Elastic Waves in Solids, Volume 2

2Scattering of Elastic Waves

In Volume 1, the propagation medium, assumed to be homogeneous, was either infinite (Chapter 1), divided into two parts by a plane interface (Chapters 2 and 3), or limited in one or two dimensions (Chapter 4), the waves propagating freely in this or other dimensions. Here, the propagation medium is locally inhomogeneous; these heterogeneities may be inherent to the structure or may result from manufacturing defects (inclusions) or from the aging of the parts (cracks). Waves scattered by an obstacle propagate away from it, possibly in privileged directions, even if the medium is isotropic. Several applications in underwater acoustics are based on target scattering: detecting mines or ships by an active sonar, locating shoals of fish, or mapping ocean floors. In non-destructive testing by ultrasound, the information carried by the scattered waves is used to characterize these heterogeneities or to prevent damage, such as the delamination of composite materials. Scatterers can be deliberately introduced, for instance, to attenuate backward waves emitted by a piezoelectric transducer and thus dampen its responses (section 3.1). Recently, the development of periodic structures (phononic crystals) or heterostructures made of resonant inclusions dispersed in a matrix (acoustic metamaterials) opened the way to the filtering and the control of elastic wave propagation.

The interaction of a (plane) elastic wave with a particle embedded in a matrix gives rise ...