Theory of Elastic Waves in Crystals

Front Cover
Springer Science & Business Media, Apr 17, 2013 - Science - 375 pages
The translation into English of Academician Fedorov's ex cellent treatise on elastic wave propagation in solids has come at an opportune time. His systematic exposition of all aspects of this field is most lucid and straightforward. The author has gone to considerable pains to develop in his mathematical background a consistent tensor framework which acts as a unifying motif through out the various aspects of the subject. In many respects his approach will appear quite novel as his treatment introduces several concepts and parameters previously unfamiliar to the literature of the West. Extensive tables in the final chapters illustrate the application of these ideas to the exist ing body of experimental data. The book is both extensive and comprehensive in al1 phases of the subject. Workers in the fields of ultrasonic propagation and elastic properties will find this treatise of great interest and direct concern. H. B. Huntington Rensselaer Polytechnic Institute Troy, New York November 1967 v Preface to the American Edition In preparing this edition I have corrected various misprints and errors appearing in the Russian edition, but I have also incorpo rated some substantial changes and additions, the latter representing some results I and my colleagues have recently obtained and pub_ lished in Russian journals. For example, in section 32 I have added a general derivation of the equation for the seetion of the wave surface by a symmetry plane for cubic, hexagonal, tetragonal, and orthorhombic crystals.
 

Contents

General Equations of the Theory
1
Hookes
8
Tensor for the elastic moduli
15
Elastic moduli of crystals of the lower systems
23
Elements of Linear Algebra
35
18
80
Special directions for elastic waves in crystals
95
Longitudinal normals and acoustic axes
103
Isotropic Media
211
Covariant form of the A tensor
215
Phase velocities and displacements
221
Comparison of a hexagonal crystal with an isotropic medium
229
Mean transverse anisotropy
231
Comparison with a transversely isotropic medium
235
Elastic Waves in Crystals of the Higher Systems
245
Cubic crystals
247

Form of the A tensor for various crystal systems
113
Energy Flux and Wave Surfaces
119
The energyflux vector and the ray velocity
123
Energy vector with acoustic axes
131
Elliptical polarization in elastic waves and the instantaneous energyflux vector
135
Wave surfaces
157
Sections of the wave surfaces by symmetry planes
165
General Theory of Elastic Waves in Crystals Based on Comparison with an Isotropic Medium
169
Mean elastic anisotropy of a crystal
173
Comparison with an isotropic medium
200
Approximate theory of quasilongitudinal waves
201
Another form of the approximate theory 119
203
89
249
Approximate theory for cubic crystals
257
Tetragonal crystals
263
Comparison with a hexagonal crystal
273
Trigonal crystals 211 211
276
of Elastic Waves
283
Reflection of elastic waves at the free boundary of an isotropic medium 283
291
Reflection at the free boundary of a crystal
301
The complex refraction vector and inhomogeneous 298 plane waves
306
Elastic Waves and the Thermal
333
LITERATURE CITED
369
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information