Sound trapping and waveguiding in locally resonant viscoelastic phononic crystals

Abstract We describe the trapping and absorption of audible sound in centimeter-scale claddings of two-dimensional, locally resonant phononic crystals. In a square lattice of local resonators consisting of steel cores and cellulose shells, embedded in a viscous foam, dual acoustic-range band gaps extending from about 200 to $$2850 \text { Hz}$$ 2850 Hz are achieved. The spectral range consists of a low-frequency, local resonance gap, separated from a higher frequency Bragg resonance gap, by narrow bands of slow-sound modes. We demonstrate that thin claddings of such phononic crystal, of only three unit cells in thickness, can effectively prevent sound transmission, by a combination of reflection and absorption, over much of the audible spectrum. Moreover, frequency-selective sound transmission can be enabled by engineering waveguide channels that transmit sound through the local resonance gap, the Bragg gap, or both. This offers a path to sound-sculpting claddings that can surround a noise-generating source. The viscoelastic foam in our cladding is treated using a fractional Voigt model, capable of describing experimentally observed responses.