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| Miklowitz J. — The theory of elastic waves and waveguides |
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| Предметный указатель |
Lerch's theorem 300
Lerch's theorem, use of 300 448
Long time-far field approximations in circular cylindrical cavity diffraction problems 529—536 551—555 569—571
Long time-far field approximations in circular cylindrical cavity diffraction problems, cavity wall rigid body velocities in 555
Long time-far field approximations in circular cylindrical cavity diffraction problems, Rayleigh waves in 529—536 551—555 569—571
Long time-far field approximations in circular cylindrical cavity diffraction problems, static solutions in 535 555
Long time-far field approximations in circular cylindrical cavity diffraction problems, waveguides see Waveguide problems
Long time-near field approximations in a semi-infinite plate 455—456 463—465
Long-time approximation 260
Long-time approximation, Watson's lemma — Laplace transform derivation of 258—261
Long-time approximation, Watson's lemma — Laplace transform derivation of, solution of static problem 261
Long-time approximation, Watson's lemma — Laplace transform derivation of, solution of static problem for cavity source problems 289 295
Long-time approximation, Watson's lemma — Laplace transform derivation of, solution of static problem for circular cylindrical cavity diffraction problems 535 555
Longitudinal impact problem of semi-infinite plate with mixed edge conditions 431—434 436—443
Longitudinal impact problem of semi-infinite rod based on Love — Rayleigh theory 382—394 478
Love waves 8 211—214
Love waves, phase velocity equation for 213
Love waves, phase velocity equation for, branches of 213
Love waves, phase velocity equation for, branches of, asymptotics of 213
Love waves, phase velocity equation for, phase velocity, group velocity, spectra, lowest two branches of 214
Love waves, scattering of, by edge of half space surface layer 576
Love — Rayleigh rod theory 8 369 371—374
Love — Rayleigh rod theory, diffusive nature of 383 (See also Waveguides approximate
Love — Rayleigh rod theory, initial data jumps governed by 393—394
Love's integral representation for displacement 95—96
mass density 43
Membrane, stretched infinite, initial value problem of 295
Membrane, stretched infinite, initial value problem of, solution of 295
Mindlin — Herrmann rod theory 392—393
Mindlin — McNiven rod theory 574
Mindlin — McNiven rod theory, head of the pulse solution for 574
Mindlin — McNiven rod theory, head of the pulse solution for, effect of station on magnitude of 574
Mindlin — McNiven rod theory, head of the pulse solution for, higher order terms in 574
Mixed boundary value problems in wave diffraction 487—517
Mixed boundary value problems in wave diffraction, dual integral equations in 491 499—500 501
Mixed edge conditions problem, uniqueness of solution of 55
Mode integral sums, waveguide 419—422 424 426 428—429 474—477 540 542—544
Mode integral sums, waveguide, solutions based on comparisons of 424 428—429 474—477 542—544
Modern work and reading 10—12
Modes of propagation in infinite plate, dilatational 182—183
Modes of propagation in infinite plate, equivoluminal 182—183
Modes, conversion of 119
Modes, conversion of, no 124—125 155—156
Modes, conversion of, partial 1 132 160—161
Modes, conversion of, total 127 132 149 140
Modes, coupling of 132 (See also “conversion of” here)
Modes, thickness 185
Modes, thickness-, dilatational 185
Modes, thickness-, equivoluminal 185
Modes, thickness-, shear 185
Modes, thickness-, stretch 185
Modulus of compression (bulk modulus) 41
Modulus of elasticity (Young's modulus) 38
Modulus of elasticity (Young's modulus), restriction on 42
Modulus of rigidity (shear modulus) 41
moment 21
Nodal points in time harmonic axially symmetric waves 70
Nodal points in transient excitation of plates 421—422
Nonaxially symmetric diffraction problems of circular cylindrical obstacles waves in 518—519 532—536 541—546 550—560
Nonaxially symmetric flexural waves in circular cylindrical rod 222—225
Nonaxially symmetric traveling point load problem in half space 347 348—362
Nonaxially symmetric traveling point load problem in half space, waves in 355—361
Nonlinear elastic media 578
Nonlinear elastic media, discontinuity surfaces and shock in 578
Nonlinear elastic media, discontinuity surfaces and shock in, geometric acoustics for waves in 578
Nonlinear waves, theory of 17
