Interface effects in elastic wave scattering [...] XD-US

Lecture Notes in Physics: Monographs 19 ......Page 1
Interference Effects in Elastic Wave Scattering ......Page 3
Contents ......Page 7
1.2 Overview ......Page 13
1.3 The pioneering work of Clebsch and Mie ......Page 18
1.4 Planar interfaces and geophysics ......Page 20
1.5 Spheres, cylinders, and mid 20th century physics ......Page 21
1.6 Modern studies of composites ......Page 22
2.1 Equations of dynamical elasticity ......Page 25
2.1.1 Cartesian coordinates ......Page 27
2.1.2 Cylindrical coordinates ......Page 29
2.1.3 Spherical coordinates ......Page 30
2.2 Boundary conditions ......Page 31
2.2.1 Planar boundary ......Page 36
2.2.2 Cylindrical boundary ......Page 38
2.2.3 Spherical boundary ......Page 40
2.3 Method of solution ......Page 42
2.3.1 Planar-cartesian coordinates ......Page 43
2.3.2 Cylindrical coordinates ......Page 44
2.3.3 Spherical coordinates ......Page 46
2.4.1 Plane wave expansions ......Page 48
2.4.2 Cylindrical wave expansions ......Page 49
2.4.3 Spherical wave expansions ......Page 51
3.1 Introduction ......Page 55
3.2 Incident longitudinal wave ......Page 59
3.2.1 Scattered fields ......Page 66
3.2.2 Dynamic stress concentrations ......Page 73
3.3 Incident coupled transverse wave ......Page 74
3.3.1 Scattered fields ......Page 75
3.4 Incident uncoupled transverse wave ......Page 78
3.4.1 Scattered field and stress concentration ......Page 81
3.5 Applications to layered composites ......Page 82
3.6.1 Normal incidence to the planar interface ......Page 90
3.6.2 Numerical inversion ......Page 92
4.1 Introduction ......Page 93
4.2 Incident longitudinal wave ......Page 98
4.2.1 Scattered fields ......Page 105
4.2.2 Dynamic stress concentrations ......Page 111
4.3 Incident coupled transverse wave ......Page 112
4.3.1 Scattered fields ......Page 114
4.3.2 Dynamic stress concentrations ......Page 117
4.4 Incident uncoupled transverse wave ......Page 118
4.4.1 Scattered field and stress concentration ......Page 121
4.5 Applications to fiber composites ......Page 123
4.6 Special cases and verification ......Page 137
5.1 Introduction ......Page 143
5.2 Incident longitudinal wave ......Page 147
5.2.1 Scattered fields ......Page 154
5.2.2 Dynamic stress concentrations ......Page 160
5.3 Incident coupled transverse wave ......Page 161
5.3.1 Scattered fields ......Page 162
5.3.2 Dynamic stress concentrations ......Page 165
5.4 Incident uncoupled transverse wave ......Page 166
5.4.1 Scattered field and stress concentration ......Page 169
5.5 Applications to particle composites ......Page 171
5.6 Special cases and verification ......Page 172
6 SUMMARY OF RESULTS ......Page 177
APPENDIX A: DERIVATIONS FOR DYNAMICAL ELASTICITY ......Page 179
B.1 Separation and solution of the vector Helmholtz equation ......Page 183
B.1.1 Solutions in cartesian coordinates ......Page 185
B.1.2 Solutions in cylindrical coordinates ......Page 186
B.1.3 Solutions in spherical coordinates ......Page 188
BIBLIOGRAPHY ......Page 191