Open Access

Elena Sokolova, Alexander Kovalev, Reinhold Timler, Andreas Mayer

• 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 materialAcoustic 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.…