Nonmixed edge displacements, problems of, for semi-infinite plate 465—466
Nonmixed edge displacements, problems of, for semi-infinite plate, cantilevered plate, symmetric face normal line loads near base 465
Nonmixed edge displacements, problems of, for semi-infinite plate, velocity shock 465—466
Nonseparable problems, semi-infinite plate with nonmixed edge conditions 430—431 444—466
Nonseparable problems, wedge, with nonmixed edge conditions see Wedge two-dimensional
Nonuniformly moving surface load problems of half space 574
Normal line load problem of infinite plate 429—430
Operator integral for bilateral Laplace transform 232
Operator integral for exponential Fourier transform 242 243 245
Operator integral for Fourier cosine transform 246
Operator integral for Fourier sine transform 246
Operator integral for Hankel transform 249
Operator integral for Laplace transform 232
Operators, linear 47
Optics 17 485—487
Order symbols, definition of 33
P wave 67
P wave, of surface type 3 (See also Dilatational waves in; Dilatational waves of)
P wave, reflection from fluid-solid interface 168—170 176—177
P wave, reflection from free boundary 125—131 135—137 139—140 144—146
P wave, reflection from free boundary at grazing incidence 136—137 144 145
P wave, reflection from free boundary at normal incidence 135 145—146
P wave, reflection from free boundary, total mode conversion in 139 140
P wave, reflection from rigid boundary 152 175
P wave, reflection from solid-solid interface 156—161 175—176
P wave, reflection from, boundary with mixed conditions 123—125
P wave, refraction from fluid-solid interface 168—170 176—177
P wave, refraction from fluid-solid interface at critical angles 169 176—177
P wave, refraction from fluid-solid interface at grazing incidence 169
P wave, refraction from fluid-solid interface at normal incidence 169
P wave, refraction from solid-solid interface 156—161 175—176
P wave, refraction from solid-solid interface at critical angles 163—165 175—176
P wave, refraction from solid-solid interface at grazing incidence 163
P wave, refraction from solid-solid interface at normal incidence 162—163
P wave, refraction from, for wave pairs 166—168
Partial differential equation, linear 47
Particle velocity 43
Parts integration in asymptotic expansions of integrals 257 261—262
Parts integration in asymptotic expansions of integrals, application of 251
Period, predominant 190
Period, predominant, -time of occurrence relations 191
Period, predominant, -time of occurrence relations, application of 471
Period, predominant, -time of occurrence relations, dimensionless variables in 190—192
Period, wave 121
Permutation symbols 20
Phase velocity, infinite plate 179
Phase velocity, infinite plate, -wave number relations, for mixed face conditions 183—184
Phase velocity, infinite plate, dimensionless 183
Phase velocity, infinite plate, equation of, for mixed face conditions 183—184
Phase velocity, infinite plate, spectra for elastically restrained faces 195
Phase velocity, infinite plate, spectra for mixed face conditions 185
Plane waves, constant phase of 65—67
Plane waves, definition of 64
Plane waves, displacement 66—67
Plane waves, harmonic P-, SV-, SH- 67
Plane waves, one-dimensional 63—64
Plane waves, phase of 65
Plane waves, potential 65—66
Plane waves, three-dimensional 65—67
Plane, strain 120
Plane, strain, conditions for 120
Plane, strain, displacement-potential relations of 121 123 158
Plane, strain, P and SV waves of 119—152 156—170
Plane, strain, strain-potential relations of 122 123
Plane, strain, stress-potential relations of 122 123 158
Plane, stress 120 (See also Plane strain)
Plastic media, waves in, book, surveys on 578
Plate, infinite, time harmonic waves in, cylindrical wave surfaces, dilatational, equivoluminal in 179—180 210
Plate, infinite, time harmonic waves in, displacement waves in 180 210
Plate, infinite, time harmonic waves in, on an elastic foundation 227—229
Plate, infinite, time harmonic waves in, on an elastic foundation, frequency equation, DasGupta, for 227—228
Plate, infinite, time harmonic waves in, on an elastic foundation, frequency equation, DasGupta, for cutoff frequencies from 228—229
Plate, infinite, time harmonic waves in, on an elastic foundation, frequency equation, DasGupta, for frequency spectra from 229
Plate, infinite, time harmonic waves in, on an elastic foundation, sandwich plate equivalent problem 228
Plate, infinite, time harmonic waves in, P waves, symmetric, antisymmetric, in 178—180
