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| Ïîèñê ïî óêàçàòåëÿì |
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| Miklowitz J. — The theory of elastic waves and waveguides |
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| Ïðåäìåòíûé óêàçàòåëü |
Rayleigh — Lamb frequency equation, generalized, branches of 411—416 447
Rayleigh — Lamb frequency equation, generalized, branches of, near branch point behavior of 200
Rayleigh — Lamb frequency equation, generalized, for complex frequency-complex wave number segments 480
Rayleigh — Lamb frequency equation, generalized, governing waves corresponding to low frequency-complex wave number segments 480
Rayleigh-Lamb waves, unbounded 446—447
Rays, equation for 76
Rays, for homogeneous medium 77
Rays, in diffraction problems 485—486 518—519 556—567 559
Rays, theory of 17
Rays, use in wavefront analysis of 76
Reciprocal theorem, Graffi 52—55
Reciprocal theorem, Graffi, applications of 54—55
Reciprocal theorem, Graffi, dynamic equilibrium states in 52
Reciprocal theorem, Graffi, extensions of 54
Reflection coefficients 123
Reflection coefficients in half space for displacements 126—127 132
Reflection coefficients in half space for energy 131 133—134 143—144
Reflection coefficients in half space for P waves 120 123—131
Reflection coefficients in half space for potentials 123—125 131 133 135 141 155—156
Reflection coefficients in half space for SH waves 152—156
Reflection coefficients in half space for stress 127 132
Reflection coefficients in half space for SV waves 120 131—134
Reflection from half space boundary, coefficients in, complex 132 141
Reflection from half space boundary, coefficients in, for displacements 126—127 132
Reflection from half space boundary, coefficients in, for energy 131 133—134 143—144
Reflection from half space boundary, coefficients in, for potentials 123—125 131 133 135 141 155—156
Reflection from half space boundary, coefficients in, for stress 127 132
Reflection from half space boundary, coefficients in, of P waves 120 123—131
Reflection from half space boundary, coefficients in, of SH waves 120 131—134
Reflection from half space boundary, coefficients in, of SV waves 152—156
Reflection principle in functions of complex variable, application of 385 399—400
Reflection, refraction from interface, coefficients in, complex 164—165 169 175—176 177
Reflection, refraction from interface, coefficients in, for displacements 161 162 163 169 172
Reflection, refraction from interface, coefficients in, for energy 161—162 165 169—170
Reflection, refraction from interface, coefficients in, for potentials 160—161 164—165 168 172 175—176
Reflection, refraction from interface, coefficients in, for stress 161 169
Reflection, refraction from interface, of P wave 156—161 168—170 175
Reflection, refraction from interface, of SH wave 170—174
Reflection, refraction from interface, of SV wave 156—160 161—162 169
Refraction see Reflection refraction
Resolution of vector, Helmholtz 60
Retarded potentials 84
Retarded potentials in body force problems 84 88 94
Riemann — Lebesgue lemma 243
Riemann — Lebesgue lemma, applications of 388 405 408 424 428—429
Rod, infinite, circular cylindrical, displacement-potential relations for, axially symmetric compression 220
Rod, infinite, circular cylindrical, displacement-potential relations for, axially symmetric torsion 217
Rod, infinite, circular cylindrical, displacement-potential relations for, general (nonaxially symmetric) 216
Rod, infinite, circular cylindrical, Lames solution for 215—216
Rod, infinite, circular cylindrical, Lames solution for, vector potentials in 215
Rod, infinite, circular cylindrical, Lames solution for, vector potentials in, gauge conditions for 215
Rod, infinite, circular cylindrical, strain-displacement relations for 217
Rod, infinite, circular cylindrical, stress-potential relations for, axially symmetric compression 221
Rod, infinite, circular cylindrical, stress-potential relations for, axially symmetric torsion 218
Rod, infinite, circular cylindrical, stress-potential relations for, general (nonaxially symmetric) 217
Rod, infinite, circular cylindrical, stress-strain relations for 217
Rod, infinite, circular cylindrical, time harmonic waves in 214—225 (See also Waveguide problems)
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric compressional 220—223
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric compressional, analog with infinite plate 221—222
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric compressional, frequency spectra for 208—209 222
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric compressional, nature of motion generated by 222—223
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric compressional, potential modes for 221
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric torsional 217—220
