Wave dynamics of generalized continua:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2016
|
| Series: | Advanced structured materials
24 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 274 S. graph. Darst. |
| ISBN: | 364237266X 9783642372667 |
Staff View
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| 100 | 1 | |a Bagdoev, Alexander G. |d 1933-2013 |e Verfasser |0 (DE-588)1078042233 |4 aut | |
| 245 | 1 | 0 | |a Wave dynamics of generalized continua |c Alexander G. Bagdoev ; Vladimir I. Erofeyev ; Ashot V. Shekoyan |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2016 | |
| 300 | |a XIII, 274 S. |b graph. Darst. | ||
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| 700 | 1 | |a Shekoyan, Ashot V. |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text |
CONTENTS
1 WAVES IN A VISCOUS SOLID WITH CAVITIES 1
1.1 INTRODUCTION 1
1.2 STATEMENT OF THE PROBLEM AND THE BASIC EQUATIONS 1
1.3 DERIVATION OF THE EVOLUTION EQUATION 2
1.4 THE SOLITON SOLUTION OF THE EVOLUTION EQUATION
OF THE FIFTH ORDER 4
1.5 DERIVATION OF THE MODULATION EQUATION FOR DIFFRACTION
AND ONE-DIMENSIONAL PROBLEMS IN THE CASE
OF QUASIMONOCHROMATIC WAVES 6
1.6 PROBLEM STATEMENT ABOUT WAVE FIELDS IN THE CASE
OF A LAYER 8
1.7 A DIFFRACTION PROBLEM FOR NARROW BEAMS 10
1.8 BOUNDARY CONDITIONS 11
1.9 THE EQUATION OF DIMENSIONLESS WIDTH OF A BEAM
FOR NONPARAXIAL RAYS 13
1.10 THE SOLUTION OF THE EQUATION FOR DIMENSIONLESS
WIDTH OF A BEAM FOR PARAXIAL RAYS 14
1.11 THE ANALYSIS OF SOLUTIONS FOR NARROW BEAMS 14
1.12 TRANSITION TO AN ONE-DIMENSIONAL CASE. THE ANALYSIS
OF DISPERSION PROPERTIES OF PLANE WAVES 15
1.13 DERIVATION OF EVOLUTION EQUATIONS BY THE METHOD
OF BOUND NORMAL WAVES 17
1.14 PHASE-GROUP SYNCHRONISM OF LOW-FREQUENCY
AND HIGH-FREQUENCY WAVES 20
1.15 NONLINEAR STATIONARY WAVES 25
2 WAVES IN VISCOUS, DISPERSIVE, NONLINEAR, PRELIMINARY
DEFORMABLE LAYER WITH A FREE SURFACE 29
2.1 INTRODUCTION 29
2.2 THE GENERAL BASIC EQUATIONS 29
2.3 EQUILIBRIUM WAVES 31
IX
HTTP://D-NB.INFO/1031595465
X"
CONTENTS
2.4 DERIVATION OF EVOLUTION EQUATIONS 33
2.5 THE EQUATION OF MODULATION AND ITS SOLUTION
FOR NARROW BUNCHES 34
2.6 BISTABILITY 38
2.7 THE "FROZEN" WAVES 39
3 WAVES IN SOLIDS WITH POROSITY FILLED BY AN ELECTRICALLY
NON-CONDUCTING LIQUID (BIOT MEDIUM) 41
3.1 INTRODUCTION 41
3.2 THE REFERENCE REVIEW 42
3.3 DERIVATION OF NONLINEAR EQUATIONS FROM THE VARIATIONAL
PRINCIPLE 44
3.4 NONLINEAR ONE-DIMENSIONAL WAVES 47
3.5 THE EVOLUTION EQUATION FOR A TWO-PHASE MEDIUM 50
3.6 THE NONLINEAR EQUATION OF MODULATION AND THE DISPERSION
EQUATION WITH ACCOUNT OF NONLINEARITIES 52
3.7 SOLUTION OF THE EVOLUTION AND MODULATION EQUATIONS 53
