Wave propagation in anisotropic viscoelasticity
Mathematical Physics
2015-07-02 v7 math.MP
Abstract
We extend the theory of complete Bernstein functions to matrix-valued functions and apply it to analyze Green's function of an anisotropic multi-dimension\-al linear viscoelastic problem. Green's function is given by the superposition of plane waves. Each plane wave is expressed in terms of matrix-valued attenuation and dispersion functions given in terms of a matrix-valued positive semi-definite Radon measure. More explicit formulae are obtained for 3D isotropic viscoelastic Green's functions. As an example of an anisotropic medium the transversely isotropic medium with a constant symmetry axis is considered.
Cite
@article{arxiv.1405.5724,
title = {Wave propagation in anisotropic viscoelasticity},
author = {Andrzej Hanyga},
journal= {arXiv preprint arXiv:1405.5724},
year = {2015}
}