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric torsional, analog with SH waves in plate 220
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric torsional, displacement modes for 220
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric torsional, frequency spectra for 219—220
Rod, infinite, circular cylindrical, time harmonic waves in, axially symmetric torsional, phase velocity spectra for 220
Rod, infinite, circular cylindrical, time harmonic waves in, nonaxially symmetric (flexural) 223—225
Rod, infinite, circular cylindrical, time harmonic waves in, nonaxially symmetric (flexural), analog with infinite plate 224
Rod, infinite, circular cylindrical, time harmonic waves in, nonaxially symmetric (flexural), displacement modes for 224
Rod, infinite, circular cylindrical, time harmonic waves in, nonaxially symmetric (flexural), frequency spectra for 224—225
Rod, infinite, circular cylindrical, time harmonic waves in, nonaxially symmetric (flexural), natire of motion generated by 224
Rod, infinite, circular cylindrical, time harmonic waves in, nonaxially symmetric (flexural), potential modes for 223
Rod, infinite, circular cylindrical, time harmonic waves in, Pochhammer frequency equation for, axially symmetric compression 221
Rod, infinite, circular cylindrical, time harmonic waves in, Pochhammer frequency equation for, axially symmetric torsion 219—220
Rod, infinite, circular cylindrical, time harmonic waves in, Pochhammer frequency equation for, nonaxially symmetric (flexure) 224
Rods See also Waveguides approximate
Rods, approximate theories, one-dimensional for 367—409
Rods, approximate theories, one-dimensional for, compressional wave, elementary 367—369
Rods, approximate theories, one-dimensional for, compressional wave, elementary, end stress problem 292
Rods, approximate theories, one-dimensional for, compressional wave, Love — Rayleigh 369 371—374
Rods, approximate theories, one-dimensional for, compressional wave, Love — Rayleigh, longitudinal impact problem based on 382—394
Rods, approximate theories, one-dimensional for, compressional wave, Mindlin — Herrmann 392—393
Rods, approximate theories, one-dimensional for, flexural wave, Bernoulli — Euler (elementary) 374—377
Rods, approximate theories, one-dimensional for, flexural wave, Timoshenko 377—382
Rods, approximate theories, one-dimensional for, flexural wave, Timoshenko, step shear force problem based on 394—409
Rods, approximate theories, one-dimensional for, torsional wave, fundamental nondispersive mode 219
Rods, approximate theories, one-dimensional for, torsional wave, fundamental nondispersive mode, initial angular twist problem 293
Rods, approximate theories, one-dimensional for, torsional wave, section warping 374
Rods, arbitrary section 436
Rods, elliptic section 217
Rods, rectangular section, photoelasticity-shock tube experiments with 437
Rods, rectangular section, warping of plane sections in 437
Rods, semi-infinite, circular cylindrical, mixed edge load problems for, axially symmetric 437
Rods, semi-infinite, circular cylindrical, mixed edge load problems for, nonaxially symmetric 435
Rods, semi-infinite, circular cylindrical, nonmixed pressure shock problem for, finite-difference numerical method in 466
Rods, semi-infinite, circular cylindrical, nonmixed pressure shock problem for, radial, axial strain responses in 466
Rods, semi-infinite, circular cylindrical, nonmixed pressure shock problem for, radial, axial strain responses in, comparison with response records 466
Rods, shock tube excitation of circular cylindrical 390—393
Rods, shock tube excitation of circular cylindrical, axial strain, radial displacement response in 391—393
Rods, shock tube excitation of circular cylindrical, axial strain, radial displacement response in, head of pulse in 391—393
Rods, shock tube excitation of circular cylindrical, axial strain, radial displacement response in, high frequency waves in 391—393
Rods, shock tube excitation of circular cylindrical, axial strain, radial displacement response in, near field cutoff waves in 391 393
Rods, vibrations of, early work on, approximate theory 6
Rods, vibrations of, early work on, exact theory 7
Saddle point 265—266
Saddle point, higher order 266
Saddle point, method, extended 271
Scattering of dilatational waves by liquid sphere or cylinder 574
Scattering of pulse by circular cylindrical obstacle 517—560
Scattering of pulse by half plane 485—517
Scattering of pulse by spherical obstacle 558 560—567
Scattering of waves by cylindrical cavity in a half space 574
Scattering of waves by cylindrical cavity in a half space, asymptotic expansions, matched, in 574
Scattering of waves by rigid spheroids, circular disk 574
Scholte wave 170 (See also Stoneley interface waves)
Seismology 16
Self-similar solutions 5 517
Self-similar solutions for wedge problems 575—576
