Asymptotic approaches in nonlinear dynamics: new trends and applications
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schriftenreihe: | Springer series in synergetics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XI, 310 S. graph. Darst. |
| ISBN: | 3540638946 |
Internformat
MARC
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| 100 | 1 | |a Awrejcewicz, Jan |d 1952- |e Verfasser |0 (DE-588)120089122 |4 aut | |
| 245 | 1 | 0 | |a Asymptotic approaches in nonlinear dynamics |b new trends and applications |c Jan Awrejcewicz ; Igor V. Andrianov ; Leonid I. Manevitch |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XI, 310 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in synergetics | |
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| 650 | 7 | |a Oscillations non linéaires |2 ram | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Nonlinear oscillations | |
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| 650 | 0 | 7 | |a Nichtlineare Schwingung |0 (DE-588)4042100-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Schwingung |0 (DE-588)4042100-4 |D s |
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| 700 | 1 | |a Andrianov, I. V. |d 1948- |e Verfasser |0 (DE-588)120089106 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008118258 | ||
Datensatz im Suchindex
| _version_ | 1804126591562809344 |
|---|---|
| adam_text | Contents
1. Introduction: Some General Principles of Asymptotology . 1
1.1 An Illustrative Example 2
1.2 Reducing the Dimensionality of a System 4
1.3 Continualization 5
1.4 Averaging 6
1.5 Renormalization 7
1.6 Localization 8
1.7 Linearization 8
1.8 Pade Approximants 9
1.9 Modern Computers and Asymptotic Methods 10
1.10 Asymptotic Methods and Teaching Physics 11
1.11 Problems and Perspectives 11
2. Discrete Systems 13
2.1 The Classical Perturbation Technique: an Introduction 13
2.2 Krylov Bogolubov Mitropolskij Method 19
2.3 Equivalent Linearization 24
2.4 Analysis of Nonconservative Nonautonomous Systems 26
2.4.1 Introduction 26
2.4.2 Nonresonance Oscillations 27
2.4.3 Oscillations in the Neighbourhood of Resonance 31
2.5 Nonstationary Nonlinear Systems 42
2.6 Parametric and Self Excited Oscillation
in a Three Degree of Freedom Mechanical System 55
2.6.1 Analysed System and Equation of Motion 55
2.6.2 Transformation of the Equations of Motion
to the Main Coordinates 59
2.6.3 Zones of Instability of the First Order 62
2.6.4 Calculation Examples 74
2.7 Modified Poincare Method 81
2.7.1 One Degree of Freedom System 81
2.7.2 General Nonlinear Systems 86
2.8 Hopf Bifurcation 93
X Contents
2.9 Stability Control of Vibro Impact Periodic Orbit 100
2.9.1 Introduction 100
2.9.2 Control of Vibro Impact Periodic Orbits 101
2.9.3 Stability Control 103
2.9.4 Simulation Results 105
2.10 Normal Modes of Nonlinear Systems with n Degrees
of Freedom 106
2.10.1 Definition 106
2.10.2 Free Oscillations and Close Natural Frequencies 108
2.11 Nontraditional Asymptotic Approaches 118
2.11.1 Choice of Asymptotic Expansion Parameters 118
2.11.2 6 Expansions in Nonlinear Mechanics 121
2.11.3 Asymptotic Solutions for Nonlinear Systems
with High Degrees of Nonlinearity 128
2.11.4 Square Well Problem of Quantum Theory 130
2.12 Pade Approximants 132
2.12.1 One Point Pade Approximants:
General Definitions and Properties 132
2.12.2 Using One Point Pade Approximants in Dynamics .... 134
2.12.3 Matching Limit Expansions 139
2.12.4 Matching Local Expansions in Nonlinear Dynamics ... 143
2.12.5 Generalizations and Problems 148
3. Continuous Systems 151
3.1 Continuous Approximation for a Nonlinear Chain 151
3.2 Homogenization Procedure in the Nonlinear Dynamics
of Thin Walled Structures 155
3.2.1 Nonhomogeneous Rod 155
3.2.2 Stringer Plate 158
3.2.3 Perforated Membrane 162
3.2.4 Perforated Plate 166
3.3 Averaging Procedure in the Nonlinear Dynamics
of Thin Walled Structures 171
3.3.1 Berger and Berger Like Equations for Plates and Shells 171
3.3.2 Method of Freezing in the Nonlinear Theory
of Viscoelasticity 176
3.4 Bolotin Like Approach for Nonlinear Dynamics 177
3.4.1 Straightforward Bolotin Approach 177
3.4.2 Modified Bolotin Approach 185
3.5 Regular and Singular Asymptotics in the Nonlinear Dynamics
of Thin Walled Structures 191
3.5.1 Circular Rings and Axisymmetric Cylindrical Shells .. 191
3.5.2 Reinforced and Isotropic Cylindrical Shells 197
3.5.3 Nonlinear Oscillations of a Cylindrical Panel 214
Contents XI
3.5.4 Stability of Thin Spherical Shells
Under Dynamic Loading 219
3.5.5 Asymptotic Investigation