Plate, infinite, time harmonic waves in, phase velocity of 179
Plate, infinite, time harmonic waves in, SH waves, symmetric, antisymmetric in 209—210
Plate, infinite, time harmonic waves in, stress waves in 181 210
Plate, infinite, time harmonic waves in, SV waves, symmetric, antisymmetric in 179—180
Plate, infinite, time harmonic waves in, wave number in propagation direction of 179
Plate, infinite, time harmonic waves in, wave number in thickness direction of 179
Plate, infinite, time harmonic waves in, wave pairs in 180
Plate, infinite, time harmonic waves in, with elastically restrained faces, coupling between P, SV waves in 194—196
Plate, infinite, time harmonic waves in, with elastically restrained faces, frequency equation for 195
| Plate, infinite, time harmonic waves in, with elastically restrained faces, frequency spectra for 195
Plate, infinite, time harmonic waves in, with elastically restrained faces, phase velocity spectra for 195
Plate, infinite, time harmonic waves in, with elastically restrained faces, roots common with mixed face conditions case 194—196
Plate, infinite, time harmonic waves in, with mixed face conditions 181—186 188—198
Plate, infinite, time harmonic waves in, with mixed face conditions, anharmonic overtones in 185
Plate, infinite, time harmonic waves in, with mixed face conditions, branches of frequency equation for, imaginary wave number segments of 185
Plate, infinite, time harmonic waves in, with mixed face conditions, branches of frequency equation for, real wave number segments of 185
Plate, infinite, time harmonic waves in, with mixed face conditions, cutoff frequencies in 188—189
Plate, infinite, time harmonic waves in, with mixed face conditions, cutoff frequencies in, P, SV waves at 189
Plate, infinite, time harmonic waves in, with mixed face conditions, edge waves in 184
Plate, infinite, time harmonic waves in, with mixed face conditions, frequency equations for 183—184
Plate, infinite, time harmonic waves in, with mixed face conditions, frequency spectra for 185
Plate, infinite, time harmonic waves in, with mixed face conditions, fundamental mode of, dilatational 185
Plate, infinite, time harmonic waves in, with mixed face conditions, fundamental mode of, equivoluminal 185
Plate, infinite, time harmonic waves in, with mixed face conditions, group velocity spectra for 191
Plate, infinite, time harmonic waves in, with mixed face conditions, high frequency-short waves in 189—190
Plate, infinite, time harmonic waves in, with mixed face conditions, high frequency-short waves in, phase, group velocities for 189—190
Plate, infinite, time harmonic waves in, with mixed face conditions, modes of propagation in 182—183
Plate, infinite, time harmonic waves in, with mixed face conditions, phase velocity equations for 183—184
Plate, infinite, time harmonic waves in, with mixed face conditions, phase velocity spectra for 185
Plate, infinite, time harmonic waves in, with mixed face conditions, phase velocity-wave number relations for 183—184
Plate, infinite, time harmonic waves in, with mixed face conditions, predominant period-time of occurrence relations for 190
Plate, infinite, time harmonic waves in, with mixed face conditions, standing waves in 184
Plate, infinite, time harmonic waves in, with mixed face conditions, thickness modes in, dilatational 185
Plate, infinite, time harmonic waves in, with mixed face conditions, thickness modes in, equivoluminal 185
Plate, infinite, time harmonic waves in, with mixed face conditions, thickness modes in, shear 185
Plate, infinite, time harmonic waves in, with mixed face conditions, thickness modes in, stretch 185
Plate, infinite, time harmonic waves in, with mixed face conditions, wavelength-frequency relation for 190
Plate, infinite, time harmonic waves in, with traction free faces 197—209
Plate, infinite, time harmonic waves in, with traction free faces, frequency equation, Rayleigh — Lamb, for 197
Plate, infinite, time harmonic waves in, with traction free faces, frequency spectra, Rayleigh — Lamb for 197
Plate, infinite, time harmonic waves in, with traction free faces, frequency spectra, Rayleigh — Lamb for complex wave number segments in 197—201 207—209
Plate, infinite, time harmonic waves in, with traction free faces, frequency spectra, Rayleigh — Lamb for general character of 197—201
Plate, infinite, time harmonic waves in, with traction free faces, frequency spectra, Rayleigh — Lamb for real, imaginary wave number segments in 197—207
