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Fundamental elastodynamic solutions for anisotropic media with ellipsoidal slowness surfaces. (English) Zbl 0793.73020
This paper examines the fundamental elastodynamic solutions for anisotropic elastic media with a slowness surface consisting of three concentric ellipsoids. The solutions of the displacement equations of motion are generated from functions satisfying the usual scalar wave equations. All the conditions on the linear elastic moduli under which the slowness surface is the union of concentric ellipsoids are found and Green’s tensor for each case is determined. The algebraic consequences of the ellipsoidal slowness surface are elicited and are shown to impose a threefold classification on the eigenvectors of the acoustical tensor. The representation of Green’s tensor is effected in terms of scalar wave functions, and the two canonical problems underlying the actual construction of Green’s tensor are solved. The structures of the fundamental solutions corresponding to the various ellipsoidal forms of the slowness surface are described, special cases are considered and, in particular, the standard Stokes solution is recovered in the degenerate case of isotropy. This well-written paper of theoretical nature may appeal to a limited number of researchers working in the area of anisotropic elasticity.

MSC:
74B10 Linear elasticity with initial stresses
74E10 Anisotropy in solid mechanics
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