Acoustic Wave Trapping in One- Dimensional Axisymmetric Arrays

The existence of acoustic, Rayleigh-Bloch modes in the vicinity of a one-dimensional periodic array of rigid, axisymmetric structures is established with the use of a variational principle. Axisymmetric modes at frequencies below the cut-off frequency are shown to exist for all piecewise smooth structures and non-axisymmetric modes are found for a class of structures whose radial dimension is sufficiently large compared to the structure spacing. The theory is illustrated with numerical calculations of the wave numbers of Rayleigh-Bloch modes for an array of circular plates. An integral equation for the acoustic wave-field in the neighbourhood of such an array is obtained and solved with the use of a Galerkin technique, which builds in the singularity in the derivative of the field at the rim of the plate.