Tractable models of solid mechanics: formulation, analysis and interpretation
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Foundations of engineering mechanics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 302 S. Ill., graph. Darst. |
| ISBN: | 9783642153716 9783642153723 |
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Record in the Search Index
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IMAGE 1
CONTENTS
1 INTRODUCTION: HISTORICAL DEVELOPMENT OF TRACTABLE MODELS 1 REFERENCES
11
2 DISCRETE FINITE SYSTEMS 13
2.1 LINEAR OSCILLATORS 13
2.1.1 LINEAR CONSERVATIVE OSCILLATOR 14
2.1.2 LINEAR OSCILLATOR WITH VISCOUS DAMPING 15
2.1.3 LINEAR OSCILLATOR WITH VISCOUS DAMPING AND PERIODIC (HARMONIC)
FORCING 21
2.1.4 TWO COUPLED OSCILLATORS 24
2.2 SINGLE-DOF NONLINEAR OSCILLATOR 34
2.2.1 QUASILINEAR OSCILLATOR 36
2.2.2 STRONGLY NONLINEAR OSCILLATOR AND VIBRO-IMPACT APPROXIMATION 39
2.2.3 OSCILLATOR WITH MULTIPLE EQUILIBRIUMS 46
2.3 FORCED NONLINEAR OSCILLATOR 47
2.3.1 GENERAL REMARKS 47
2.3.2 GOVERNING EQUATIONS 48
2.3.3 THE DYNAMICS OF THE OSCILLATOR WITHOUT DISSIPATION AND THE LPT 50
2.3.4 THE TRANSIENT DYNAMICS OF A WEAKLY DAMPED OSCILLATOR. 53 2.3.5
QUASI-LINEAR OSCILLATIONS 61
2.4 ENTRAINMENT, SYNCHRONIZATION AND RESONANCE CAPTURE 64
2.4.1 PENDULUM WITH CONSTANT EXTERNAL TORQUE 65
2.4.2 ENTRAINMENT OF THE VAN DER POL OSCILLATOR BY EXTERNAL HARMONIC
FORCE 68
2.4.3 SYNCHRONIZATION OF OSCILLATORS AND RELATED MODELS . . . 75 2.4.4
RESONANCE CAPTURE 77
2.4.5 FORCED OSCILLATOR WITH MULTIPLE STATES OF EQUILIBRIUM . . 81 2.5
SYMMETRIC SYSTEMS OF COUPLED NONLINEAR OSCILLATORS BEATING PHENOMENA 84
2.5.1 EXERCISE 93
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1005009694
DIGITALISIERT DURCH
IMAGE 2
(J CONTENTS
2.6 2DOF SYSTEMS OF NONLINEAR OSCILLATORS WITH ESSENTIAL ASYMMETRY
TARGETED ENERGY TRANSFER (TET) 94
2.6.1 TARGETED ENERGY TRANSFER IN AN UNFORCED 2D0F SYSTEM . 94 2.6.2
TARGETED ENERGY TRANSFER IN FORCED 2D0F SYSTEM . . . 105 2.7 COUPLED
NONLINEAR OSCILLATORS WITH TIME DELAYS 133
2.7.1 ANALYTIC MODEL 133
2.7.2 NUMERIC VERIFICATION - STRAIGHT MODES 141
2.7.3 NUMERIC VERIFICATION - "OVAL" MODES AND PHASE - LOCKED SOLUTIONS
144
2.8 LOW-DOF DISCRETE NONLINEAR SYSTEMS 147
2.9 CONCLUDING REMARKS 160
REFERENCES 161
3 INFINITE DISCRETE SYSTEMS 167
3.1 DYNAMICS OF INFINITE NONLINEAR CHAINS 167
3.1.1 LONG-WAVELENGTH APPROXIMATION. EQUATION OF SUPERSONIC EXTENSION
SOLITONS IN AN INFINITE FPU CHAIN 167
3.1.2 ZIGZAG CHAIN AND LONG-WAVE SOLITONS 169
3.1.3 ENVELOPE SOLITONS 171
3.1.4 OPTICAL BREATHERS IN A ZIGZAG CHAIN 176
3.1.5 TORSIONAL SOLITONS 186
3.1.6 APPROXIMATION OF IMMOBILE NEIGHBOUR CHAINS 188 3.2 DYNAMICS OF
ESSENTIALLY NONLINEAR AND VIBRO-IMPACT CHAINS . . 192 3.2.1 OSCILLATORY
CHAIN WITH RIGID BARRIERS 193
3.2.2 DISCRETE BREATHERS IN A VIBRO-IMPACT CHAIN 198
3.3 THE PROBLEM OF HEAT CONDUCTION IN DIELECTRICS 207
3.4 SOLITONS IN ENERGETICALLY NONDEGENERATE QUASI-ONE- DIMENSIONAL
MODELS 217
3.4.1 QUASI-ONE-DIMENSIONAL MODEL OF A MOLECULAR CRYSTAL: SOLITON MODES
OF MOTION IN A BISTABLE NONLINEAR SYSTEM 219
3.5 DYNAMICS OF ENSEMBLES OF INTERACTING NONLINEAR CHAINS 225 3.6
CONCLUDING REMARKS 233
REFERENCES 233
4 CONTINUOUS SYSTEMS 237
4.1 ONE-DIMENSIONAL MODELS 237
4.1.1 BOLOTIN MODEL 237
4.1.2 SIMPLIFICATION OF THE TIMOSHENKO BEAM 241
