PREFACE ......................................................... x
INTRODUCTION .................................................. xii
1 Fundamentals of linear thermoelasticity with finite wave
speeds ....................................................... 1
1.1 Fundamentals of classical thermoelasticity .............. 1
1.1.1 Basic considerations ............................. 1
1.1.2 Global balance law in terms of (ui,  ) ........... 7
1.1.3 Global balance law in terms of (Sij,qi) ........... 9
1.2 Fundamentals of thermoelasticity with one relaxation
time ................................................... 11
1.2.1 Basic considerations ............................ 11
1.2.2 Global balance law in terms of (ui, ) .......... 14
1.2.3 Global balance law in terms of (Sij,qi) .......... 15
1.3 Fundamentals of thermoelasticity with two relaxation
times .................................................. 18
1.3.1 Basic considerations ............................ 18
1.3.2 Global balance law in terms of (ui, ) .......... 25
1.3.3 Global balance law in terms of (Sij, ) ......... 26
2 Formulations of initial-boundary value problems ............. 30
2.1 Conventional and non-conventional characterization
of a thermoelastic process ............................. 30
2.1.1 Two mixed initial-boundary value problems in
the L-S theory .................................. 31
2.1.2 Two mixed initial-boundary value problems in
the G-L theory .................................. 33
2.2 Relations among descriptions of a thermoelastic
process in terms of various pairs of thermomechanical
variables .............................................. 34
3 Existence and uniqueness theorems ........................... 37
3.1 Uniqueness theorems for conventional and non-
conventional thermoelastic processes ................... 37
3.2 Existence theorem for a non-conventional
thermoelastic process .................................. 43
4 Domain of influence theorems ................................ 51
4.1 The potential-temperature problem in the Lord-Shulman
theory ................................................. 51
4.2 The potential-temperature problem in the Green-
Lindsay theory ......................................... 59
4.3 The natural stress-heat-flux problem in the Lord-
Shulman theory ......................................... 65
4.4 The natural stress-temperature problem in the Green-
Lindsay theory ......................................... 71
4.5 The displacement-temperature problem for an
inhomogeneous anisotropic body in the L-S and G-L
theories ............................................... 80
4.5.1 A thermoelastic wave propagating in an
inhomogeneous anisotropic L-S model ............. 80
4.5.2 A thermoelastic wave propagating in an
inhomogeneous anisotropic G-L model ............. 83
5 Convolutional variational principles ........................ 86
5.1 Alternative descriptions of a conventional
thermoelastic process in the Green-Lindsay theory ...... 86
5.2 Variational principles for a conventional
thermoelastic process in the Green-Lindsay theory ...... 93
5.3 Variational principle for a non-conventional
thermoelastic process in the Lord-Shulman theory ...... 103
5.4 Variational principle for a non-conventional
thermoelastic process in the Green-Lindsay theory ..... 106
6 Central equation of thermoelasticity with finite wave
speeds ..................................................... 111
6.1 Central equation in the Lord-Shulman and Green-
Lindsay theories ...................................... 111
6.2 Decomposition theorem for a central equation of
Green-Lindsay theory. Wave-like equations with a
convolution ........................................... 114
6.3 Speed of a fundamental thermoelastic disturbance in
the space of constitutive variables ................... 127
6.4 Attenuation of a fundamental thermoelastic
disturbance in the space of constitutive variables .... 139
6.4.1 Behavior of functions  1.2 for a fixed
relaxation time to ............................. 140
6.4.2 Behavior of functions 1.2 for a fixed  ........ 141
6.5 Analysis of the convolution coefficient and kernel .... 143
6.5.1 Analysis of  at fixed t0 ...................... 143
6.5.2 Analysis of at fixed ...................... 144
6.5.3 Analysis of the convolution kernel ............. 146
7 Exact aperiodic-in-time solutions of Green—Lindsay
theory ..................................................... 152
7.1 Fundamental solutions for a 3D bounded domain ......... 152
7.2 Solution of a potential-temperature problem for a 3D
bounded domain ........................................ 164
