Time-modulated phononic crystal of oscillating bimetallic rods

Mathematical treatment of space- and time-modulated structures is similar. However, the practical realization of time dependence on elastic properties is a much more difficult problem than the fabrication of a phononic crystal where elastic properties are space periodic. The most common method of temporal modulation is applying AC voltage to a piezoelectric constituent. This method allows high-frequency modulation, but the depth of modulation is relatively weak. Here, we propose a mechanical method of temporal modulation which requires a complicated engineering scheme but provides deep modulation. The scatterers of a phononic crystal are bimetallic rods driven by an external force to oscillate along their axes in a solid (or fluid) matrix. Due to mechanical oscillations, a propagating sound wave suffers time-dependent scattering. High elastic contrast between the components of the bimetallic rods provides deep time modulation and high contrast between the metals and the background matrix provides deep space modulation. The band structure of a mechanically time-modulated phononic crystal is calculated for aluminum-copper rods in an epoxy matrix. Mix band gaps with complex values of ω and k are predicted and analytical properties of the dispersion relation in complex ω-k plane are studied. [This work is supported by the NSF Grant No. 1741677 and by the AFOSR grant FA9550-23-1-0630.]