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Eringen A.C., Suhubi E.S. — Elastodynamics (vol. 2) Linear theory
Eringen A.C., Suhubi E.S. — Elastodynamics (vol. 2) Linear theory

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Название: Elastodynamics (vol. 2) Linear theory

Авторы: Eringen A.C., Suhubi E.S.

Аннотация:

This present volume (Volume II) of "Elastodynamics" is devoted to an
exposition of the dynamical theory of linear isotropic elasticity. The plan
and the scope of this treatise includes a thorough discussion of the fundamental theorems concerning elastodynamics and various mathematical methods of solutions and their applications to a class of problems in one, two, and three dimensions. The uniqueness and reciprocal theorems are presented and applied. The solutions by means of potentials, singular solutions, complex function technique, methods of integral equations, and integral transforms are explored. Free and forced vibrations of bodies, of finite and infinite extent, having boundaries that are plane, cylindrical (circular, elliptic), ellipsoidal, and spherical shapes are discussed in some detail. Both initial- and boundary-value problems, including displacement
traction and mixed boundary conditions, are solved. The book closes with a chapter on diffraction theory. Various tables and graphs displaying frequencies, displacement, and stress fields should be useful to practitioners. Originally it was our intention to include accounts of anisotropic, imhomogeneous elastic, and thermoelastic solids, and lattice dynamics. Unfortunately, owing to length limitations, this project had to be abandoned.