of the Nonlinear Dynamic Boundary
Value Problem for a Rod 228
3.6 One Point Pade Approximants
Using the Method of Boundary Condition Perturbation 229
3.7 Two Point Pade Approximants:
A Plate on Nonlinear Support 236
3.8 Solitons and Soliton Like Approaches
in the Case of Strong Nonlinearity 240
3.9 Nonlinear Analysis of Spatial Structures 247
3.9.1 Introduction 247
3.9.2 Modified Envelope Equation 248
4. Discrete—Continuous Systems 253
4.1 Periodic Oscillations of Discrete Continuous Systems
with a Time Delay 253
4.1.1 The KBM Method 253
4.2 Simple Perturbation Technique 267
4.3 Nonlinear Behaviour of Electromechanical Systems 280
4.3.1 Introduction 280
4.3.2 Dynamics Equations 281
4.3.3 Averaging 282
4.3.4 Numerical Results 285
General References 291
Detailed References (d) 299
Index 303
|
| any_adam_object | 1 |
| author | Awrejcewicz, Jan 1952- Andrianov, I. V. 1948- Manevič, Leonid I. 1938- |
| author_GND | (DE-588)120089122 (DE-588)120089106 (DE-588)120089157 |
| author_facet | Awrejcewicz, Jan 1952- Andrianov, I. V. 1948- Manevič, Leonid I. 1938- |
| author_role | aut aut aut |
| author_sort | Awrejcewicz, Jan 1952- |
| author_variant | j a ja i v a iv iva l i m li lim |
| building | Verbundindex |
| bvnumber | BV011995454 |
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| callnumber-raw | QA867.5 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 810 SK 950 |
| ctrlnum | (OCoLC)39052635 (DE-599)BVBBV011995454 |
| dewey-full | 531/.32/01515355 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531/.32/01515355 |
| dewey-search | 531/.32/01515355 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV011995454 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:53Z |
| institution | BVB |
| isbn | 3540638946 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008118258 |
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| physical | XI, 310 S. graph. Darst. |
| publishDate | 1998 |
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| publisher | Springer |
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| series2 | Springer series in synergetics |
| spelling | Awrejcewicz, Jan 1952- Verfasser (DE-588)120089122 aut Asymptotic approaches in nonlinear dynamics new trends and applications Jan Awrejcewicz ; Igor V. Andrianov ; Leonid I. Manevitch Berlin [u.a.] Springer 1998 XI, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics Literaturangaben Développements asymptotiques ram Oscillations non linéaires ram Asymptotic expansions Nonlinear oscillations Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Andrianov, I. V. 1948- Verfasser (DE-588)120089106 aut Manevič, Leonid I. 1938- Verfasser (DE-588)120089157 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Awrejcewicz, Jan 1952- Andrianov, I. V. 1948- Manevič, Leonid I. 1938- Asymptotic approaches in nonlinear dynamics new trends and applications Développements asymptotiques ram Oscillations non linéaires ram Asymptotic expansions Nonlinear oscillations Asymptotische Methode (DE-588)4287476-2 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4042100-4 |
| title | Asymptotic approaches in nonlinear dynamics new trends and applications |
| title_auth | Asymptotic approaches in nonlinear dynamics new trends and applications |
| title_exact_search | Asymptotic approaches in nonlinear dynamics new trends and applications |
| title_full | Asymptotic approaches in nonlinear dynamics new trends and applications Jan Awrejcewicz ; Igor V. Andrianov ; Leonid I. Manevitch |
| title_fullStr | Asymptotic approaches in nonlinear dynamics new trends and applications Jan Awrejcewicz ; Igor V. Andrianov ; Leonid I. Manevitch |
| title_full_unstemmed | Asymptotic approaches in nonlinear dynamics new trends and applications Jan Awrejcewicz ; Igor V. Andrianov ; Leonid I. Manevitch |
| title_short | Asymptotic approaches in nonlinear dynamics |
| title_sort | asymptotic approaches in nonlinear dynamics new trends and applications |
| title_sub | new trends and applications |
| topic | Développements asymptotiques ram Oscillations non linéaires ram Asymptotic expansions Nonlinear oscillations Asymptotische Methode (DE-588)4287476-2 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd |
| topic_facet | Développements asymptotiques Oscillations non linéaires Asymptotic expansions Nonlinear oscillations Asymptotische Methode Nichtlineare Schwingung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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