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Eringen A.C., Suhubi E.S. — Elastodynamics (vol.1) Finite motions
Eringen A.C., Suhubi E.S. — Elastodynamics (vol.1) Finite motions

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Название: Elastodynamics (vol.1) Finite motions

Авторы: Eringen A.C., Suhubi E.S.

Аннотация:

From the inception of the theory of elasticity with Navier A821) and Cauchy A828), the dynamical problems of elasticity and the subject of wave propagations in elastic solids have been under intense study by a large number of workers. In fact the literature is so extensive that any desire to write accounts on the subject immediately induces discouragement on the part of a prospective author. For it is impossible to do justice to all aspects of this wide field in any one- or two-volume treatise. Perhaps, partially, it is this concern that kept this important field barren of books for nearly two centuries.


Язык: en

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 341

Добавлена в каталог: 17.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\delta$-time derivative      82
Absolute scalar      35 302
Absolute temperature      25 35 97
Absolute vector      302
Acceleration front      114 209
Acceleration jump (discontinuity)      114 137
Acceleration potential      147 150 162 163
Acceleration vector      20 114
Acceleration waves      95 113
Acceleration waves in incompressible elastic solids      127
Acceleration waves in incompressible isotropic solids      129
Acceleration waves in incompressible local speed of propagation      128 129
Acceleration waves in incompressible principal transverse waves      131
Acceleration waves in isotropic elastic solids      118
Acceleration waves in isotropic quadratic elastic solids      126
Acceleration waves, amplitude of      115 131
Acceleration waves, compressive      115
Acceleration waves, expansive      115
Acceleration waves, local speed of propagation      114
Acceleration waves, longitudinal      115
Acceleration waves, principal wave      119 120 123 124
Acceleration waves, principal wave, longitudinal wave speed      120 124
Acceleration waves, principal wave, matrix of wave speeds      121
Acceleration waves, principal wave, transverse wave speed      120 124
Acceleration waves, speed of propagation      116
Acceleration waves, transverse      115
Acoustical axes      116 117
Acoustical fringes      264
Acoustical tensor      116 118
Acoustoelastic effect      264
Acoustoelastic law      264
Acoustoelastic sensitivity      264
Adjacent states      321
Anholonomic components      304
Anisotropic materials      42
Antiplane motion      236
Apparent Lame constants      257
Baker — Ericksen inequalities      63 123 154 165
Balance laws      26 37 65
Balance laws, global      22
Balance laws, local      25 31
Balance laws, local in the reference frame      31
Base vectors      3 299
Base vectors, reciprocal      300
Basic local laws of continuum mechanics      30
Bianchi's identities      313
Bicharacteristics      210 214
Birefringence      264
Body forces      23
boundary conditions      58
bulk modulus      63
Cauchy's equation of motion      30
Cauchy's equation of motion in cylindrical coordinates      73
Cauchy's equation of motion in spherical coordinates      75
Cauchy's equation of motion in the reference state      32 55
Cauchy's problem      208
Cauchy's theorem      36
Cayley — Hamilton theorem      44 45
Centered simple wave      195 196 226 325
Characteristic condition      213 253
Characteristic surface      208 209 210 212 213
Characteristic values      174
Characteristics      317 318 320 323
Characteristics, method of      173
Christoffel symbols      69 305 306
Christoffel symbols in cylindrical coordinates      310
Christoffel symbols in spherical coordinates      311
Christoffel symbols of the first kind      69 80 305
Christoffel symbols of the second kind      69 80 305
Circular cylinder, incremental stresses      278
Circular cylinder, initially stretched      277
Circular cylinder, initially twisted      285
Circular cylinder, longitudinal oscillations      281
Circular cylinder, longitudinal oscillations, frequency equation      282
Circular cylinder, longitudinal oscillations, incompressible materials      282
Circular cylinder, longitudinal oscillations, incompressible materials, frequency equation      283
