Bandstructure of phononic crystal of rotating heterogeneous cylinders: Time periodicity due to pure mechanical modulation

Existing designs of elastic spatiotemporal periodic structures usually require electric/piezoelectric elements that provide temporal modulation of elastic properties. While this method has advantages in many aspects, it usually allows relatively low modulation depth. Here we propose a design for spatiotemporal elastic media that is experimentally feasible, involves pure mechanical elements, and may provide any desired temporal modulation depth. In our scheme the scatterers of a phononic crystal are cylinders composed of two (or more) semi-cylinders (parts) of different materials. The cylinders are capable for rotation with high speed in a stationary fluid environment that provides time-dependent medium for propagating sound wave. Adjusting the elastic contrast between the materials of solid semi-cylinders the necessary modulation depths can be achieved. Different regimes of temporal modulation, from adiabatic to rapid oscillations can be realized by varying the frequency of rotation. We report momentum/energy gaps and other features of the bandstructure that are theoretically obtained using plane wave expansion. Nonreciprocal effects are studied for a phononic crystal with a square unit cell containing two heterogeneous cylinders rotating synchronically with a constant phase shift. [This work is supported by the NSF under EFRI Grant No. 1741677.]