7.3 Solution for a thermoelastic layer .................... 170
7.4 Solution of Nowacki type; spherical wave of
a negative order ...................................... 175
7.5 Solution of Danilovskaya type; plane wave of a
negative order ........................................ 192
7.6 Thermoelastic response of a half-space to laser
irradiation ........................................... 197
8 Kirchhoff-type formulas and integral equations in Green-
Lindsay theory ............................................. 217
8.1 Integral representations of fundamental solutions ..... 217
8.2 Integral equations for fundamental solutions .......... 221
8.3 Integral representation of a solution to a central
system of equations ................................... 222
8.4 Integral equations for a potential-temperature
problem ............................................... 232
9 Thermoelastic polynomials .................................. 241
9.1 Recurrence relations .................................. 241
9.2 Differential equation ................................. 249
9.3 Integral relation ..................................... 252
9.4 Associated thermoelastic polynomials .................. 254
10 Moving discontinuity surfaces .............................. 257
10.1 Singular surfaces propagating in a thermoelastic
medium; thermoelastic wave of order n ( 0) .......... 257
10.2 Propagation of a plane shock wave in a thermoelastic
half-space with one relaxation time ................... 261
10.3 Propagation of a plane acceleration wave in
a thermoelastic half-space with two relaxation
times ................................................. 270
11 Time-periodic solutions .................................... 280
11.1 Plane waves in an infinite thermoelastic body with
two relaxation times .................................. 280
11.2 Spherical waves produced by a concentrated source of
heat in an infinite thermoelastic body with two
relaxation times ...................................... 294
11.3 Cylindrical waves produced by a line heat source in
an infinite thermoelastic body with two relaxation
times ................................................. 302
11.4 Integral representation of solutions and radiation
conditions in the Green-Lindsay theory ................ 310
11.4.1 Integral representations and radiation
conditions for the fundamental solution in
the Green-Lindsay theory ....................... 310
11.4.2 Integral representations and radiation
conditions for the potential-temperature
solution in the Green-Lindsay theory ........... 314
12 Physical aspects and applications of hyperbolic
thermoelasticity ........................................... 321
12.1 Heat conduction ....................................... 321
12.1.1 Physics viewpoint and other theories ........... 321
12.1.2 Consequence of Galilean invariance ............. 323
12.1.3 Consequence of continuum thermodynamics ........ 325
12.2 Thermoelastic helices and chiral media ................ 329
12.2.1 Homogeneous case ............................... 329
12.2.2 Heterogeneous case and homogenization .......... 332
12.2.3 Plane waves in non-centrosymmetric micropolar
thermoelasticity ............................... 333
12.3 Surface waves ......................................... 336
12.4 Thermoelastic damping in nanomechanical resonators .... 339
12.4.1 Flexural vibrations of a thermoelastic
Bernoulli-Euler beam ........................... 339
12.4.2 Numerical results and discussion ............... 342
12.5 Fractional calculus and fractals in
thermoelasticity ...................................... 343
12.5.1 Anomalous heat conduction ...................... 343
12.5.2 Fractal media .................................. 346
13 Non-linear hyperbolic rigid heat conductor of the Coleman
type ....................................................... 352
13.1 Basic field equations for a ID case ................... 352
13.2 Closed-form solutions ................................. 355
13.2.1 Closed-form solution to a time-dependent
heat-conduction Cauchy problem ................. 355
13.2.2 Travelling-wave solutions ...................... 358
13.3 Asymptotic method of weakly non-linear geometric
optics applied to the Coleman heat conductor .......... 366
REFERENCES .................................................... 383
ADDITIONAL REFERENCES ......................................... 392
NAME INDEX .................................................... 404
SUBJECT INDEX ................................................. 408
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