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Mathematics and Mechanics of Solids
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Uniqueness of the Surface-Wave Speed: A Proof That Is Independent of the Stroh Formalism

Alexander Mielke

Inst. fur Analysis, Dynamik und Modellierung, Univ Stuttgart, D-70569 Stuttgart

Yibin B. Fu

Department of Mathematics, Keele University, Staffordshire ST5 5BG, UK

It is well-known in surface-wave theory that the secular equation for the surface-wave speed v can be written as det M = 0 in terms of the surface impedance matrix M. It has recently been shown by the present authors that M satisfies a simple algebraic Riccati equation. It is shown in the present paper that a purely matrix algebraic analysis of this equation suffices to prove that whenever a surface wave exists it is unique.

Key Words: Stroh fornalism • surface waves • elastic half-space • surface impedance matrix

Mathematics and Mechanics of Solids, Vol. 9, No. 1, 5-15 (2004)
DOI: 10.1177/1081286503035196
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