Elastic Surface Waves in Crystals

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Abstract
Elastic surface waves in a general semi-infinite, anisotropic medium are discussed in terms of a six-dimensional vector formalism. The six-dimensional state vectors have the physical significance that their first three components constitute the displacement of and their last three components the force on the surface of the medium. For a semi-infinite medium with no sources of energy in its interior, a definite relation exists between force and particle velocity at the surface. This relation defines an impedance matrix for the semiinfinite medium which is a function of frequency, wave vector, and material parameters. The impedance matrix exhibits interesting symmetry properties and provides us with some generally valid relations for surface waves. In particular, formulas for energy and power relations attain attractive forms especially suitable for numerical computation. Finally, some characteristic properties of surface waves along free surfaces are discussed, including undamped and damped ("leaky") surface waves.

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