Circular cylinder, longitudinal oscillations, Mooney materials      284
Circular cylinder, longitudinal oscillations, Mooney materials, wave velocity      284
Circular cylinder, Mooney materials      290
Circular cylinder, Mooney materials, correction to the frequency      295
Circular cylinder, Mooney materials, perturbative solution      290
Circular cylinder, Mooney materials, recurrence relations      291
Circular cylinder, neo-Hookean materials      288
Circular cylinder, neo-Hookean materials, frequency equation      289
Circular cylinder, torsional oscillations      279
Circular cylinder, torsional oscillations, frequency equation      280
Circular cylinder, torsional oscillations, Mooney materials      280
Clausius — Duhem inequality      37 94
Compatibility conditions for special deformations      237 238
Compatibility conditions for strain tensor      17
Compatibility conditions for strain tensor, infinitesimal strain tensor      18
Compatibility conditions on singular surfaces      87 90
Compatibility conditions on singular surfaces, dynamical      94 97 102
Compatibility conditions on singular surfaces, geometrical, first order      87
Compatibility conditions on singular surfaces, geometrical, second and higher order      88
Compatibility conditions on singular surfaces, kinematical, first order      90
Compatibility conditions on singular surfaces, kinematical, second and higher order      91
Compressibility conditions      63
Conductivities      56
Conservation of energy      24 32
Conservation of mass      23 27 31
Constitutive equations      see "Thermoelastic solids"
Continua with local structure      30
Continuity, axiom of      5 91
Continuity, equation of      27
Contravariant components      300
Coordinate transformations      298
Coordinates, convective      251
Coordinates, curvilinear      18 69 298
Coordinates, curvilinear, orthogonal      70 71 299 309
Coordinates, curvilinear, orthogonal, cylindrical      300 310
Coordinates, curvilinear, orthogonal, spherical      311
Coordinates, dragged      251
Coordinates, eulerian      3
Coordinates, Lagrangian      3
Coordinates, material      3 19
Coordinates, rectangular      18 298
Coordinates, spatial      3 19
Covariant derivative      69 81 306
Covariant derivative of relative tensors      307
Crystalline materials      42
Curl      307
Curvature, Gaussian (total)      82 141
Curvature, mean      82 141
Curvature, tensor      312
Curvilinear coordinate lines      298
Curvilinear coordinate surfaces      298
Deformation      4
Deformation gradients      6 172
Deformation gradients, second      114
Deformation rate tensor      21
Deformation tensors      6 150
Deformation tensors in curvilinear coordinates      69
Deformation tensors, Cauchy      6
Deformation tensors, Finger      6 93
Deformation tensors, Green      6 172
Deformation tensors, Piola      6
Deformed area element      16
Deformed volume element      16
Discontinuity surface      26 33
Displacement derivative      82 84
Displacement vector      7
Divergence      307
Eigenvalues      317
Eigenvectors      318
Eigenvectors, left      318
Eigenvectors, right      175 323
Elasticities      56 116 118
Energy curves      155 156
Energy of surface tractions      24
Energy, balance of      24
Energy, balance of in cylindrical coordinates      73
Energy, balance of in spherical coordinates      75
Energy, balance of in the reference state      30 55
Energy, internal      24
Energy, kinetic      24
entropy      25
Entropy, behind the shock      99
Entropy, density      25
Entropy, inequality      25 30 37
Entropy, inequality in the reference state      32
Entropy, influx      25 39
Entropy, influx, source      25
Entropy, influx, total production of      25
Equipresence      35
Eulerian description      59
Extension      10
External loads      5
Form invariance      35 42
Fourier's law      50 71
Fracture      5
Free energy      35
Generalized shear motion      236
Global equilibrium condition      59
Gradient      72 307
Green — Gauss Theorem      26 308
Group velocity      211
Growth of acceleration waves      131 138
Growth of arbitrary form      139
Growth of arbitrary form, cylindrical      143
Growth of arbitrary form, longitudinal      140 141
Growth of arbitrary form, spherical      143
Growth of arbitrary form, transverse      141
Growth of plane form      136 143
