|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Miklowitz J. — The theory of elastic waves and waveguides |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Fourier integral, theorem of 231
Fourier integral, theorem of, conditions in, relaxation of 232 236
Fourier series, quarter-range 450
Fourier sine and cosine transforms 246—248
Fourier sine and cosine transforms, appropriate selection of 248
Fourier sine and cosine transforms, conditions on 243 247
Fourier sine and cosine transforms, conditions on inverse 231—233 244 247
Fourier sine and cosine transforms, inversion integrals of 246
Fourier sine and cosine transforms, of derivatives 247—248
Fourier sine and cosine transforms, operator integrals of 246
Fourier sine and cosine transforms, pairs 246
Fourier sine and cosine transforms, properties of, other 248
Fourier sine and cosine transforms, relation to exponential transform 246 248
Fourier sine and cosine transforms, tables of 248
Fourier sine and cosine transforms, use of 432—435
Fourier transform, exponential see Exponential Fourier transform
Fourier — Bessel series, for incident pulse transform 538
Fourier — Bessel series, for incident pulse transform, generating function for 538
Fourier — Mellin inversion theorem 236
Fracture, second VIII
frequency 121
Frequency, circular 69
Frequency, cutoff, for waveguides see Cutoff frequencies
Frequency, dimensionless, for infinite plate 183
Frequency, equations, for waveguides 6—7 185 Pochhammer
Frequency, spectra, for waveguides 7—8 11 185
Fresnel integrals 405 438
Friedlander's representation of solution, in exterior cylinder diffraction problems 520—521
Friedlander's representation of solution, in interior cylinder refraction-reflection problems 558—559
Friedlander's representation of solution, wave form of function in 521
Friedlander's representation of solution, wave sum in 521
Gauge conditions 62—63
Gauge conditions, use of 153 350
Gauge invariance 63
Geometrical acoustics, optics 71 78
Geometrical wave solution in halfplane diffraction 515
Governing equations in cylindrical coordinates 215—217
Governing equations in cylindrical coordinates, and axially symmetric compression 220—221
Governing equations in cylindrical coordinates, and axially symmetric plane strain 284
Governing equations in cylindrical coordinates, and axially symmetric torsion 217—218
Governing equations in cylindrical coordinates, and plane strain 522
Governing equations in rectangular Cartesian coordinates 32 40 42 44—46 59 66
Governing equations in rectangular Cartesian coordinates, and antiplane strain 152—155
Governing equations in rectangular Cartesian coordinates, and plane strain 121—123
Governing equations in spherical coordinates 45—46 59—60
Governing equations in spherical coordinates, and axial symmetry 561
Governing equations in spherical coordinates, and spherical symmetry 278—279
Grazing incidence of P wave 4 136—137 146 163 166 314
Grazing incidence of SH wave 173
Grazing incidence of SV wave 4 137—138 146 163 166
Grazing reflection of P wave 141 164
Grazing reflection of SV wave 138
Grazing refraction of P wave 164 165—166
Grazing refraction of SV wave 164 165—166
Green's function for three dimensions 83
Green's function for two dimensions 86
Group, wave, in spectral analysis of wave train 189—192
Group, wave, simple 186
Group, wave, simple, carrier wave in 187
Group, wave, simple, carrier wave in, modulation of 187
Group, wave, stationary phase condition for 187—188
Group, wave, velocity of 186
Group, wave, velocity of, relation with velocity of energy transmission 192—193
Group, wave, velocity of, relation with velocity of spectra for infinite plate 191
Guided surface waves on a half space 576
Guided waves 178 (See also Waveguide problems; Waveguides approximate
Half space problems, antiplane surface tangential line load 363
Half space problems, antiplane surface tangential line load, displacement solution 363
Half space problems, axially symmetric vertical point load 5 333—348
Half space problems, axially symmetric vertical point load, boundary-initial value problem 333—334
Half space problems, axially symmetric vertical point load, displacement response, interior 340—344
Half space problems, axially symmetric vertical point load, displacement response, interior, surface load 340—344
Half space problems, axially symmetric vertical point load, displacement response, interior, wavefronts in 340—344
Half space problems, axially symmetric vertical point load, displacement response, surface 338—340 345—348
Half space problems, axially symmetric vertical point load, displacement response, surface, buried load 345—348
Half space problems, axially symmetric vertical point load, displacement response, surface, surface load 338—340
Half space problems, axially symmetric vertical point load, displacement response, surface, wavefronts in 339—340 347
