Wave Propagation in Anisotropic Viscoelasticity

摘要

The theory of complete Bernstein functions is extended to matrix-valued functions and applied to analyze Green's function of an anisotropic multi-dimensional 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.