Plate, infinite, time harmonic waves in, with traction free faces, generalized frequency equation, Rayleigh — Lamb, for 200
Plate, infinite, time harmonic waves in, with traction free faces, generalized frequency equation, Rayleigh — Lamb, for branches of, near branch point behavior of 200 (See also Rayleigh — Lamb frequency equation)
Plate, velocity 222 471
Plate, vibrations of, flexural, thin plate 7
Plate, vibrations of, nodal figures in 7
Plates, infinite, axially symmetric loadings in 466—477
Plates, infinite, plane strain loadings in 409—430
Plates, semi-infinite, mixed edge condition loadings in 430—443
Plates, semi-infinite, nonmixed edge condition loadings in 444—466 (See also Waveguide problems)
Plates, semi-infinite, thin, infinite, bending theory of Timoshenko — Uflyand — Mindlin 404
Plates, semi-infinite, thin, infinite, bending theory of Timoshenko — Uflyand — Mindlin, point shear force problem based on 404
Pochhammer frequency equations 7 219 221 224
Pochhammer frequency equations, general branches of 219 221—222 224—225
Pochhammer frequency equations, general branches of, complex wave number segments of 208—209 222
Pochhammer frequency equations, general branches of, further detail of see Rayleigh — Lamb frequency equations general
Pochhammer frequency equations, general branches of, imaginary wave number segments of 220 208—209 222 224—225
Pochhammer frequency equations, general branches of, real wave number segments of 220 208—209 222 224—225 infinite circular
Point, load problem in infinite medium 4 86—91 93—94
Point, load problem in infinite medium, time harmonic 93—94
Point, load problem in infinite medium, time harmonic, steady state solution for 94
Point, shear load problem, in infinite plate based on Timoshenko — Uflyand — Mindlin theory 404
Point, source problem, in two welded half spaces 6
Poisson's integral formula 4
Poisson's ratio 41
Poisson's ratio, coupling 393 436—437
Poisson's ratio, restriction on 42
Poisson's summation formula 520—521
Poisson's summation formula, Fourier series, applied to 520—521
Poisson's summation formula, square integrability, for functions of 520
Poisson's summation formula, sufficient conditions for 520
Potential, displacement 59
Potential, energy of deformation 49
Potential, integral representation for 4
Potential, retarded 4 84
Potential, scalar 3—4 59
Potential, vector 3 59
Power input 48
Pressure shock problem of semi-infinite plate, with mixed edge conditions 431—432 434—435 436—443
Pressure shock problem of semi-infinite plate, with nonmixed edge conditions 431—432 444—448 449—457
Principal value integrals 311 359 360
Principle of reflection in complex variables, use of 286
Propagating surface of discontinuity 71—78 (See also Wavefronts; Characteristics)
Pulse diffraction, Cagniard — deHoop method for 12 490—516
Pulse diffraction, from half plane rigid barrier 11—12 496 517
Pulse diffraction, from half plane slit 11—12 485—517
Pulse diffraction, from plane finite obstacles 12 574
Pulse diffraction, self-similar solutions for 12 517 575—576
Pulse diffraction, Wiener — Hopf method for 12 488—504
Pulse propagation 8 (See also Diffraction problems)
Quarter plane, problems see Wedge two-dimensional
Quarter plane, rigid scatterer in infinite solid, incident compressional pulse 575
Quarter planes 575
Quarter planes, two welded, mixed, nonmixed edge condition problems 575—576
Rayleigh function 301
Rayleigh surface waves in diffraction problems 513 529—536 551—555 565—571
Rayleigh surface waves in half space buried line dilatational source 331—332
Rayleigh surface waves in half space buried line dilatational source, far-field domination of 332
Rayleigh surface waves in half space buried line dilatational source, nondecaying nature of 331—332
Rayleigh surface waves in half space buried line dilatational source, nonsingular nature of 331—332
Rayleigh surface waves in half space buried line dilatational source, two-sided nature of 331—332
Rayleigh surface waves in half space surface normal line load problem 313—318
Rayleigh surface waves in half space surface normal line load problem, far-field domination of 317—318
Rayleigh surface waves in half space surface normal line load problem, nondecaying nature of 316—317
Rayleigh surface waves in half space surface normal line load problem, response to delta function of 315—317
Rayleigh surface waves in half space surface normal line load problem, response to step function of 318
Rayleigh surface waves in half space surface normal line load problem, singular, nonsingular nature of 313 315—317