Half space problems, axially symmetric vertical point load, displacement-potential relations 335
Half space problems, axially symmetric vertical point load, Laplace — Hankel transform method 334—339 344
Half space problems, axially symmetric vertical point load, Laplace — Hankel transform method, inversion in 336—339
Half space problems, axially symmetric vertical point load, reflected wave system, buried load, analog of surface source system 347
Half space problems, axially symmetric vertical point load, stress-potential relations 335
Half space problems, axially symmetric vertical point load, symmetric delta function for 333—334
Half space problems, axially symmetric vertical point load, wavefronts compared with line load case 339—340 344
Half space problems, buried line dilatational source 5 329—332
Half space problems, buried line dilatational source, boundary-initial value problem 329
Half space problems, buried line dilatational source, Laplace-exponential Fourier transform method 329—331
Half space problems, buried line dilatational source, Laplace-exponential Fourier transform method, Cagniard — deHoop method in 330—331
Half space problems, buried line dilatational source, Lapwood's representation for transformed source 330
Half space problems, buried line dilatational source, Lapwood's representation for transformed source, inverse of 331
Half space problems, buried line dilatational source, surface response 331—332
Half space problems, buried line dilatational source, surface response, Rayleigh waves in, development of 331—332
Half space problems, dipole source 573
Half space problems, dipole source, surface displacement response to surface dipole 573
Half space problems, expanding ring, disk surface loads particle trajectory dependence on load speeds 361—362
Half space problems, expanding ring, disk surface loads particle trajectory dependence on load speeds, solution dependence on load speeds 361—362
Half space problems, finite distributed surface sources, displacement responses 573—574
Half space problems, finite distributed surface sources, displacement responses, impulsive twisting moment 573
Half space problems, finite distributed surface sources, displacement responses, load over rectangular area 574
Half space problems, finite distributed surface sources, displacement responses, torsional loading over circular area 573—574
Half space problems, finite distributed surface sources, displacement responses, uniform pressure over circular area 573
Half space problems, finite distributed surface sources, displacement responses, uniform pressure over infinite strip 573
Half space problems, surface nonuniformly traveling loads 574
Half space problems, surface normal line load 4 299—328
Half space problems, surface normal line load, boundary-initial value problem 299—300
Half space problems, surface normal line load, displacement-potential relations 301
Half space problems, surface normal line load, Laplace-exponential Fourier transform method 300—313
Half space problems, surface normal line load, Laplace-exponential Fourier transform method, Cagniard — deHoop method in 302—319
Half space problems, surface normal line load, solution 312—314
Half space problems, surface normal line load, solution, plane of symmetry response in 318—319
Half space problems, surface normal line load, solution, stress-potential relations 301
Half space problems, surface normal line load, solution, surface displacement response in 314—318
Half space problems, surface normal line load, solution, wavefront approximations 319—328
Half space problems, surface normal point traveling load 347 349—362
Half space problems, surface normal point traveling load, boundary-initial value problem 349
Half space problems, surface normal point traveling load, displacement component, symmetries of 352
Half space problems, surface normal point traveling load, gauge condition in 350
Half space problems, surface normal point traveling load, Laplace-double exponential Fourier transform method 349—359
Half space problems, surface normal point traveling load, Laplace-double exponential Fourier transform method, Cagniard — deHoop method in 351—359
Half space problems, surface normal point traveling load, load speed ranges 352
Half space problems, surface normal point traveling load, solution, displacement, conical 358 360
Half space problems, surface normal point traveling load, solution, displacement, hemispherical 357 359—360
Half space problems, surface normal point traveling load, solution, displacement, interior, supersonic load, dilatation waves 355 357—360
Half space problems, surface normal point traveling load, solution, displacement, principal value integrals in 359 360
Half space problems, surface normal point traveling load, solution, displacement, regions and conditions for 354—355
