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arXiv · 1405.5724

Wave propagation in anisotropic viscoelasticity

Andrzej Hanyga
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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.

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Andrzej Hanyga. 2014-05-22. Wave propagation in anisotropic viscoelasticity. https://arxiv.org/abs/1405.5724

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