Ultra-wide acoustic band gaps in pillar-based phononic crystal strips

Abstract

An original approach for designing a one dimensional phononic crystal strip with an ultra-wide band gap is presented. The strip consists of periodic pillars erected on a tailored beam, enabling the generation of a band gap that is due to both Bragg scattering and local resonances. The optimized combination of both effects results in the lowering and the widening of the main band gap, ultimately leading to a gap-to-midgap ratio of 138%. The design method used to improve the band gap width is based on the flattening of phononic bands and relies on the study of the modal energy distribution within the unit cell. The computed transmission through a finite number of periods corroborates the dispersion diagram. The strong attenuation, in excess of 150 dB for only five periods, highlights the interest of such ultra-wide band gap phononic crystal strips.

Accordion-like metamaterials with tunable ultra-wide low-frequency band gaps

“…The reported data refer to three-dimensional or two-dimensional (in-plane waves) configurations of continuous (bold lines) or cellular (dashed lines) structures. The band-gap widths have been re-calculated for a unit cell size of 10mm, based on the data provided in the original works [17][18][19][20][21]35], for a uniform comparison.…”

“…The unit cell size is h uc =10 mm and the material volume fraction V m are indicated for each structure. The initial data are taken from [17] for coated Au circles in epoxy; [21] for convex and concave holes in copper; [35] for cross-like holes in a polymer; [20] for polymeric spheres joined by ligaments; [19] for Tg scatterers in epoxy; [18] for Si strip with Tg pillars. + + versus frequency f for an accordion-like meta-chain (30 unit cells).…”

“…The local resonance effect is induced by coated inclusions or pillars, increasing the total structural weight. In this case, wave attenuation is efficient only at the resonator eigenfrequencies and abruptly decreases away from them [5,14,[17][18][19]. Therefore, broadband control of low-frequency waves using lightweight structures remains a challenge.…”

“…Band-gap widths can be enlarged by exploiting rainbow-trapping designs [5], topology optimization techniques [20,21], or coupling the Bragg and local resonant mechanisms [18,22]. Alternatively, the incorporation of slender elements with small values of effective stiffness can lower the Bragg scattering limit [20].…”

Phononic Crystal Plate with Hollow Pillars Actively Controlled by Fluid Filling

“…Assouar and Oudich [18] reported that, by using double-sided stubbed phononic plates, locally resonant band gaps could be enlarged. Coffy et al [19] designed a strip consisting of periodic pillars deposited on a tailed beam, enabling the generation of an ultra-wide band gap resulting from both Bragg scattering and local resonance. Midtvedt et al [20] considered a graphene membrane that is deposited on top of a square lattice of cylindrical pillars to exhibit coupled localized modes with nonlinear dynamics.…”