Spiral-based metamaterials: from local resonance to inertial amplification and Bragg scattering

Materials with engineered structural periodicity, obtained repeating in space unit cells with predetermined properties, can be used to modify the propagation of waves. In solids, such materials have been suggested for application in vibration insulation, acoustic focusing or elastic wave cloaking. Unit cells consisting of Archimedean spirals have rich dynamic properties and can be fabricated at the micro- and macro-scales, targeting different frequency ranges. Here, we show that by tuning the geometry of the spirals and arranging them in a lattice, they can act as Bragg scatterers, locally resonant metamaterials, or inertially amplified systems. We analyze the parametric transition between these three different band gap-opening mechanisms. We focus on the effect of inertial amplification and observe experimentally ultra-low and ultra-wide frequency bandgaps.