Acoustic performance of periodic steel cylinders embedded in a viscoelastic medium

Abstract

The acoustic performance of a locally resonant phononic crystal comprising steel cylindrical scatterers arranged periodically in a viscoelastic medium is analytically and numerically studied. Analytical expressions for the damping and dipole resonance frequency of the phononic array of solid cylinders embedded in a viscoelastic medium are derived. Based on effective medium approximation, effective geometric and material properties of the composite layer with embedded cylindrical scatterers are also derived. Results from the analytical model are compared with those from a numerical model based on the finite element method. The phononic crystal is immersed in water and the effects of water backing and steel-air backing on its acoustic performance are investigated. Dipole resonance of the cylinders as well as constructive interference between waves scattered by the cylinders and reflected from the steel backing plate are shown to lead to high sound absorption, attributed to conversion of longitudinal to shear waves which are subsequently dissipated in the rubber medium. Different geometric and material parameters are examined to provide further insight into the physical mechanisms associated with high sound absorption of the phononic crystal.