Half space problems, surface normal point traveling load, solution, displacement, wavefronts, conical 361
Half space problems, surface normal point traveling load, solution, displacement, wavefronts, hemispherical 361
Half space problems, surface tangential point load 573
Half space problems, surface tangential point load, horizontal displacement response along axis below load 573
Half space problems, surface tangential point load, surface displacement response 573
Half space, superficial layer on, Love waves in 211—214
Hamilton's principle 371
Hamilton's principle, approximate theories, application in 380 371—379
Hamilton's principle, condition of existence of strain energy function 371
Hamilton's principle, derivation of 369—371
Hankel functions 70
Hankel functions, asymptotic expansions for 70 529—530
Hankel integral theorem 248—249
Hankel transform 248—250
Hankel transform, applications of 250 334—339 468—471
Hankel transform, conditions on 249
Hankel transform, conditions on inverse 248—249
Hankel transform, convergence of 249
Hankel transform, extended (exterior domain) 471 473—474
Hankel transform, extended (exterior domain), application of 471 474
Hankel transform, inversion integral of 248
Hankel transform, of derivatives 249—250
Hankel transform, operator integral of 249
Hankel transform, pairs 248—249
Hankel transform, properties of, other 250
| Hankel transform, tables of 250
Head of the pulse approximation 389 436—437
Head of the pulse approximation, effect of station on magnitude of 574
Head of the pulse approximation, elementary theory relation to 389
Head of the pulse approximation, higher order terms in 574
Head of the pulse approximation, momentum equation for 390
Head of the pulse approximation, nondecaying nature of 389
Head wave in diffraction of dilatational pulse by traction free half plane 510 512 516
Head wave in half space surface normal line load problem 312—316 321—322 326—327
Head wave in half space surface normal line load problem, interior 312—314
Head wave in half space surface normal line load problem, wavefronts of 322 327
Head wave in half space surface normal point load problem 340—344
Head wave in half space surface normal point traveling load problem 361
Head wave in half space surface normal point traveling load problem, wavefronts of 361
Head wave in semi-infinite plate, mixed edge conditions 440—443
Head wave in semi-infinite plate, mixed edge conditions, wavefronts of 440—443
Helmholtz resolution of vector 60—61
Hemispherical waves 357 359—360 361
History, early 2—10
Homogeneous solutions 517 (See also Self-similar solutions)
Hooke's law, generalized 38—39
Hooke's law, generalized, homogeneous, isotropic case 39—40
Huyghen's construction of wavefronts 77
Huyghen's principle 77
Hydrostatic pressure, uniform 41
Hyperbolic equations 17
Illuminated zone 486—487 518—519 526 541
impact 9—10
Incident P wave 120 121 157
Incident Rayleigh surface waves 146—151
Incident SH wave 154 170—171
Incident Stoneley interface waves 165—168
Incident SV wave 120 121 157
Incident wave in diffraction problems 485—486 496 518 541
Infinite medium problems, antiplane displacement source, displacement solution of 363—364 (See also Body force problems; Cavity source problems; Initial value problems; Diffraction problems)
Inhomogeneous media, waves in 577
Inhomogeneous media, waves in, early work on 577
Inhomogeneous media, waves in, recent work on 577
Inhomogeneous media, waves in, recent work on by Cagniard — deHoop method 577
Inhomogeneous media, waves in, recent work on by geometrical optics 577
Inhomogeneous media, waves in, recent work on for high frequency cylindrical and spherical waves 577
Inhomogeneous wave equation, solution of 116
Initial value problem, Huyghen's principle in 106—107
Initial value problems 3—4 96—112
Initial value problems, displacement solutions for two- and three-dimensional 106
Initial value problems, one-dimensional 96—103
Initial value problems, one-dimensional, characteristics in 98
Initial value problems, one-dimensional, discontinuities in initial values in 102—103
Initial value problems, one-dimensional, initial conditions in 96
Initial value problems, one-dimensional, method of characteristics in 107—112
Initial value problems, one-dimensional, point domain of dependence in 98
Initial value problems, one-dimensional, point domain of influence in 98
Initial value problems, one-dimensional, solution for initial displacement of 98—99
Initial value problems, one-dimensional, solution for initial velocity of 98—102
Initial value problems, three-dimensional 103—105
Initial value problems, three-dimensional, Kirchhoff's formula for 103
Initial value problems, three-dimensional, point domain of dependence in 106
Initial value problems, three-dimensional, Poisson's solution for potentials in 105
Initial value problems, two-dimensional 105—106
Initial value problems, two-dimensional, method of descent for 105—106
