Dispersion curves for bending waves in a meta-plate made with a periodic lattice of ABH like scatterers

Acoustic Black Holes (ABH) have been studied for the twenty past years for their attractive vibration damping properties. In the case of 2D thin plate, ABH can consist in a pit of radial power law thickness profile that can highly reduce the flexural vibration field above a threshold frequency, depending on its relative size to the wavelength. This paper presents a study of bending waves propagation properties in an infinite thin plate on which ABH are periodically inserted. In such a periodic structure, the possible Bragg and resonant band gaps are studied in order to reach attractive damping properties over a wide frequency range including low frequencies below the ABH threshold frequency. A numerical model based on the Plane Wave Expansion method (PWE) is presented. The wave dispersion curves are numerically studied to evaluate the links between the band gap features and the unit cell design parameters.