Язык: en

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 673

Добавлена в каталог: 17.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel integral equation      764
Absolute temperature      345
Adjoint operator      646
Admissible displacement field      451
Admissible state      444
Admissible stress field      452
Amplitude function      957
Analytic continuation      587 593
Antiplane motion      413
Antiplane motion of a slab      690
Antiplane motion of a slab of a finite slab      692
Antiplane motion of a slab of a semi-infinite slab      692
Associated Legendre functions      730 808 811
Associated Legendre functions, orthogonality      812
Asymptotic solutions for elastic waves      969
Asymptotic solutions for scalar wave equation      956
Asymptotic solutions for scalar wave equation, cylindrical waves      959
Asymptotic solutions for scalar wave equation, diffraction from a half-plane      966
Asymptotic solutions for scalar wave equation, diffraction from a half-plane, cylindrical waves      966
Asymptotic solutions for scalar wave equation, spherical waves      967
Asymptotic solutions from a parabolic cylinder      960
Asymptotic solutions from a screen      962
Asymptotic solutions from a slit      967
Balance of momenta      344
Balance of momenta in orthogonal coordinates      718
Beltrami — Michell compatibility equations      356
Bessel equation      693
Bessel functions      388 493 694 775
Bicharacteristics      970
Bilinear concomitant      646
Body force      345
boundary conditions      346 347 443
Bromwich contour      651
Buried line impulse      665
Buried line impulse, displacements      666
Buried line impulse, jump conditions      665 666
Buried line impulse, surface displacements      672
Buried pressure source      652
Buried pressure source, surface displacements      663 664
Cagniard — de Hoop method      651 656 668 874
Carrier wave      551
Caustic      958
Caustic, points      958
Chaplygin transformation      601
Characteristic equation      970
Characteristic equation, surface      970
Characteristics      459 602 605
Circular cavity, dynamic pressure      490
Circular cavity, plane motion, dynamic tractions      708
Circular cavity, plane motion, dynamic tractions, concentrated loads      711
Circular cavity, plane motion, dynamic tractions, moving loads      711 713
Circular cavity, plane motion, dynamic tractions, periodic moving loads      712
Circular cavity, plane motion, dynamic tractions, uniform tractions      710 711
Circular cylinder problem, displacements      774 776
Circular cylinder problem, flexural oscillations      785
Circular cylinder problem, flexural oscillations, cross-sectional distortions      789
Circular cylinder problem, flexural oscillations, group velocity      787 788
Circular cylinder problem, flexural oscillations, phase velocity      787 788
Circular cylinder problem, harmonic solutions      774
Circular cylinder problem, Helmholtz potentials      773 776
Circular cylinder problem, hollow cylinders      792
Circular cylinder problem, hollow cylinders, frequencies      794 796—801
Circular cylinder problem, hollow cylinders, Lame modes      795 796
Circular cylinder problem, longitudinal oscillations      780
Circular cylinder problem, longitudinal oscillations, group velocity      784
Circular cylinder problem, longitudinal oscillations, phase velocity      783
Circular cylinder problem, plane motion      693
Circular cylinder problem, plane motion, displacements      694
Circular cylinder problem, plane motion, dynamic tractions      700
Circular cylinder problem, plane motion, dynamic tractions, concentrated loads      703 704
Circular cylinder problem, plane motion, dynamic tractions, displacements      701
Circular cylinder problem, plane motion, dynamic tractions, moving loads      704 706
Circular cylinder problem, plane motion, dynamic tractions, periodic moving loads      705
Circular cylinder problem, plane motion, dynamic tractions, stresses      701
Circular cylinder problem, plane motion, dynamic tractions, uniform tractions      703
Circular cylinder problem, plane motion, free vibrations      696
Circular cylinder problem, plane motion, free vibrations, axisymmetric oscillations      696
Circular cylinder problem, plane motion, free vibrations, extensional axisymmetric oscillations      697
Circular cylinder problem, plane motion, free vibrations, nonaxisymmetric oscillations      699
Circular cylinder problem, plane motion, free vibrations, shear vibrations      698
Circular cylinder problem, plane motion, harmonic waves      693
Circular cylinder problem, plane motion, Lam6 potentials      693
Circular cylinder problem, plane motion, stresses      695
Circular cylinder problem, stresses      774 777
Circular cylinder problem, surface tractions      802
Circular cylinder problem, thickness shear vibrations      791
Circular cylinder problem, thickness shear vibrations, frequencies      791 792
Circular cylinder problem, torsional oscillations      779
Circular cylinder problem, torsional oscillations, group velocity      781
Circular cylinder problem, torsional oscillations, phase velocity      781
Classical energy identity      365
Compatibility conditions      345
Complex potentials, uniformly moving sources      568 571
Complex potentials, uniformly moving sources, singular solution      571 572
Complex variables      565 567
Conservation of energy      344
Conservation of mass      344
Constitutive equations      345 443
Convoluted forms of field equations, displacement formulation      359
Convoluted forms of field equations, stress formulation      359 443
Cylinder functions      694
Cylindrical waves      488
Cylindrical waves, initial-value problem      496
D'Alembert solution      457 458
Delta distribution      370 371 382
Diffraction      863
Diffraction coefficient      966
Diffraction of elastic waves      864—869
Diffraction of elastic waves, displacement boundary values      868
Diffraction of elastic waves, traction boundary values      868
Diffraction of P-waves from a finite crack      944
Diffraction of P-waves from a finite crack, normal incidence      951
Diffraction of P-waves from a finite crack, numerical results      953—955
Diffraction of P-waves from a finite crack, radiation field      955
Diffraction of P-waves from a rigid half-plane      880
Diffraction of P-waves from a rigid strip      932 939
Diffraction of SH-waves from a finite crack      952
Diffraction of SH-waves from a finite crack, numerical results      953—955
Diffraction of SH-waves from a rigid half-plane      870
Diffraction of SH-waves from a rigid strip      941
Diffraction of SH-waves from a semi-infinite crack      877
Diffraction of SV-waves from a finite crack      944
Diffraction of SV-waves from a rigid strip      932 941
Diffusion      383 492
Dilatation      348
dispersion      550
Dispersion, anomalous      552
Dispersion, normal      552
Dispersion, relation      551
Displacement vector      345
Double layer distribution      378 407
Dual integral equations      936 942 947
Dynamical admissible stress field      452
Eiconal equation      957
