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| Miklowitz J. — The theory of elastic waves and waveguides |
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Thermoelasticity, uncoupled dynamic, governing equations of 474 577
Thermoelasticity, uncoupled dynamic, governing equations of, infinite plate problem, application to 474—477
Time average of harmonic waves 130—131
Time harmonic body waves 69—70
Time harmonic waves in half space 119—156 174—175
Time harmonic waves in infinite medium 60—70 93—94
Time harmonic waves in two welded half spaces 156—177
Time harmonic waves in waveguides 178—230
Timoshenko beam theory see Timoshenko bending theory
Timoshenko bending theory 8 377—382 394—409
Timoshenko bending theory, hyperbolicity of 397
Timoshenko bending theory, wave speeds in 395
Timoshenko — Uflyand — Mindlin plate theory 404 (See also Waveguides approximate
Torsional waves in a thin plate with circular cylindrical cavity, cavity wall rotary velocity, generated by 290
Torsional waves in a thin plate with circular cylindrical cavity, cavity wall shear stress, generated by 290
Torsional waves in a thin rod, initial angular twist, generated by 293
Torsional waves in a thin rod, nondispersive fundamental mode in 219
Torsional waves in a thin rod, section warping theory of 374
Torsional waves in an infinite, semi-infinite circular cylindrical rod, displacement modes for 220
Torsional waves in an infinite, semi-infinite circular cylindrical rod, frequency equation for 219—220
Torsional waves in an infinite, semi-infinite circular cylindrical rod, frequency spectra for 219—220
Torsional waves in an infinite, semi-infinite circular cylindrical rod, phase velocity spectra for 220
Total reflection 139—144 164—165 169—170 173—174 177
Transient waves See Infinite medium problems; Half space problems; Waveguide problems
Transmission coefficients 160
Transmission coefficients, at interface for displacements 161—162 163 169 172
Transmission coefficients, at interface for energy 161—162 165 169—170
Transmission coefficients, at interface for P waves 156—161 168—170 175
Transmission coefficients, at interface for potentials 160—161 164—165 168 172 175—176
Transmission coefficients, at interface for SH waves 170—174
Transmission coefficients, at interface for stress 161 169
Transmission coefficients, at interface for SV waves 156—160 161—162 169
Traveling sources 5 347 349—362 574—576
Uniqueness of solution for 47 50—52
Uniqueness of solution for discontinuous loadings 52
Uniqueness of solution for finite body 47 50—51
Uniqueness of solution for infinite anisotropic body 51
Uniqueness of solution for infinite body 51
Uniqueness of solution, conditions for in half-plane diffraction problems 489 491 498
Unloading waves VI VIII
Van der Waerden's method for asymptotic expansion of integrals 270
Vector, components of 20
Vector, decomposition of 60—61
Vector, in tensor notation 20
Vector, Laplacian of 45
Vector, law of transformation of 25
Vector, operators 45—46
Vector, potential 59
Vector, scalar product for 20
Vector, vector product for 20
Viscoelastic media, linear, books, surveys on waves in 578
Viscoelastic media, linear, Maxwell material rod in, boundary-initial value problem for 295
Viscoelastic media, linear, Maxwell material rod in, boundary-initial value problem for, solution of 296
Viscoelastic media, linear, Rayleigh waves diffracted from circular cylindrical cavity in 536
Viscoelastic media, linear, Rayleigh waves diffracted from circular cylindrical cavity in, by correspondence principle 636
von Schmidt wave See Head wave
Water waves 17
Watson's lemma 257
Watson's lemma, application to asymptotics of Laplace transform and inverse 257—261
Watson's lemma, application to asymptotics of Laplace transform and inverse, examples of long time approximations, static solution of 289 295 535 555
Watson's lemma, application to asymptotics of Laplace transform and inverse, examples of wavefront approximations 289 323—328 550—551 565—567
Watson's transformation in spherical obstacle diffraction problems 563—564
Wave diffraction 10 485—567
Wave dispersion 1 8 9 178—230
Wave group, analysis 8 186—188
Wave group, composition of 188
Wave group, simple 186—187
Wave group, velocity 8 186—187
Wave guide 1 6 16—17 178—230 approximate
Wave in piezoelectric-elastic solid 17
Wave number, along boundary 124
Wave number, in infinite plate rod 11 178—225
Wave number, in propagation direction 179 183
Wave number, in thickness direction 179 197
Wave number, of P wave 121
Wave number, of SH wave 154
Wave number, of SV wave 121
Wave pairs, reflection of 145—146
Wave pairs, refraction of 166—168
Wave reflection 120 123—134 152—162 168—175
Wave refraction 156—162 168—175
Wave trains, harmonic, finite number of 187
Wave trains, harmonic, finite number of, stationary phase condition for 187—188
Wave trains, harmonic, infinite 7 186
Wave trains, harmonic, infinite, spectral analysis of 188—192
Wave unloading VI-VIII
Wave velocity along boundary 124
Wave, length of P wave 121
Wave, length of SH wave 154
Wave, length of SV wave 121
Wave, phase velocity 179
Wave, propagation studies, early history of 2—10
Wave, propagation studies, early history of, diffraction in 10
Wave, propagation studies, early history of, fundamental representations in 2—4
Wave, propagation studies, early history of, half space in 4—6
Wave, propagation studies, early history of, impact in 9
Wave, propagation studies, early history of, two welded half spaces in 6
Wave, propagation studies, early history of, waveguides in 6—9
Wave, propagation studies, modern work in 10—12
Wavefront approximations by Randles — Miklowitz method 443
Wavefront approximations by Randles — Miklowitz method for response of plate 443
Wavefront approximations by Watson's lemma — Laplace transform expansions 257—258
Wavefront approximations by Watson's lemma — Laplace transform expansions for response to cavity diffraction 565—567
Wavefront approximations by Watson's lemma — Laplace transform expansions for response to cavity sources 289
Wavefront approximations in Cagniard — deHoop method 319—323
Wavefront approximations in Cagniard — deHoop method for response of half space 319—323
Wavefront approximations in Cagniard — deHoop method for response of plate 438—443
Wavefront approximations, steepest descents, by method of 264—271
Wavefront approximations, steepest descents, by method of, for response of half space 323—328
Wavefronts approximations 71 78
Wavefronts cusp type, in anisotropic plates 443
Wavefronts in a half space, conical 361
Wavefronts in a half space, head 322 327 341—344 361
