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

•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.