Eigenfunction expansions      437—442
Eigenfunction expansions, eigenfunctions      438
Eigenfunction expansions, eigenfunctions, completeness of      440
Eigenfunction expansions, eigenfunctions, orthonormality of      439
Eigenfunctions for cylindrical domains      492
Eigenfunctions for finite strips      468
Eigenfunctions for spherical domains      484
Elastodynamic state      361 363 365 437
Elastodynamic state of quiescent past      361 363 673 674
Elastodynamic state, addition      362
Elastodynamic state, convolution      362
Elastodynamic state, equality      362
Elastodynamic state, multiplication by scalars      362
Elliptic coordinates      920
Elliptic coordinates, wave equation in      920
Elliptic equation      567 601
Elliptic integrals      685 750
Energy flux vector      557
Energy propagation velocity      556—558
Entire function      632 769
Entropy density      345
Equivoluminal displacements      354 719
Field equations      346
Finite line source      727—734
Finite line source, Lame potentials      731 732
Finite strip, boundary-value problem      470
Finite strip, eigenfunctions      468
Finite strip, initial-value problem      467 468
Formulation of boundary-value problems      421—430
Formulation of boundary-value problems, Green's function      425—430
Formulation of boundary-value problems, Green's function for first problem      426
Formulation of boundary-value problems, Green's function for second problem      429
Formulation of boundary-value problems, Green's function, fundamental      427 428 430
Formulation of boundary-value problems, integral equations      421—425
Formulation of boundary-value problems, integral equations, first problem      423
Formulation of boundary-value problems, integral equations, second problem      424
Fourier kernel      645
Fourier transform      476 652 654 665 687 701 708
Fourier — Legendre expansion      834 837 845
Fredholm integral equation      936 942 948
Frenet equations      963
frequency      385
Frequency, fundamental      469
Fundamental singular solution of elastodynamics      390 394 395
Fundamental singular solution of elastodynamics, dynamic doublet state      401—403
Fundamental singular solution of elastodynamics, stress field      396 397
Fundamental singular solution of wave equation      371
Galerkin solution of elastostatics      355
Generalized energy identity      362
Generalized plane motion      455
Generalized Rayleigh waves      539 547
Generalized Rayleigh waves, group velocity      550
Generalized Rayleigh waves, phase velocity      550
Green's function in infinite region of elastodynamics      400
Green's function in infinite region of elastodynamics, two-dimensional      412
Green's function in infinite region of wave equation      372 374
Green's function in infinite region of wave equation, symmetry      372
Green's state, first kind      425
Green's state, second kind      428
Group velocity      551 552 557 558
Hamilton's principle      556
Hankel function      387 388 491 694 775
Hankel function, asymptotic values      390 775
Hankel transform      497
Harmonics      469
Head wave      581 603 620
Heat source density      345
Helmholtz equation      386
Helmholtz potentials      722 742
Helmholtz resolution theorem      348 349 719
Hilbert problem      594 596
Homogeneous function      600
Hooke's law      345 719
Huygens's principle      378
Hyperbolic equation      567 601
Hyperelliptic integral      638
Infinite slab      687
Infinite slab, antisymmetric normal loading      689
Infinite slab, symmetric normal loading      689
Initial conditions      346 443
Integral representation theorems of elastodynamics for displacements      404 406
Integral representation theorems of elastodynamics for stresses      409
Integral representation theorems of elastodynamics, two-dimensional      410 411
Integral representation theorems of wave equation      372 373 381
Integral transform methods in elastodynamics      649
Integral transform methods in elastodynamics, Fourier transforms      649
Integral transform methods in elastodynamics, Fourier transforms of stresses and displacements      650
Integral transform methods in elastodynamics, Fourier — Laplace transforms      651
Integral transforms      645
Integral transforms, Fourier      647
Integral transforms, Fourier cosine and sine      647
Integral transforms, Hankel      648
Integral transforms, Hilbert      648
Integral transforms, Kantorovich — Lebedev      648
Integral transforms, kernel of      645
Integral transforms, Laplace      647
Integral transforms, Laplace, two-sided      647
Integral transforms, Mellin      648
Internal energy density      345
Irrotational displacements      354 719
Jacobian      958 965
Jump conditions      344
Kinematically admissible displacement field      451
Kinematically admissible state      444
Kirchhoff integral representation      376 383
Lagrange equations      556
Lagrangian      556
Lamb's problem, axisymmetric      741—752
Lamb's problem, axisymmetric, displacements      747 749
Lamb's problem, axisymmetric, moving-point load      752
Lamb's problem, plane      614—626 652
Lamb's problem, plane, displacement field      615—617 621
Lamb's problem, plane, stress field      623 624 626
Lame potentials      348 353 355 503 693
Lame potentials, completeness of      350
Landau notation      380
Laplace transform      653 665 687 691 731 742 872 877 881
Laplace transform, convolution theorem      660
Laplace transform, two-sided      873 877
Laplacian      348
Laplacian in orthogonal coordinates      721
Longitudinal waves in half-space      462—467
Love waves      542
Love waves, cut-off frequency      543
Love waves, group velocity      544 545
Love waves, phase velocity      545
Love's integral identity      404
Mach angle      581
Mach line      581 603
Mach numbers      567 591
Mach numbers, subsonic      567
Mach numbers, supersonic      567
Mach numbers, transonic      567
Mach wave      581
mass density      345
Material moduli      345
Mathieu equation      921
Mathieu equation, characteristic values      921
Mathieu equation, modified      921
Mathieu functions      922
Mathieu functions, modified      923
mixed boundary-value problem      347
Modified Bessel functions      654
Modulated wave      551
Modulation      551
Monochromatic excitation      385
Moving Griffith crack      584—591
Moving Griffith crack, stressed at the tip      589
Moving load in infinite space      723—726
Moving punch      591—600
Moving punch, circular      597
Moving punch, rectangular      599
Natural frequency      438
Navier's equations      347 719
Navier's equations, solution in orthogonal coordinates      719—722
Neuber — Papkovich representation      356
Oblate spheroidal coordinates      735
One-dimensional motions      455
Phase function      555 957
phase velocity      551
Physical components      718
Piecewise regular function      445
Plane harmonic waves      504 505
Plane harmonic waves, dilatation      506
Plane harmonic waves, distortion      506
Plane harmonic waves, equivoluminal      506
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