Growth of plane form, longitudinal waves      137
Growth of plane form, transverse waves      139
Growth, growth equation      133
Growth, growth equation in spatial form      133 135
Growth, method of bicharacteristics      131
Hadamard materials      243
Hadamard's lemma      87
Hardening materials      138 230 232
Harmonic materials      243
Heat, conduction, equation of      41
Heat, conduction, matrix of      41
Heat, conduction, with finite speed      38
Heat, radiation      68
Heat, source      24
Heat, vector      24
Hemitropic materials      42
Hodograph equation      225
Homogeneous material      42
Homogeneous reference configuration      56
Hooke's law      50 217 221
Horizontally polarized shear waves      240
Hydrostatic stress      46 124 257
Hyperbolic systems      209
Hyperelastic materials      97
Hyperelastic materials, constitutive equations      97
Hyperelastic materials, stress potential      97
Impedance      219 221
Impenetrability      5 91
Implicit function theorem      5
Independent processes      37
Indestructibility      5 91
Infinitesimal deformation theory      34
Infinitesimal rotation tensor      9 11 48
Infinitesimal rotation tensor in curvilinear coordinates      71
Infinitesimal rotation tensor in curvilinear coordinates in cylindrical coordinates      73
Infinitesimal rotation tensor in curvilinear coordinates in spherical coordinates      75
Infinitesimal strain tensor      9 11 48 254
Infinitesimal strain tensor in curvilinear coordinates      71
Infinitesimal strain tensor in curvilinear coordinates in cylindrical coordinates      73
Infinitesimal strain tensor in curvilinear coordinates in spherical coordinates      75
Initial conditions      68
Integrability condition      122
Integral theorems      25
Isotropic functions      43
Isotropic materials      42
Jump conditions      31 65
Jump conditions in material form      33
Killing theorem      22
Kronecker symbol      3 299
Lagrange multipliers      11 41
Lagrangian viewpoint      20
Lame constants      126
Laplacian      308
Legendre transformation      211
Limit surface      215
Loading wave      185
Locking strain      222
Material derivative of a vector      20
Material derivative of arc length      21
Material derivative of deformation gradient      21
Material derivative of jacobian      22
Material derivative of volume element      22
Material symmetry, axiom of      42
Mean rotation      11
Metric tensor      69 299
Metric tensor in cylindrical coordinates      73
Metric tensor in spherical coordinates      74
Minimal stored energy      62
Mixed boundary-value problems      58
Moment of body forces      24
Moment of momentum, balance of      23
Moment of surface tractions      24
Momentum, balance of      23 29 31
Mooney material      157 160 167 170 238 239 266 274
Motion      4 19
Motion, inverse      4
Moving surface      78 82 91
Moving surface, spatial      91
Navier — Duhamel equations      59
Navier — Duhamel equations in curvilinear coordinates      72
Navier — Duhamel equations in cylindrical coordinates      73
Navier — Duhamel equations in spherical coordinates      76
Neo — Hookean material      176 266 276
Nonreflecting boundaries      172
Normal parametrization      83
Normal strain      8
Normal strain, infinitesimal      10
Normal stress      28
Normal vector      79
Objectivity, axiom of      35
Orthogonal transformations      35 260
Orthogonal transformations, full group of      42
Orthogonal transformations, proper group of      35 36 42
Parallel propagation      85
Parallel surfaces      141
Partitioned matrices      174
Permutation (alternation) symbol      6 306
Permutation (alternation) symbol, two-dimensional      80
Phase plane      155 159
phase velocity      211
Physical components      70 304
Physical components in orthogonal coordinates      71 305
Piezocaloric effect      39
Piola — Kirchhoff stress      32 95
Plane, motion      172
Plane, shear wave      240
Plane, wave      171
Plane, waves in homogeneously deformed media      259
Plane, waves in incremental stresses      265
Plane, waves in isotropic materials      261
Plane, waves in longitudinal wave      263
Plane, waves in principal plane wave      263
Plane, waves in shear wave      263
Plane, waves, velocity      260
Poisson's ratio      63
Polar media      30
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