analytic finite element calculations. The dependence of the frequency on wavelength is derived for all three cases, and quantitative results are presented for the dispersion laws of example systems.

► Weak dispersion of wedge acoustic waves was investigated by perturbation theory.
► Coating, modifications of the wedge tip and of material properties were analysed.
► The dispersion laws have been established mainly for the long-wavelength regime.
► Numerical results were obtained for anisotropic wedges.