Waves in porous materials, Plenary Lecture by Keith Attenborough (The Open University)

DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017

Website of DENORMS Action

Programme of the Workshop

Session on New trends in traditional noise treatments – porous materials and microperforated plates

Speaker: Keith Attenborough (The Open University)

Abstract:

Many observations of waves in porous materials are explained by Biot theory for dynamic poroelasticity. An important prediction of Biot theory is that, as well as a shear wave, there are two kinds of dilatational waves (i.e. a ‘fast’ and a ’slow’) that can propagate in a fluid-saturated poroelastic medium. ‘Slow’ waves are known to be important in determining the acoustical properties of air-saturated porous elastic solid materials with open connected pores since they are the most easily excited by fluid-borne excitation. There is considerable argument about the ability of Biot-type theories to explain the frequency-dependence of dilatational wave attenuation in underwater sediments in part because a viscous grain shearing theory is able to explain the observed frequency dependence of attenuation in underwater sediments without including a ‘slow’ wave. Direct evidence for the arrival of two distinct compressional wave types can be found in data for ultrasonic transmission through water-saturated bone and air-filled foam layers. Indirect evidence is provided by the results of measurements using separate acoustical- and mechanical-excitation of air-filled polyurethane foam. Biot-based predictions of the relative importance of the ‘fast’ and ‘slow’ waves in water- and air-saturated contexts are discussed. Also the effects of pore size distribution are explored in view of the facts that they are more important than pore shape effects and that parameters introduced by modifications to Biot theory due to Allard, Champoux, Lafarge and Pride can be related to parameters of the pore size distribution. A consequence of the two compressional waves in air-filled poroelastic layers is that two types of surface wave can be generated associated with the slow and shear waves respectively. The former is related to the surface wave created by a point source over a rough surface and the latter represents an air-coupled Rayleigh wave.