Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals

The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design custom acoustic filters. While nonlinear viscoelastic behaviour is one main features soft solids, it has been rarely incorporated in study such phononic media. Here, we response solids within a 'small-on-large' acoustoelasticity framework, that consider propagation small amplitude waves superimposed on large static deformation. Incompressible whose described Fung-Simo quasi-linear viscoelasticy theory (QLV) are considered. We derive incremental equations using stress-like memory variables governed linear evolution equations. Thus, show wave dispersion follows strain-dependent generalised Maxwell rheology. Illustrations cover plane under homogeneous tensile strain QLV Mooney-Rivlin solid. then applied to crystals lattice hollow cylinders, making use dedicated perturbation approach. In particular, results highlight influence dissipation location first band gap. shifts gap frequencies, simultaneously increasing width. These relevant practical applications subject pre-stress.