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Anisotropic ElasticityTheory and Applications$
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T. T. C. Ting

Print publication date: 1996

Print ISBN-13: 9780195074475

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195074475.001.0001

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Steady State Motion and Surface Waves

Steady State Motion and Surface Waves

Chapter:
(p.440) Chapter 12 Steady State Motion and Surface Waves
Source:
Anisotropic Elasticity
Author(s):

T. C. T. Ting

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195074475.003.0015

The Stroh formalism for two-dimensional elastostatics can be extended to elastodynamics when the problem is a steady state motion. Most of the identities in Chapters 6 and 7 remain applicable. The Barnett-Lothe tensors S, H, L now depend on the speed υ of the steady state motion. However S(υ), H(υ), L(υ) are no longer tensors because they do not obey the laws of tensor transformation when υ≠0. Depending on the problems the speed υ may not be prescribed arbitrarily. This is particularly the case for surface waves in a half-space where υ is the surface wave speed. The problem of the existence and uniqueness of a surface wave speed in anisotropic materials is the crux of surface wave theory. It is a subject that has been extensively studied since the pioneer work of Stroh (1962). Excellent expositions on surface waves for anisotropic elastic materials have been given by Farnell (1970), Chadwick and Smith (1977), Barnett and Lothe (1985), and more recently, by Chadwick (1989d).

Keywords:   Monge cone, Rayleigh waves, Stoneley waves, acoustic tensor, bicharacteristics, conjugate radii, eigenplane, half-space, identities, kinetic energy

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