3.8 NONLINEAR WAVES IN A POROUS LIQUID-FILLED MEDIUM
WITH CAVITIES 55
3.9 THE EQUATIONS OF DEFORMATION OF THE TWO-PHASE BIOT
MEDIUM, WITH ACCOUNT OF THE TEMPERATURE OF BOTH PHASES. 59
3.10 THE LINEAR DISPERSION EQUATION WITH ACCOUNT
OF TEMPERATURE EFFECTS AND ITS SOLUTION 64
4 WAVES IN A SOLID WITH POROSITY FILLED BY ELECTRICALLY
CONDUCTING LIQUID LOCATED IN A CONSTANT ELECTRIC FIELD 67
4.1 INTRODUCTION 67
4.2 BASIC EQUATIONS 68
4.3 ONE-DIMENSIONAL CASE 71
4.4 THE LINEAR DISPERSION EQUATION AND ITS SOLUTION 72
4.5 EVOLUTION EQUATION 73
4.6 DERIVATION OF THE SCHRODINGER EQUATION AND THE DISPERSION
NONLINEAR EQUATION 76
4.7 SOLUTIONS OF THE EVOLUTION AND SCHRODINGER EQUATIONS 76
5 PIESOELASTIC WAVES 79
5.1 INTRODUCTION ' 79
5.2 THE INITIAL EQUATIONS OF DEFORMATION OF A PIEZOELECTRIC
MEDIUM 80
5.3 THE EQUATIONS OF DEFORMATION OF PIEZODIELECTRICS
WITH BALL HETEROGENEITIES 81
5.4 DERIVATION OF THE MODULATION EQUATION FROM THE INITIAL
EQUATIONS FOR PIEZOELECTRIC WITH BALL HETEROGENEITIES 84
5.5 THE LINEAR DISPERSION EQUATION AND ITS ANALYSIS 87
CONTENTS XI
5.6 THE STABILITY CONDITIONS OF A MODULATED NONLINEAR
ELECTROELASTIC WAVE 88
5.7 FOCUSING OF GAUSSIAN BUNCHES 91
5.8 THE EVOLUTION EQUATION AND ITS ANALYSIS 95
5.9 GENERALIZATION OF THE EVOLUTION EQUATION ONTO A RHOMBIC
CRYSTAL LATTICE AND CONTINUOUSLY INHOMOGENEOUS MEDIUM. 99
5.10 THE MODULATION EQUATION AND ITS ANALYSIS
FOR A PIEZOELECTRIC COMPOSITE 100
5.11 NONLINEAR WAVES IN A PIEZO-SEMICONDUCTOR MEDIUM 106
6 MAGNETOELASTIC WAVES 113
6.1 INTRODUCTION 113
6.2 THE MODULATION STABILITY OF NONLINEAR MAGNETOELASTIC
WAVES 114
6.3 DISPERSION AND ATTENUATION OF MAGNETOELASTIC WAVES 124
6.4 MAGNETOELASTIC WAVES IN A MICROSTRUCTURED MEDIUM 129
6.5 THE GENERALIZED NONLINEAR EQUATIONS
FOR A MAGNETOHYDRODYNAMIC MEDIUM 139
7 WAVES IN SOLID TWO-COMPONENT SHEAR MIXTURES 143
7.1 BRIEF REVIEW OF PAPERS ON MECHANICS OF MIXTURES 143
7.2 THE BASIC HYPOTHESIS AND THE MATHEMATICAL MODEL 145
7.3 THE DISPERSION PROPERTIES 149
7.4 DERIVING OF THE EVOLUTION EQUATIONS BY THE METHOD
OF BOUND NORMAL WAVES 150
7.5 PHASE-GROUP SYNCHRONISM OF LOW-FREQUENCY
AND HIGH-FREQUENCY WAVES 152
7.6 NONLINEAR STATIONARY WAVES 157
8 WAVES IN THE MIXTURE OF GAS AND DROPLETS 163
8.1 INTRODUCTION 163
8.2 LITERATURE OVERVIEW 163
8.3 EQUATIONS WHICH DESCRIBES ACOUSTIC WAVES
IN THE ATMOSPHERE WITH ACCOUNT OF DROPLETS
COAGULATION, CONDENSATION OF WATER VAPORS
.AND GAS VISCOSITY 165
8.4 DISPERSION EQUATION AND ITS STUDYING 168
8.5 THE INFLUENCE OF THE ACOUSTIC WAVE ON SIZE
AND CONCENTRATION OF DROPLETS 172
8.6 THE GENERAL EQUATIONS OF THE THEORY OF ELECTROACOUSTIC
WAVES IN A CLOUDY ATMOSPHERE 175
8.7 LINEARIZED SYSTEM AND DISPERSION EQUATION 180
XII CONTENTS
