1302.0402 (Andrzej Hanyga)

Wave propagation in linear viscoelastic media with completely monotonic
relaxation moduli    [PDF]

Andrzej Hanyga

It is shown that the wave propagation characteristics of a viscoelastic medium with a completely monotonic relaxation modulus are described by the wave propagation speed and the dispersion-attenuation spectral measure. The dispersion and attenuation functions are expressed in terms of the the dispersion-attenuation spectral measure. An alternative expression of the implicit mutual dependence of the dispersion and attenuation functions, known as the Kramers-Kronig dispersion relation, is also derived from the theory. The minimum phase aspect of the filters involved in the Green's function is another consequence of the theory. As an example, an explicit integral expression is obtained for the attenuation and dispersion in a few analytical relaxation models.

View original: http://arxiv.org/abs/1302.0402