Lamb wave propagation in a plate with a grooved surface with several spatial periodicities

In order to investigate non-destructively the bonding between rough plates, the problem of Lamb waves propagating on a rough plate is addressed in this paper. Numerical analysis is performed on periodical gratings made of identical triangular grooves. If the surface profile is made up of grooves with one periodicity, then a mode conversion is observed. In the wave-number/frequency space, a phonon relation is written between phonons related to the grating and to the incident and reflected-converted modes. If the grooved surface is made up of several spatial periodicities, then the phonon relation is still verified. Signal processing allows us to give an interpretation of the results in the dual space (wave-number/frequency). An experimental study is also performed to corroborate the numerical predictions.