Guided acoustic waves at periodically structured edges: Linear modes and nonlinear generation of Lamb and surface waves

• Published in: Journal of sound and vibration 2022-06, Vol.527, p.116854, Article 116854
• Main Authors: Nedospasov, Ilya A., Pupyrev, Pavel D., Bechler, Nikolaus, Tham, Jingxue, Kuznetsova, Iren E., Mayer, Andreas P.
• Format: Article
• Language: English
• Subjects: Brillouin zones; Edge waves; Elastic bodies; Elastic media; Elastic plates; Elastic properties; Finite element analysis; Finite element method; Grooves; Group velocity; Inclusions; Materials elasticity; Nonlinear equations; Nonlinearity; Periodic structures; Phononic crystal; Propagation modes; Radiation; Sound waves; Surface acoustic waves; Surface waves; Wave generation; Wedge waves
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2022.116854

•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.