Initial value problems, two-dimensional, point domain of dependence in 106
Initial value problems, two-dimensional, solution for potentials in 106
Initial value problems, two-dimensional, stretched infinite membrane in 295
Integral equations, dual 491 499—500 501
Integral equations, dual, Clemmow's method for solving 490—492 499—501
Integral representations, in diffraction problems 12 96 488
Integral representations, Kirchhoff's formula for potential 4 95
Integral representations, Love's formula for displacement 4 95—96
Integral transform methods see Bilateral Laplace Laplace Exponential Fourier Hankel extended
Integral transforms 232—250
Interface waves 6 57 165—168
Interface, reflection and refraction from see Reflection refraction SH-wave
Inversion integral, bilateral Laplace transform 242
Inversion integral, exponential Fourier transform 242 243 245
Inversion integral, Fourier cosine transform 246
Inversion integral, Fourier sine transform 246
Inversion integral, Hankel transform 248
Inversion integral, Laplace transform 232
Isotropy 39—42
Jordan's inequality 259
Jordan's lemma, application of 259 305
Kelvin's method of stationary phase 271—277
kinetic energy 48
Kinetic energy, density 48—49
Kirchhoff's integral representation 95
Kronecker delta 20
Lagrange multipliers, method of 29
Lamb's problem for buried line dilatational source 329—332
Lamb's problem for surface normal line load 299—328
Lamb's problem for surface normal point traveling load 347 349—362
Lamb's problem for transversely isotropic half space 576
Lamb's problem for vertical point load 333—348
Lamb's problem for vertical point load, buried 333—336 334—348
Lamb's problem for vertical point load, surface 336—344
Lamb's problem, early, techniques for 11
Lamb's problem, early, work on 11
Lame solution of displacement equations of motion 58—62
Lame solution of displacement equations of motion for body force problems 79—80
Lame solution of displacement equations of motion, completeness of 61—62 116
Lame solution of displacement equations of motion, dilatation in 59
Lame solution of displacement equations of motion, displacement vector field of 59
Lame solution of displacement equations of motion, potentials in 59
Lame solution of displacement equations of motion, rotation in 59
Lame solution of displacement equations of motion, wave equations in 59
Laplace integral 256
Laplace integral, asymptotic expansion of 256—261
Laplace integral, asymptotic expansion of by parts integration 257
Laplace integral, asymptotic expansion of by Watson's lemma 257
Laplace integral, asymptotic expansion of by Watson's lemma, for Laplace transform, large parameter-short time (wavefront) approximation 257—258
Laplace integral, asymptotic expansion of by Watson's lemma, for Laplace transform, small parameter-long time approximation and static solution 258—261
Laplace transform 232—241
Laplace transform of derivatives 238
Laplace transform, applications of 278—360 383—420 432—474 489—550 562—566
Laplace transform, asymptotic expansions of 257—261
Laplace transform, asymptotic expansions of for long time (static solution) 258—261
Laplace transform, asymptotic expansions of for short time (wavefront) 257—258
Laplace transform, conditions on 236
Laplace transform, conditions on inverse 231—233 236
Laplace transform, conditions on inverse, relaxation of 232 236
Laplace transform, division by parameter 239
Laplace transform, Fourier — Mellon inversion theorem 236
Laplace transform, inversion integral of 232
Laplace transform, negative parameter, inversion for 328
Laplace transform, operator integral of 232
Laplace transform, operator integral of, convergence of 233 236—237
Laplace transform, operator integral of, linearity of 237
Laplace transform, operator integral of, use of 233—234
Laplace transform, pairs 232
Laplace transform, parameter, transformation 233
Laplace transform, product and convolution theorem 238—239
Laplace transform, product and convolution theorem, application of 52—54
Laplace transform, shift rule 239—240
Laplace transform, tables 241
Laplace transform, transforms of singular inverses 240—241
Laplace transform, transforms of singular inverses, delta function, Dirac 241
Laplace transform, uniqueness of 237
Laplace's method for asymptotic expansion of integrals 262—264
Laplace's method for asymptotic expansion of integrals, critical points in; corresponding approximations 264
Laplacian in cylindrical coordinates 217
Laplacian in rectangular Cartesian coordinates 45
Laplacian of vector 45—46
Laws of P-wave, reflection 124
Laws of P-wave, refraction 158—159 164
Laws of SH-wave, refraction 171
Laws of SV-wave, reflection 124
Laws of SV-wave, refraction 158—159 164
Layer see Plates infinite semi-infinite;
Layered media 16
Layered media, time harmonic waves in 226
Legendre polynomials 562—565
|
|
|
| Ðåêëàìà |
|
|
|
|
|
|
|
|
Î ïðîåêòå