Low-frequency spatial wave manipulation via phononic crystals with relaxed cell symmetry

Phononic crystals enjoy unique wave manipulation capabilities enabled by their periodic topologies. On one hand, they feature frequency-dependent directivity, which allows directional propagation of selected modes even at low frequencies. However, the stellar nature of the propagation patterns and the inability to induce single-beam focusing represent significant limitations of this functionality. On the other hand, one can realize waveguides by defecting the periodic structure of a crystal operating in bandgap mode along some desired path. Waveguides of this type are only activated in the relatively high and narrow frequency bands corresponding to total bandgaps, which limits their potential technological applications. In this work, we introduce a class of phononic crystals with relaxed cell symmetry and we exploit symmetry relaxation of a population of auxiliary microstructural elements to achieve spatial manipulation of elastic waves at very low frequencies, in the range of existence of the acoustic modes. By this approach, we achieve focusing without modifying the default static properties of the medium and by invoking mechanisms that are well suited to envision adaptive configurations for semi-active wave control