Time-harmonic, homogeneous and inhomogeneous plane waves propagating in isotropic and anisotropic viscoelastic media are investigated. The componental specification of the slowness vector p is used, in which the slowness vector p is computed from its known projection pΣ to an arbitrarily chosen plane Σ. The vectors p and pΣ are, in general, complex-valued. The most important step in the procedure consists in the determination of the component σ of the slowness vector p to the normal nΣ to Σ. For general anisotropic viscoelastic media, the component σ is a root of an algebraic equation of the sixth degree, with complex-valued coefficients. For isotropic viscoelastic media, the algebraic equation of the sixth degree factorizes to simple quadratic equations. For SH plane waves propagating in the plane of symmetry of a monoclinic (orthorhombic, hexagonal) viscoelastic medium it also factorizes providing a quadratic equation for SH waves. The componental specification of the slowness vector plays an important role in the solution of the problem of the reflection/transmission of plane waves at a plane interface between two viscoelastic anisotropic media.
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