9 NONLINEAR QUASIMONOCHROMATIC ACOUSTIC, ELASTIC
AND ELECTROMAGNETIC WAVES IN A MEDIA WITH MICROSTRUCTURE . 183
9.1 INTRODUCTION 183
9.2 THE EQUATIONS OF MOTION FOR VISCOUS THERMOELASTIC
COMPOSITE WITH BALL INHOMOGENEITIES 185
9.3 THE NONLINEAR MODULATION EQUATION FOR VISCOUS
THERMOELASTIC COMPOSITE WITH HOMOGENEOUS MATRIX 186
9.4 STABILITY AND FOCUSING VISCO THERMOELASTIC WAVES
IN A MEDIUM WITH BALL INHOMOGENEITIES
IN THE STATIONARY CASE 188
9.5 STABILITY AND FOCUSING OF UNSTEADY MODULATION WAVE 190
9.6 MODULATION EQUATION FOR VISCOUS THERMOELASTIC
CONTINUOUSLY INHOMOGENEOUS MEDIUM 192
9.7 THE BASIC EQUATIONS OF THE ACOUSTIC WAVE IN MEDIA
WITH RELAXATION 193
9.8 A DETAILED DERIVATION OF SPLITTING OF EVOLUTION EQUATIONS
FOR THE TWO WAVES 194
9.9 THE BASIC EQUATIONS OF MOTION OF AN INHOMOGENEOUS
MICROPOLAR CONDUCTIVE LIQUID WITH GAS BUBBLES 196
9.10 DERIVATION OF STABILITY CONDITIONS FROM VARIATIONAL
PRINCIPLES 198
9.11 SELF-ACTION OF ELECTROMAGNETIC WAVES IN A TWO-LEVEL
MEDIUM, TAKING INTO ACCOUNT NONLINEAR DISSIPATION 201
9.11.1 THE INITIAL EQUATIONS OF THE LASER BEAM
IN A TWO-LEVEL MEDIUM 201
9.11.2 NONLINEAR SCHRODINGER EQUATION 202
9.11.3 THE EQUATIONS FOR WAVES PROPAGATING
IN OPPOSITE DIRECTIONS (THE PROBLEM
OF THE RESONATOR) 205
9.11.4 THE BEHAVIOR OF THE AXIAL BEAMS 206
9.11.5 NONAXIAL BEAMS 208
9.11.6 STABILITY CONDITIONS 209
10 STABILITY OF SOLITON-LIKE WAVES AND SOME SOLUTIONS
OF DISSIPATIVE EVOLUTION EQUATIONS WITHOUT DISPERSION 211
10.1 INTRODUCTION 211
10.2 INFLUENCE OF DISSIPATION, DISPERSION AND DIFFRACTION
ON THE AMPLITUDE AND TRANSVERSE STABILITY OF SOLITONS 212
10.3 THE LONGITUDINAL STABILITY OF A SOLITON-LIKE SOLUTION
OF EQ. (10.1) 219
CONTENTS XIII
11 WAVES IN THE COSSERAT MEDIUM 223
11.1 THE COSSERAT BROTHERS AND MECHANICS
OF GENERALIZED CONTINUA 223
11.2 THE BASIC RELATIONS OF THE THEORY OF MICROPOLAR
ELASTICITY 227
11.3 DISPERSION PROPERTIES OF SPATIAL WAVES 232
11.4 WAVE REFLECTION FROM THE FREE SURFACE
OF A MICROPOLAR HALF-SPACE 234
11.5 THE SURFACE RAYLEIGH WAVES 236
11.6 NORMAL WAVES IN A LAYER OF MICROPOLAR MATERIAL 237
11.7 MACROMECHANICAL MODELING OF THE ELASTIC
AND VISCOELASTIC COSSERAT MEDIA 242
11.8 THE THERMOELASTICITY PROBLEM AND SOME NONLINEAR
GENERALIZATIONS 248
11.9 THE NONLINEAR STATIONARY WAVE OF ROTATIONAL TYPE 251
11.10 GENERATION OF STRAIN SOLITONS IN THE COSSERAT CONTINUUM
WITH CONSTRAINED ROTATION [117J 254
REFERENCES 263 |
| any_adam_object | 1 |
| author | Bagdoev, Alexander G. 1933-2013 Erofeev, Vladimir Ivanovič Shekoyan, Ashot V. |
| author_GND | (DE-588)1078042233 |
| author_facet | Bagdoev, Alexander G. 1933-2013 Erofeev, Vladimir Ivanovič Shekoyan, Ashot V. |
