Theory of Elastic Waves in CrystalsThe 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
1 | |
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 |
369 | |
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Common terms and phrases
a₁ acoustic axes analogy anisotropy approximation axis B₁ b₂ c₁ C₂ coincide components condition cone considered coordinate corresponding cubic crystal curve D₁ defined degree derived differs displacement vector dyad eigenvalues eigenvectors elastic constants elastic moduli elastic properties elastic waves ellipse elliptically polarized equation expression formulas gives Hence hexagonal hexagonal crystal homogeneous homogeneous function implies inverse linear linearly longitudinal normal longitudinal wave m₁ matrix multiply n₁ ne)² ne]² ns)² orthogonal parameters phase velocity plane perpendicular propagate purely longitudinal wave purely transverse waves quasilongitudinal wave quasitransverse waves radius vector refraction vector rotation s₁ scalar section 13 section 26 shows solution special directions subscripts Substitution symmetric matrix symmetric tensor symmetry plane tetragonal tion transformation transversely isotropic medium triclinic u₁ unit tensor unit vector v₁ wave normal wave surface zero ди