Semi-infinite elastic plate, problems of, with mixed edge conditions 430 432—443
Semi-infinite elastic plate, problems of, with nonmixed edge conditions 430—431 444—466
SH wave 67
SH wave in half space antiplane tangential surface load problem 363
SH wave in infinite medium antiplane displacement source problem 363—364
SH wave in infinite plate 209—211 (See also Plate infinite time
SH wave in superficial layer of half space 8 (See also Love waves)
SH wave, diffracted 485—486
SH wave, reflection from free boundary 155—156
SH wave, reflection from rigid boundary 156
SH wave, reflection, refraction from solid-solid interface at critical angle 173
SH wave, reflection, refraction from solid-solid interface at grazing incidence 173
SH wave, reflection, refraction from solid-solid interface at normal incidence 173
SH wave, reflection, refraction from solid-solid interface for total transmission 174
SH wave, surface 3
Shadow zone 486 518 526 541 561
Shear force problem of infinite rod (beam) based on Timoshenko theory 394—409
Shear force problem of infinite thin plate based on Timoshenko — Uflyand — Mindlin theory 404
Shear modulus (Modulus of rigidity) 41
Shells, circular cylindrical, waves in 223
Shift rule, exponential Fourier transform 244—245
Shift rule, Laplace transform 239—240
Simple shear 41
Sine integral 462
Slowness 167
Slowness diagrams, use of in study of wave reflection and refraction 573
Sommerfeld optics diffraction problem 485—487
Spherically symmetric cavity source problem 277—282
Spherically symmetric waves 67—68 281—282
standing waves 189
Standing waves in transient response of plate 421—422
| Static problem, solution of 258—261
Stationary phase 186—188
Stationary phase, condition of 187—188
Stationary phase, method of 9 271—277
Stationary phase, method of, applications of 275—277 291 387—388 404—408 423—424 428—429 436—437 469—472
Stationary phase, method of, as special case of steepest descents method 274—275
Stationary phase, method of, asymptotic expansion of integral in 273
Stationary phase, method of, asymptotic expansion of integral in, for continuous distribution of wave groups 274 275—276
Stationary phase, method of, asymptotic expansion of integral in, for second order stationary phase point 274 277
Steady-state solution for time harmonic body force problem 94
Steepest descents, method of 264—271
Steepest descents, method of, applications of 269
Steepest descents, method of, applications of, for wavefronts 323—328 550—551
Steepest descents, method of, applications of, in waveguides 271
Steepest descents, method of, deformation of integration path to steepest paths 267 269
Steepest descents, method of, deformation of integration path to traverse paths 267
Steepest descents, method of, in asymptotic expansion of integral 269
Steepest descents, method of, in asymptotic expansion of integral, extended saddle point method 271
Steepest descents, method of, in asymptotic expansion of integral, when singularities occur 269—271
Steepest descents, method of, saddle surfaces in, geometric features of 265—267
Steepest descents, method of, saddle surfaces in, geometric features of, example of 266—267
Steepest descents, method of, saddle surfaces in, geometric features of, hills 265 266
Steepest descents, method of, saddle surfaces in, geometric features of, level curves 265
Steepest descents, method of, saddle surfaces in, geometric features of, relief surface 265
Steepest descents, method of, saddle surfaces in, geometric features of, saddle point, conditions at 265—266
Steepest descents, method of, saddle surfaces in, geometric features of, saddle points, higher order 266
Steepest descents, method of, saddle surfaces in, geometric features of, steepest paths 265
Steepest descents, method of, saddle surfaces in, geometric features of, valleys 265 266
Step function, Heaviside 86
Stoneley, interface waves, time harmonic 165—168
Stoneley, interface waves, time harmonic, early work on 9
Stoneley, interface waves, time harmonic, equation for velocity of 167
Stoneley, interface waves, time harmonic, existence of 168
Stoneley, interface waves, time harmonic, velocity of 168
Strain tensor 37
Strain tensor, components of 36—37
Strain tensor, law of transformation of 37
Strain, analysis of 30—38
Strain, dilatation 38
Strain, energy 3 49
Strain, energy density 39 49 55
Strain, energy density, Clapyron's form for 49
Strain, finite 31—32
Strain, finite, components of 32
Strain, finite, linearization of 32
Strain, infinitesimal 20 32
Strain, infinitesimal, components of 32
Strain, infinitesimal, extension 35—36
Strain, infinitesimal, nature of 35—36
Strain, infinitesimal, shear 36
Strain, invariants 38
Strain, principal 37—38
Strain, principal directions of 37
Strain, principal planes of 37
Strain, quadric of Cauchy 37—38
Strain-stress relations, Cartesian 42
Strained elastic body 30—31
