Acoustics - Propagation in a solid

In an isotropic solid, displacement appears as the sum of a divergence-free vector and an irrotational vector. These vectors give rise to a decomposition of the propagation equation into two independent parts:

• one describes a transverse wave (shear motion) ;

• the other a longitudinal wave (a series of compressions and dilations).

In an anisotropic solid such as a crystal, the propagation equation admits three solutions and therefore three elastic waves. The acoustical slowness surface, analogous to the optical index surface, comprises three layers. The interest of this surface lies in the fact that its normal indicates the direction of energy progression for any direction, and in the fact that it illustrates the phenomena of reflection and refraction at the interface of two solids.

Plane-guided waves (Rayleigh waves) play an important role not only in geophysics, but also in electrical signal processing. They are discussed in the final section of this article. Lamb waves (plate modes), Love waves (modes in a layer and its substrate) and waves propagating in a cylinder are also described.

The "Acoustics" article is the subject of several booklets:

AF 3 810 General equations

AF 3 812 Propagation in a fluid

AF 3 814 Propagation in solids

The subjects are not independent of each other.

Readers will need to refer back to the other issues often enough.

In addition, you will find at the end of the booklet a table of the main notations used.