Thermoelasticity with finite wave speeds:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2010
|
| Edition: | 1. publ. |
| Series: | Oxford mathematical monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 413 S. graph. Darst. |
| ISBN: | 9780199541645 |
Staff View
MARC
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| 100 | 1 | |a Ignaczak, Józef |d 1935- |e Verfasser |0 (DE-588)14229702X |4 aut | |
| 245 | 1 | 0 | |a Thermoelasticity with finite wave speeds |c Józef Ignaczak, Martin Ostoja-Starzewski |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2010 | |
| 300 | |a XVIII, 413 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford mathematical monographs | |
| 650 | 4 | |a Thermoelasticity / Mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Thermoelasticity |x Mathematics | |
| 650 | 0 | 7 | |a Thermoelastizität |0 (DE-588)4185143-2 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017748060 | ||
Record in the Search Index
| _version_ | 1804139406785773569 |
|---|---|
| adam_text | CONTENTS
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
{щ,д)
7
1.1.3
Global balance law in terms of
(Ѕц,9ѓ)
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
(щ,
ΰ)
14
1.2.3
Global balance law in terms of
(5¿j,9í)
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
(щ,
ϋ)
25
1.3.3
Global balance law in terms of
(Sy,
ϋ)
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
Contents
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
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
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
ίο
140
6.4.2
Behavior of functions ¿i.2 for a fixed
є
141
6.5
Analysis of the convolution coefficient and kernel
143
6.5.1
Analysis of
λ
at fixed t0
143
6.5.2
Analysis of
λ
at fixed
e
144
6.5.3
Analysis of the convolution kernel
146
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
Kirchhoff-type formulas and integral equations in
Green-Lindsay theory
217
8.1
Integral representations of fundamental solutions
217
Contents
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
η (^
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
viii Contents
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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| author | Ignaczak, Józef 1935- Ostoja-Starzewski, Martin |
| author_GND | (DE-588)14229702X (DE-588)142297100 |
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| dewey-ones | 531 - Classical mechanics |
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
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| indexdate | 2024-07-09T21:43:35Z |
| institution | BVB |
| isbn | 9780199541645 |
| language | English |
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| physical | XVIII, 413 S. graph. Darst. |
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| spelling | Ignaczak, Józef 1935- Verfasser (DE-588)14229702X aut Thermoelasticity with finite wave speeds Józef Ignaczak, Martin Ostoja-Starzewski 1. publ. Oxford Oxford University Press 2010 XVIII, 413 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Thermoelasticity / Mathematics Mathematik Thermoelasticity Mathematics Thermoelastizität (DE-588)4185143-2 gnd rswk-swf Thermoelastizität (DE-588)4185143-2 s DE-604 Ostoja-Starzewski, Martin Verfasser (DE-588)142297100 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017748060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ignaczak, Józef 1935- Ostoja-Starzewski, Martin Thermoelasticity with finite wave speeds Thermoelasticity / Mathematics Mathematik Thermoelasticity Mathematics Thermoelastizität (DE-588)4185143-2 gnd |
| subject_GND | (DE-588)4185143-2 |
| title | Thermoelasticity with finite wave speeds |
| title_auth | Thermoelasticity with finite wave speeds |
| title_exact_search | Thermoelasticity with finite wave speeds |
| title_full | Thermoelasticity with finite wave speeds Józef Ignaczak, Martin Ostoja-Starzewski |
| title_fullStr | Thermoelasticity with finite wave speeds Józef Ignaczak, Martin Ostoja-Starzewski |
| title_full_unstemmed | Thermoelasticity with finite wave speeds Józef Ignaczak, Martin Ostoja-Starzewski |
| title_short | Thermoelasticity with finite wave speeds |
| title_sort | thermoelasticity with finite wave speeds |
| topic | Thermoelasticity / Mathematics Mathematik Thermoelasticity Mathematics Thermoelastizität (DE-588)4185143-2 gnd |
| topic_facet | Thermoelasticity / Mathematics Mathematik Thermoelasticity Mathematics Thermoelastizität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017748060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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