Rayleigh surface waves in half space surface normal line load problem, two-sided nature of 313—314 317
Rayleigh surface waves in half space vertical point load problem 339—343 345—348
Rayleigh surface waves in half space vertical point load problem, for buried load case 345—348
Rayleigh surface waves in half space vertical point load problem, for buried load case, development of 345—348
Rayleigh surface waves in half space vertical point load problem, for buried load case, nonsingular nature of 346 348
Rayleigh surface waves in half space vertical point load problem, for buried load case, two-sided nature of 346 348
Rayleigh surface waves in half space vertical point load problem, for surface load case 339—343
Rayleigh surface waves in half space vertical point load problem, for surface load case, interior response of 340—343
Rayleigh surface waves in half space vertical point load problem, for surface load case, one-sided nature of 339—340
Rayleigh surface waves in half space vertical point load problem, for surface load case, singular nature of 339—340
Rayleigh surface waves in half space vertical point load problem, for surface load case, spatial decay of 340
Rayleigh surface waves, time harmonic 146—151
Rayleigh surface waves, time harmonic, displacement amplitudes of 149—150
Rayleigh surface waves, time harmonic, early work on 4—5 8
Rayleigh surface waves, time harmonic, equation for velocity of 147
Rayleigh surface waves, time harmonic, experimental studies of 150—151
Rayleigh surface waves, time harmonic, generalized 151—152
Rayleigh surface waves, time harmonic, particle motion of 148—149
Rayleigh surface waves, time harmonic, scattering of, by edge of half space surface layer 576
Rayleigh surface waves, time harmonic, stress amplitudes of 149—150
Rayleigh surface waves, time harmonic, ultrasonic, use of 152
Rayleigh surface waves, time harmonic, velocity of 147—148
Rayleigh — Lamb frequency equation 7 197
Rayleigh — Lamb frequency equation, general branches of 197—201
Rayleigh — Lamb frequency equation, general branches of, analytical continuation in 197—200
Rayleigh — Lamb frequency equation, general branches of, branch points in 197—200
Rayleigh — Lamb frequency equation, general branches of, complex wave number segments of 197—201
Rayleigh — Lamb frequency equation, general branches of, complex wave number segments of, further on 207—209
Rayleigh — Lamb frequency equation, general branches of, complex wave number segments of, further on, analytic continuation scheme 207—209
Rayleigh — Lamb frequency equation, general branches of, complex wave number segments of, further on, low frequency behavior 209
Rayleigh — Lamb frequency equation, general branches of, cutoff in 197—200
Rayleigh — Lamb frequency equation, general branches of, cutoff, behavior near, of 197—200 227
Rayleigh — Lamb frequency equation, general branches of, edge waves governed by 200
Rayleigh — Lamb frequency equation, general branches of, imaginary wave number segments of 197—201
Rayleigh — Lamb frequency equation, general branches of, modes associated with 200—201
Rayleigh — Lamb frequency equation, general branches of, real wave number segments of 197—201
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on 201—207
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, bounds 195 196 201
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, critical Poisson's ratio and cutoff 204—205
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, cutoff frequencies 203
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, frequency spectra 198 202
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, grazing incidence waves 206 207
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, high frequency-short wave behavior 207
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, modes, thickness-strech, -shear, simple 204
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, phase, group velocities and curvature at cutoff 205
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, Rayleigh waves 207
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, spectra, related modes and waves 205—207
Rayleigh — Lamb frequency equation, general branches of, real-, imaginary-wave number segments of, further on, terracing 196
Rayleigh — Lamb frequency equation, general branches of, wave pairs associated with 201
Rayleigh — Lamb frequency equation, generalized 200 411 434 447 infinite time
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