Sound generation by turbulence near an elastic wall

Abstract

The Lighthill theory has been extended to describe the sound generated by turbulence near an elastic wall. The case of a thin elastic slab with identical fluid in contact with both faces is investigated in detail by solving the elastic equations in the slab together with the acoustic boundary-layer equations in the fluid, with all stresses and displacements continuous across the fluid-elastic interface. The low-wavenumber elements of the pressure spectrum under the plate are determined, and it is found that the surface pressure spectrum has considerable structure which is not predicted by simple bending plate theory. This is because admitting that the elastic medium can support general elastic deformations introduces new modes of vibration that are not present in the simple plate theory. In addition to the flexural waves displayed by bending plate theory the elastic region can support a symmetric mode which propagates with the compressive wave speed √ E ϱ M (1 − ν 2) , where E is Young's modulus, ν is Poisson's ratio and ϱ M is the density of the elastic medium. The surface pressure spectrum under the plate is found to have a local maximum for spectral elements whose phase speeds are equal to either the compressive or the flexural wave speeds. The spectrum of the fluctuating shear stress is also investigated. The low-wavenumber spectrum of the surface shear stress is found to have considerable structure with peaks for spectral elements whose phase speeds are nearly equal to speed of sound in the fluid, to the compressive wave speed in the plate and to the bending wave speed if it is subsonic.