Guided acoustic waves at periodically structured edges: Linear modes and nonlinear generation of Lamb and surface waves - Nedospasov, Ilya A.; Pupyrev, Pavel D.; Bechler, Nikolaus; Tham, Jingxue; Kuznetsova, Iren E.; Mayer, Andreas P. (Journal of sound and vibration, 2022)
•Acoustic waves guided at periodically structured edges and wedge tips were studied.•Dispersion relation and displacements computed for periodic notches/inclusions.•Second harmonic of a wedge/edge mode radiates energy into the bulk/plate.•Zero-group velocity points in the dispersion branches of edge/wedge modes identified.•Cherenkov radiation of 2nd harmonic from edge of the homogeneous plate shown to exist. Acoustic waves are investigated which are guided at the edge (apex line) of a wedge-shaped elastic body or at the edge of an elastic plate. The edges contain a periodic sequence of modifications, consisting either of indentations or inclusions with a different elastic material which gives rise to high acoustic mismatch. Dispersion relations are computed with the help of the finite element method. They exhibit zero-group velocity points on the dispersion branches of edge-localized acoustic modes. These special points also occur at Bloch-Floquet wavenumbers away from the Brillouin zone boundary. Deep indentations lead to flat branches corresponding to largely non-interacting, Einstein-oscillator like vibrations of the tongues between the grooves of the periodic structure. Due to the nonlinearity of the elastic media, quantified by their third-order elastic constants, an acoustic mode localized at a periodically modified edge generates a second harmonic which partly consists of surface and plate modes propagating into the elastic medium in the direction vertical to the edge. This acoustic radiation at the second-harmonic frequency is investigated for an elastic plate and a truncated sharp-angle wedge with periodic inclusions at their edges. Unlike nonlinear bulk wave generation by surface acoustic waves in an interdigital structure, surface and plate mode radiation by edge-localized modes can be visualized directly in laser-ultrasound experiments.