Wavefronts in a half space, hemispherical 361
Wavefronts in a half space, regular, equivoluminal, dilatational 318 320—321 326 340—348 361
Wavefronts in a half space, SP wave (P wave grazing reflection) 346—348
Wavefronts in a half space, two-sided equivolumnal 313—314 322—323 327—328 341—344 346—348 361
Wavefronts in cavity source problems 281 289
Wavefronts in diffraction 485—487 516 550—551 558—560 565—567
Wavefronts in homogeneous medium 76—77
Wavefronts in waveguides 438—443 (See also “in a half space” here)
Wavefronts velocities 74—75
Wavefronts, dynamical conditions at 74
Wavefronts, Huyghen's construction of 77
Wavefronts, kinematical conditions at 73
Wavefronts, magnitude variations of 77—78
Waveguide problems See also Waveguides approximate
Waveguide problems, approximate theories for rod 382—409
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory 382—394
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, boundary-initial value problem 382
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, Laplace transform method 383—387
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, solution 383 386
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, solution, comparison with experiment, exact and approximate theories 393
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, solution, initial data jumps in 393—394
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, solution, long time-far field head of pulse response 388—389
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, solution, long time-far field head of pulse response, effect of station on magnitude of 574
Waveguide problems, approximate theories for rod, longitudinal impact, Love — Rayleigh theory, solution, long time-far field head of pulse response, higher order terms in, based on Mindlin — McNiven rod 574
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory 394—409
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory, boundary-initial value problem 394 396
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory, Laplace transform method 394—409
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory, solution 398 403—404
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory, solution, admissible parts 404
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory, solution, comparison with Bernoulli — Euler result 404 409
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory, solution, long time approximation of 404—409
Waveguide problems, approximate theories for rod, shear force, Timoshenko theory, solution, verification 404
Waveguide problems, approximate theory for plate, Timoshenko — Uflyand — Mindlin 404
Waveguide problems, approximate theory for plate, Timoshenko — Uflyand — Mindlin, on elastic foundation, line shear load response 420—421
Waveguide problems, approximate theory for plate, Timoshenko — Uflyand — Mindlin, point shear load 404
Waveguide problems, for infinite plate and axial symmetry 466—477
Waveguide problems, for infinite plate and axial symmetry, normal displacement on circular cavity wall with mixed edge conditions 471 473—474
| Waveguide problems, for infinite plate and axial symmetry, normal displacement on circular cavity wall with mixed edge conditions, Laplace-extended Hankel transform method 471 473—474
Waveguide problems, for infinite plate and axial symmetry, normal displacement on circular cavity wall with mixed edge conditions, solution, long-time approximation 474
Waveguide problems, for infinite plate and axial symmetry, normal point load 574
Waveguide problems, for infinite plate and axial symmetry, normal point load, early time response to 574
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem 466—467
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, boundary-initial value problem 466—467
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, displacement-potential relations 467—471
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, Laplace — Hankel transform method 468—471
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, solution, displacements 468—469
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, solution, displacements, long time-far field 470—472
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, solution, displacements, long time-far field, derivation of 469—471
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, solution, displacements, maximum response 471
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, solution, displacements, predominant period—time of occurrence criterion in longtime solution 471
Waveguide problems, for infinite plate and axial symmetry, symmetric normal point loads; equivalent layer—half space problem, stress-potential relations 468
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by 474—477
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by, Gaussian temperature distribution on plate face 474
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by, Laplace — Hankel transform method 475
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by, stresses, near-field response of midplane 475—477
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by, stresses, near-field response of midplane, comparisons based on mode integral sums 475—477
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by, stresses, near-field response of midplane, cutoff frequencies, influence of 475—477
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by, stresses, near-field response of midplane, mode integrals, numerical evaluation of 475—477
Waveguide problems, for infinite plate and axial symmetry, time-dependent thermal field, excitation by, stresses, near-field response of midplane, non-zero heating time 475
Waveguide problems, for infinite plate in plane strain 409—430
Waveguide problems, for infinite plate in plane strain, antisymmetric normal line loads 429
Waveguide problems, for infinite plate in plane strain, antisymmetric normal line loads, solution of 429
Waveguide problems, for infinite plate in plane strain, inversion of time transform first 425—429
Waveguide problems, for infinite plate in plane strain, inversion of time transform first, frequency branches, real Rayleigh — Lamb in 425—428
Waveguide problems, for infinite plate in plane strain, inversion of time transform first, path integrals in 425—426
Waveguide problems, for infinite plate in plane strain, Laplace-exponential Fourier transform method 410—420
Waveguide problems, for infinite plate in plane strain, normal line load, decomposition of 429—430
Waveguide problems, for infinite plate in plane strain, normal line load, direct solution of 429
