Effect of damage on Rayleigh wave propagation in second gradient lattice materials

The frequencies of the Rayleigh waves propagating in periodic lattice materials prone to internal damage is analysed, using a second gradient displacement effective model as an enriched substitution continuum to capture the dispersive wave features. In this work, we model the damage by randomly eliminating beams from the full networks constructed from periodic unit cells. The apparent mechanical properties of progressively damaged structures are evaluated using dedicated homogenization techniques in the context of second gradient continuum mechanics. The wave frequency is computed, for different relative densities, versus the amount of damage for the square and hexagonal networks. Results reveal that the hexagonal lattice has higher values of frequency compared to the square lattice. Charts of the wave frequencies versus wavenumber for different amounts of global lattice damage can serve as a non-destructive technique to infer the amount of damage that exists in beam-lattice materials.