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| ctrlnum | (OCoLC)864643149 (DE-599)DNB1031595465 |
| discipline | Maschinenbau / Maschinenwesen Physik |
| format | Book |
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| indexdate | 2024-09-10T01:55:02Z |
| institution | BVB |
| isbn | 364237266X 9783642372667 |
| language | English |
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| oclc_num | 864643149 |
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| physical | XIII, 274 S. graph. Darst. |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer |
| record_format | marc |
| series | Advanced structured materials |
| series2 | Advanced structured materials |
| spelling | Bagdoev, Alexander G. 1933-2013 Verfasser (DE-588)1078042233 aut Wave dynamics of generalized continua Alexander G. Bagdoev ; Vladimir I. Erofeyev ; Ashot V. Shekoyan Berlin [u.a.] Springer 2016 XIII, 274 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced structured materials 24 Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 s Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Erofeev, Vladimir Ivanovič Verfasser aut Shekoyan, Ashot V. Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-37267-4 Advanced structured materials 24 (DE-604)BV036859877 24 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4258626&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028376610&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bagdoev, Alexander G. 1933-2013 Erofeev, Vladimir Ivanovič Shekoyan, Ashot V. Wave dynamics of generalized continua Advanced structured materials Kontinuumsmechanik (DE-588)4032296-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| subject_GND | (DE-588)4032296-8 (DE-588)4121912-0 |
| title | Wave dynamics of generalized continua |
| title_auth | Wave dynamics of generalized continua |
| title_exact_search | Wave dynamics of generalized continua |
| title_full | Wave dynamics of generalized continua Alexander G. Bagdoev ; Vladimir I. Erofeyev ; Ashot V. Shekoyan |
| title_fullStr | Wave dynamics of generalized continua Alexander G. Bagdoev ; Vladimir I. Erofeyev ; Ashot V. Shekoyan |
| title_full_unstemmed | Wave dynamics of generalized continua Alexander G. Bagdoev ; Vladimir I. Erofeyev ; Ashot V. Shekoyan |
| title_short | Wave dynamics of generalized continua |
| title_sort | wave dynamics of generalized continua |
| topic | Kontinuumsmechanik (DE-588)4032296-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| topic_facet | Kontinuumsmechanik Wellenausbreitung |
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| volume_link | (DE-604)BV036859877 |
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