Antiplane elastic wave propagation in pre-stressed periodic structures; tuning, band gap switching and invariance

The effect of nonlinear elastic pre-stress on antiplane elastic wave propagation in a two-dimensional periodic structure is investigated. The medium consists of cylindrical annuli embedded on a periodic square lattice in a uniform host material. An identical inhomogeneous deformation is imposed in each annulus and the theory of small-on-large is used to find the incremental wave equation governing subsequent small-amplitude antiplane waves. The plane-wave-expansion method is employed in order to determine the permissable eigenfrequencies. It is found that pre-stress significantly affects the band gap structure for Mooney–Rivlin and Fung type materials, allowing stop bands to be switched on and off. However, it is also shown that for a specific class of materials, their phononic properties remain invariant under nonlinear deformation, permitting some rather interesting behaviour and leading to the possibility of phononic cloaks

Tunable elastodynamic band gaps

AbstractThe effect of nonlinear elastic pre-stress on coupled compressional and vertically polarised shear elastic wave propagation in a two-dimensional periodic structure is investigated. The medium consists of cylindrical annuli embedded on a periodic lattice in a uniform host material. An identical inhomogeneous deformation is imposed in each annulus and the theory of small-on-large is used to find the incremental wave equations governing subsequent small-amplitude elastic waves. The plane-wave-expansion method is employed in order to determine the permissable eigenfrequencies. It is found that the application of pre-stress has a significant effect on the band structure, allowing stop bands to be controlled. The sensitivity of the choice of constitutive behaviour is studied and it is shown that the fundamental shear wave mode is largely unchanged for the class of strain energy functions considered here, whereas the compressional mode is considerably more sensitive to this choice