Waveguide problems, for infinite plate in plane strain, normal line load, solution by addition of symmetric and antisymmetric parts 429—430
Waveguide problems, for infinite plate in plane strain, solution by inverting spatial transform first 419—420
Waveguide problems, for infinite plate in plane strain, solution by inverting spatial transform first, anomalous dispersion in 421
Waveguide problems, for infinite plate in plane strain, solution by inverting spatial transform first, cutoff frequencies, influence of 420
Waveguide problems, for infinite plate in plane strain, solution by inverting spatial transform first, long time-far field approximations to integrals of 423—424
Waveguide problems, for infinite plate in plane strain, solution by inverting spatial transform first, responses from wave number branch segment (real, imaginary, complex) integrals in 420—422
Waveguide problems, for infinite plate in plane strain, solution by inverting spatial transform first, standing waves in 421—422
Waveguide problems, for infinite plate in plane strain, solution by inverting spatial transform first, validity of, for near field, restriction to moderately sharp inputs 424
Waveguide problems, for infinite plate in plane strain, solution by inverting time transform, first 426
Waveguide problems, for infinite plate in plane strain, solution by inverting time transform, first, branch integrands in, proof of nonsingular nature of 426—428
Waveguide problems, for infinite plate in plane strain, solution by inverting time transform, first, long time-far field approximations 428—429 481
Waveguide problems, for infinite plate in plane strain, solution by inverting time transform, first, negative x-traveling waves in 428—429
Waveguide problems, for infinite plate in plane strain, solution by inverting time transform, first, static 426
Waveguide problems, for infinite plate in plane strain, solution by inverting time transform, first, uniqueness of the solution 428
Waveguide problems, for infinite plate in plane strain, solution by inverting time transform, first, uniqueness of the solution, comparison of two forms of solution and inversion techniques 428—429
Waveguide problems, for infinite plate in plane strain, symmetric normal line loads 409—429
Waveguide problems, for infinite plate in plane strain, symmetric normal line loads, boundary-initial value problem 409—410
Waveguide problems, for infinite plate in plane strain, symmetric normal line loads, generalized Rayleigh — Lamb frequency equation, wave number branches and their properties 411—416
Waveguide problems, for infinite plate in plane strain, symmetric normal line loads, inversion of spatial transform first 411—420
Waveguide problems, for infinite plate in plane strain, symmetric normal line loads, path integrals in 417—418
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions 430—443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, anti-symmetric excitation 435
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, long time-far field approximations 436—437
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact 431—434 436—443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, boundary-initial value problem 431—434
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, inversion techniques 411—420 425—429 (detail under “infinite plate” here)
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, Laplace-sine, cosine transform method 432—434
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, long time-far field approximations 436—437
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, solution, formal axial, thickness, strains 434
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, stress-strain relations 431
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations 438—443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, amplitude coefficients 441 443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, by Cagniard — deHoop method 438—443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, by Randles — Miklowitz method 443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, comparison with experiment 443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, for strain 441
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, rays, family of S, P 440
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, sources, rays and wavefront 440
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, longitudinal impact, wavefront approximations, wavefront positions 441—442
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, mixed pressure shock 431—432 434—435 436—443
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, mixed pressure shock, boundary-initial value problem 431—435
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, mixed pressure shock, Laplace-sine, cosine transform method 435
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, mixed pressure shock, Laplace-sine, cosine transform method, inversion techniques 411—420 425—429
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, solution, formal axial thickness strains 435
Waveguide problems, for semi-infinite plate in plane strain with mixed edge conditions, wavefront approximations 438—443 (detail under “longitudinal impact” here)
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions 444—466
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, long-time solution, restriction to 444
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, method preliminaries 444—448
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, method preliminaries, boundedness condition on solution and corresponding integral equations 446—448
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, method preliminaries, double Laplace transform, use of 444
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, method preliminaries, double transformed displacements 445—446
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, method preliminaries, edge unknowns, time transformed 444
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, method preliminaries, quasi-formal solution 445—446
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, method preliminaries, Rayleigh — Lamb exponentially unbounded waves and corresponding generalized complex wave numbers in 446—447
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, nonseparability of 430—431 444
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock 431—432 444—448 449—457
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock, boundary-initial value problem 431—432 445 449