4.2 THE PLANAR DYNAMICAL PROBLEM AND TRACTABLE ONE-DIMENSIONAL MODELS OF
AN ELASTIC SOLID 248
4.3 THE TWO-DIMENSIONAL ORTHOTROPIC MODEL AND ITS APPLICATION TO A
COMPLEX CONTACT PROBLEM 253
IMAGE 3
CONTENTS XIII
4.3.1 BASIC ASYMPTOTIC DECOMPOSITION OF THE ORTHOTROPIC PLATE PROBLEM
253
4.3.2 THE CONTACT PROBLEM FOR A PLANAR ORTHOTROPIC STRIP . . 259 4.4
MODELS OF ELASTIC FOUNDATION 264
4.4.1 GENERAL EQUATIONS AND ASYMPTOTIC ANALYSIS 264
4.4.2 EXAMPLE - DYNAMICAL PROBLEM 268
4.4.3 EXAMPLE - AN AXISYMMETRIC STAMP 270
4.5 ON THE CONCEPT OF SOLIDS 281
4.6 MODELS OF NON-FOURIER HEAT CONDUCTION 284
4.7 CONCLUDING REMARKS 291
REFERENCES 291
AFTERWORD 295
INDEX 297 |
| any_adam_object | 1 |
| author | Manevič, Leonid I. 1938- Gendelman, Oleg V. |
| author_GND | (DE-588)120089157 |
| author_facet | Manevič, Leonid I. 1938- Gendelman, Oleg V. |
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| dewey-full | 620.105015118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.105015118 |
| dewey-search | 620.105015118 |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen |
| format | Book |
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| institution | BVB |
| isbn | 9783642153716 9783642153723 |
| language | English |
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| physical | XIII, 302 S. Ill., graph. Darst. |
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| publisher | Springer |
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| series2 | Foundations of engineering mechanics |
| spelling | Manevič, Leonid I. 1938- Verfasser (DE-588)120089157 aut Tractable models of solid mechanics formulation, analysis and interpretation Leonid I. Manevitch ; Oleg V. Gendelman Berlin [u.a.] Springer 2011 XIII, 302 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Foundations of engineering mechanics Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Gendelman, Oleg V. Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3517478&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=024507824&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Manevič, Leonid I. 1938- Gendelman, Oleg V. Tractable models of solid mechanics formulation, analysis and interpretation Mathematisches Modell (DE-588)4114528-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4129367-8 |
| title | Tractable models of solid mechanics formulation, analysis and interpretation |
| title_auth | Tractable models of solid mechanics formulation, analysis and interpretation |
| title_exact_search | Tractable models of solid mechanics formulation, analysis and interpretation |
| title_full | Tractable models of solid mechanics formulation, analysis and interpretation Leonid I. Manevitch ; Oleg V. Gendelman |
| title_fullStr | Tractable models of solid mechanics formulation, analysis and interpretation Leonid I. Manevitch ; Oleg V. Gendelman |
| title_full_unstemmed | Tractable models of solid mechanics formulation, analysis and interpretation Leonid I. Manevitch ; Oleg V. Gendelman |
| title_short | Tractable models of solid mechanics |
| title_sort | tractable models of solid mechanics formulation analysis and interpretation |
| title_sub | formulation, analysis and interpretation |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd |
| topic_facet | Mathematisches Modell Festkörpermechanik |
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