Gespeichert in:
| Titel: | Applied asymptotic methods in nonlinear oscillations |
|---|---|
| Von: |
by Yu. A. Mitropolskii and Nguyen Van Dao
|
| Person: |
Mitropolʹskij, Jurij Alekseevič
1917-2008 Verfasser aut Nguyen Van Dao |
| Hauptverfassende: | , |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad.
1997
|
| Schriftenreihe: | Solid mechanics and its applications
55 |
| Schlagworte: | |
| Online-Zugang: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008076685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | X, 341 S. graph. Darst. |
| ISBN: | 079234605X |
Internformat
MARC
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| 100 | 1 | |a Mitropolʹskij, Jurij Alekseevič |d 1917-2008 |e Verfasser |0 (DE-588)104890029 |4 aut | |
| 245 | 1 | 0 | |a Applied asymptotic methods in nonlinear oscillations |c by Yu. A. Mitropolskii and Nguyen Van Dao |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. |c 1997 | |
| 300 | |a X, 341 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Solid mechanics and its applications |v 55 | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differential equations, Nonlinear |x Asymptotic theory | |
| 650 | 4 | |a Nonlinear oscillations | |
| 650 | 0 | 7 | |a Nichtlineare Schwingung |0 (DE-588)4042100-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Asymptotische Methode |0 (DE-588)4287476-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1819355959211851776 |
|---|---|
| adam_text | CONTENTS
Preface ix
Chapter 1. Free Oscillations of Quasi linear Systems 1
1. Free oscillations of systems governed by a general second order diffe¬
rential equation 1
2. Conservative systems 10
3. Dissipative systems 17
4. Stationary amplitudes and their stability 20
5. Equivalent linearization of nonlinear oscillatory systems 22
6. Nonlinear oscillatory systems with slowly varying parameters. Adia
batic invariants. 25
7. Free oscillations of systems governed by a third order differential equa¬
tion 41
8. Free oscillations of systems governed by TV order differential equation 49
Chapter 2. Self excited Oscillations 58
1. Lienard and Routh Hurwitz criteria. Stability of equilibrium states 58
2. Self excited oscillations of a mechanical system 72
3. Dynamic absorber for quenching self excited oscillations of the mecha¬
nical systems having one degree of freedom 75
4. Dynamic absorber for quenching self excited oscillations of systems
having two degrees of freedom 85
5. Self excited oscillation of a system with N degrees of freedom 90
6. Dynamic absorber for a beam undergoing self excited oscillation 94
7. Absorber for self excited oscillations of a plate 100
Chapter 3. Forced Oscillations 107
1. Statement of the problem 107
2. Nonresonance case 109
3. Resonance case 118
4. External harmonic excitation of a nonlinear oscillator.
Duffing s equation. Jump phenomenon 129
5. Subharmonic oscillations 137
6. Nonstationary oscillations 145
7. Multi frequency oscillations in systems with one degree of freedom 156
8. Forced oscillation of systems governed by TV order differential equation 164
9. Single frequency oscillations in nonlinear systems with multiple degrees
of freedom 178
10. Multi frequency oscillations in nonlinear systems with multiple degrees
of freedom 180
Chapter 4. Parametrically excited Oscillations 196
1. Some examples of parametrically excited oscillators 196
2. Behaviour of oscillators governed by a Mathieu equation 199
3. Oscillators governed by a nonlinear Mathieu equation 206
4. Some generalized Mathieu equations 211
5. Parametric oscillations of mechanical systems with hysteresis 226
viii
6. Indirectly excited parametric oscillations 234
7. Parametrically excited oscillations in an electromechanical system 239
Chapter 5. Interaction of Nonlinear Oscillations 245
1. Forced oscillations of systems with self excitation. Synchronization
effect 245
2. Interaction between self excited and parametric oscillations 254
3. Generalized Van Der Pol equation 257
4. Interaction of subharmonic oscillations 263
5. Interaction between parametric and forced oscillations in multidimen¬
sional systems 272
Chapter 6. Averaging Method 282
1. The idea of averaging by Bogoliubov 283
2. Averaging differential equations with slowly varying parameters 291
3. Averaging in systems excited by impulsive forces 293
4. Conditions for uniformity in the averaging method 297
5. Averaging in systems containing slow and rapid motions 300
6. Averaging in systems containing rotation. Motion of satellites 303
7. Modified averaging methods 319
8. Averaging method and stability of motion in the critical case 322
Appendix 1. Principal Coordinates 327
Appendix 2. Some Trigonometric Formulae Often Used in the
Averaging Method 331
References 332
Index 336
|
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| author | Mitropolʹskij, Jurij Alekseevič 1917-2008 Nguyen Van Dao |
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| id | DE-604.BV011946795 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:21:31Z |
| institution | BVB |
| isbn | 079234605X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008076685 |
| oclc_num | 36857066 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | X, 341 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer Acad. |
| record_format | marc |
| series | Solid mechanics and its applications |
| series2 | Solid mechanics and its applications |
| spellingShingle | Mitropolʹskij, Jurij Alekseevič 1917-2008 Nguyen Van Dao Applied asymptotic methods in nonlinear oscillations Solid mechanics and its applications Differentiable dynamical systems Differential equations, Nonlinear Asymptotic theory Nonlinear oscillations Nichtlineare Schwingung (DE-588)4042100-4 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| subject_GND | (DE-588)4042100-4 (DE-588)4287476-2 |
| title | Applied asymptotic methods in nonlinear oscillations |
| title_auth | Applied asymptotic methods in nonlinear oscillations |
| title_exact_search | Applied asymptotic methods in nonlinear oscillations |
| title_full | Applied asymptotic methods in nonlinear oscillations by Yu. A. Mitropolskii and Nguyen Van Dao |
| title_fullStr | Applied asymptotic methods in nonlinear oscillations by Yu. A. Mitropolskii and Nguyen Van Dao |
| title_full_unstemmed | Applied asymptotic methods in nonlinear oscillations by Yu. A. Mitropolskii and Nguyen Van Dao |
| title_short | Applied asymptotic methods in nonlinear oscillations |
| title_sort | applied asymptotic methods in nonlinear oscillations |
| topic | Differentiable dynamical systems Differential equations, Nonlinear Asymptotic theory Nonlinear oscillations Nichtlineare Schwingung (DE-588)4042100-4 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| topic_facet | Differentiable dynamical systems Differential equations, Nonlinear Asymptotic theory Nonlinear oscillations Nichtlineare Schwingung Asymptotische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008076685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004342211 |
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