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock, edge unknowns, determination of 449—452
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock, edge unknowns, determination of, boundedness condition for coefficients of, algebraic 452
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock, edge unknowns, determination of, boundedness condition for small p 454—455
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock, edge unknowns, determination of, time transformed 449—452
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock, formal long-time solution 445—446 455
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem A: nonmixed pressure shock, long-time solution, displacement strains 455—457
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load 431—432 444—448 457—466
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, boundary-initial value problem 431—432 445 457
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, edge unknowns, determination of time transformed 458—461
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, edge unknowns, determination of time transformed, decomposition of problem into Flammant singular, selfequilibrated residual and nonmixed pressure shock problems 458—461
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, edge unknowns, determination of time transformed, edge unknowns, Flammant problem singular 458—460
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, edge unknowns, determination of time transformed, edge unknowns, regular 461
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, edge unknowns, time transformed 461
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, edge unknowns, time transformed, boundedness condition for coefficients of, algebraic 461
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, edge unknowns, time transformed, boundedness condition for small p 462
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, formal long-time solution 445—446
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, long-time solution, displacements, strains 463—465
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problem B: nonmixed line load, method of reduction for coefficients of edge unknowns 462—463
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problems of nonmixed displacements 465—466
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problems of nonmixed displacements, cantilevered plate, symmetric face normal line loads near base 465
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problems of nonmixed displacements, head of the pulse long time—far field solution for reflected disturbance 465
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problems of nonmixed displacements, velocity shock problem 465
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problems of nonmixed displacements, velocity shock problem, by finite-difference numerical method 465
Waveguide problems, for semi-infinite plate in plane strain with nonmixed edge conditions, problems of nonmixed displacements, velocity shock problem, longitudinal strain responses 465—466
Waveguides, approximate theories for, one-dimensional 367—382 (See also Waveguide problems)
Waveguides, approximate theories for, one-dimensional, compressional wave, rod 367—374
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, elementary theory 367—369
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, elementary theory, displacement equation of motion 368
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, elementary theory, frequency spectrum 368—369
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, elementary theory, use of 368—369
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, Love — Rayleigh theory 369 371—374
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, Love — Rayleigh theory, boundary conditions 373—374
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, Love — Rayleigh theory, displacement equation of motion 373
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, Love — Rayleigh theory, frequency spectrum 369
Waveguides, approximate theories for, one-dimensional, compressional wave, rod, Love — Rayleigh theory, use of 369 373—374
Waveguides, approximate theories for, one-dimensional, flexural wave, rod 374—382
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory 374—377
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, boundary conditions 376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, curvature theorem 375—376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, deflection equation of motion 376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, element motion 375
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, frequency spectrum 377
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, moment-deflection relation 375
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, section normal stress-moment relation 376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, section shear stress-shear force relation 376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, transverse shear force-deflection relation 376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Bernoulli — Euler (elementary) theory, use of 377
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory 377—382
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, advantages of 381—382
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, boundary conditions 380
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, deflection equations of motion 380
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, deflection slope 378
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, element motion 377—378
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, extensions to thin plate 382
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, frequency spectrum, comparison with exact, Bernoulli — Euler theory 381
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, moment, transverse shear force 379
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, moment-deflection relation 379
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, potential energy 379
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, section normal stress-moment relation 376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, section shear stress-shear force relation 376
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, shear coefficient  379
Waveguides, approximate theories for, one-dimensional, flexural wave, rod, Timoshenko bending theory, shear force-deflection relation 379
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