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Existence and uniqueness of a Rayleigh surface wave propagating along the free boundary of a transversely isotropic half space. (English) Zbl 0606.73024

The author proves the existence and uniqueness of the Rayleigh surface wave that can propagate along the free boundary of a transversely isotropic elastic half-space. The axis of symmetry is normal to the boundary. In his proof the author uses a spectral method, i.e., he studies the spectral properties of the self-adjoint operator that governs the wave propagation problem. The cylindrical symmetry of the medium is used in order to reduce the full problem to a simpler one represented by a family of \(3\times 3\) Sturm-Liouville operators. The existence and uniqueness of the surface wave solution then are associated with the existence and uniqueness of a simple eigenvalue for each of the \(3\times 3\) systems.
Reviewer: G.A.Maugin

MSC:

74J15 Surface waves in solid mechanics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74E10 Anisotropy in solid mechanics
47B25 Linear symmetric and selfadjoint operators (unbounded)
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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