Strained elastic body, continuity conditions on 31
Stress tensor 24
Stress tensor, components of 25
Stress tensor, law of transformation of 25
Stress tensor, symmetry of 24
Stress vector 22—26
Stress vector, plane of action of 22
Stress, analysis of 21—30
Stress, components of 22—25
Stress, components of, normal 22 24 26—28
Stress, components of, shear 22 28
Stress, components of, transformation of 24—25
Stress, compression 22
Stress, early work on 2
Stress, equations of motion 44
Stress, invariants 28
Stress, maximum shear 28—30
Stress, principal 27—28
Stress, principal directions of 27
Stress, principal planes of 27
Stress, quadric of Cauchy 26—28
Stress, tension 22
Stress-strain relations 38—42
Stress-strain relations, Hooke's law, generalized 38—39
Stress-strain relations, Hooke's law, generalized, elastic coefficients for 39
Stress-strain relations, Hooke's law, generalized, elastic coefficients for homogeneous, anisotropic body 39
Stress-strain relations, Hooke's law, generalized, elastic coefficients for symmetry relation for 39
Stress-strain relations, Hooke's law, homogeneous, isotropic body 39
Stress-strain relations, Hooke's law, homogeneous, isotropic body, Lame constants for 40—41
Stress-strain relations, Hooke's law, homogeneous, isotropic body, Lame constants for, in terms of Young's modulus, Poisson's ratio 41
Stress-strain relations, Hooke's law, homogeneous, isotropic body, Lame constants for, restrictions on 42
Stretched elastic string, initial value problem of 96—103
Superposition principle 47
Supplementary reading on 573—580
Supplementary reading on, additional effects 576—578
Supplementary reading on, text material 573—576
Surface of discontinuity, propagating 4 71—78
Surface of discontinuity, propagating, dynamical conditions at 74
Surface of discontinuity, propagating, for inhomogeneous medium 71 78
Surface of discontinuity, propagating, kinematical conditions at 73
Surface of discontinuity, propagating, velocities of 74—75
Surface waves 57
Surface waves, guided by thin film 576
Surface waves, P- 141
Surface waves, Rayleigh 146—151 (See also Rayleigh surface waves)
Surface waves, SV- 138
Surface, load problems of half space, antiplane tangential line 363
Surface, load problems of half space, normal line 299—328
Surface, load problems of half space, normal point 333—344
Surface, load problems of half space, normal point traveling 347 349—362
Surface, load problems of half space, tangential point 573
SV-wave 67
SV-wave, of surface type 3 (See also Equivoluminal waves in; Equivoluminal wave of)
SV-wave, reflection from boundary with mixed conditions 123—125
SV-wave, reflection from elastically restrained boundary 133—135
SV-wave, reflection from fluid-solid interface 169
SV-wave, reflection from free boundary 131—134 137—146
SV-wave, reflection from free boundary at  angle 138
SV-wave, reflection from free boundary at critical angle 139—144
SV-wave, reflection from free boundary at grazing incidence 137—138
SV-wave, reflection from free boundary at normal incidence 145—146
SV-wave, reflection from free boundary, rigid boundary 152
SV-wave, reflection from free boundary, solid-solid interface 156—160 161—162
SV-wave, reflection from free boundary, total mode conversion in 139 140
SV-wave, refraction from fluid-solid interface 169
SV-wave, refraction from fluid-solid interface at critical angles 169
SV-wave, refraction from fluid-solid interface at grazing incidence 169
SV-wave, refraction from fluid-solid interface at normal incidence 169
SV-wave, refraction from solid-solid interface 156—162
SV-wave, refraction from solid-solid interface at critical angles 163—165
SV-wave, refraction from solid-solid interface at grazing incidence 163
SV-wave, refraction from solid-solid interface at normal incidence 162—163
SV-wave, refraction from, for wave pairs 166—168
Tables, exponential Fourier transforms and inverses 248
Tables, Hankel transforms and inverses 250
Tables, Laplace transforms and inverses 241
Tables, sine and cosine transforms and inverses 248
Tables, sine and cosine transforms and inverses, relation with 246
Tauberian theorems 328
Tauberian theorems for negative Laplace transform parameter 328
Tensor, Cartesian 20
Tensor, Cartesian, first order 25
Tensor, Cartesian, law of transformation, first order 25
Tensor, Cartesian, law of transformation, second order 25
Tensor, Cartesian, notation of 20
Tensor, Cartesian, second order 24
Tensor, Cartesian, subscripts of 20
Tensor, Cartesian, summation convention of 20
Thermal effects 577
Thermal effects, equations of motion for linear thermoelastic medium 577
Thermal effects, equations of motion for linear thermoelastic medium, harmonic waves based on 577
Thermal effects, equations of motion for linear thermoelastic medium, transient waves based on 577
Thermal effects, surveys on 577
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