Propagation of elastic waves in two-dimensional phononic crystals composed of viscoelastic materials

We have investigated the transmission characteristics of acoustic waves through two-dimensional phononic crystals composed of viscoelastic materials such as silicon rubber. In the present work, we improve a previously proposed method in which it was assumed that the Poisson ratio of silicon rubber is independent of time. The improved method removes the assumption and independently handles two parameters that describe a viscoelastic material: time-dependent bulk modulus and shear rate. We find that the time-dependent shear rates can modulate the frequency dependences of the transmission rate to various degrees. Therefore, in acoustic wave transmission, we can obtain large gaps in the audible domain by choosing the substrate material appropriately. In addition, we find that the viscoelasticity of the substrate makes the fine structure for the transmission rates smooth.