Nonlinear dynamical systems in engineering: some approximate approaches
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
2011
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XI, 395 S. graph. Darst. |
| ISBN: | 9783642227349 9783642227356 3642227341 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
2 PERTURBATION METHOD: LINDSTEDT-POINCARE 9
2.1 THE OSCILLATOR WITH CUBIC ELASTIC RESTORING FORCE 14
2.1.1 THE EXACT SOLUTION OF DUFFING EQUATION 14
2.1.2 USE OF THE PERTURBATION METHOD FOR DUFFING OSCILLATOR WITH SMALL
PARAMETER 17
2.1.3 USE OF THE PERTURBATION METHOD FOR DUFFING OSCILLATORS WITH STRONG
PARAMETER 19
3 THE METHOD OF HARMONIC BALANCE 31
3.1 FREE VIBRATIONS OF CANTILEVER BEAM 35
3.2 RATIONAL HARMONIC BALANCE METHOD 40
4 THE METHOD OF KRYLOV AND BOGOLYUBOV 47
4.1 OSCILLATOR WITH LINEAR AND CUBIC ELASTIC RESTORING FORCE AND WEAK
ASYMMETRIC QUADRATIC DAMPING 53
4.2 USE OF THE METHOD OF KRYLOV-BOGOLYUBOV AND ITERATION METHOD TO
WEAKLY NONLINEAR OSCILLATORS 60
4.2.1 "NONRESONANCE" CASE (* ^ E Q) 61
4.2.2 "RESONANCE" CASE CA ^I2 A 66
4.2.3 NUMERICAL EXAMPLES 72
5 THE METHOD OF MULTIPLE SCALES 83
5.1 DUFFING OSCILLATOR WITH SOFTENING NONLINEARITY 89
5.2 A PARAMETRIC SYSTEM WITH CUBIC NONLINEARITY COUPLED WITH A
LANCHESTER DAMPER 96
6 THE OPTIMAL HOMOTOPY ASYMPTOTIC METHOD 103
6.1 BASIC IDEA OF OHAM 106
6.2 DUFFING OSCILLATOR 112
6.2.1 NUMERICAL EXAMPLES 114
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1012996352
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
6.3 THIN FILM FLOW OF A FOURTH GRADE FLUID DOWN A VERTICAL CYLINDER 116
6.4 DAMPED OSCILLATOR WITH FRACTIONAL-ORDER RESTORING FORCE 120 6.4.1
NUMERICAL EXAMPLES 125
6.5 NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER 127
6.5.1 COOLING OF A LUMPED SYSTEM WITH VARIABLE SPECIFIC HEAT 127
6.5.2 THE TEMPERATURE DISTRIBUTION EQUATION IN A THICK RECTANGULAR FIN
RADIATION TO FREE SPACE 131 6.6 BLASIUS' PROBLEM 133
6.7 OSCILLATIONS OF A UNIFORM CANTILEVER BEAM CARRYING AN INTERMEDIATE
LUMPED MASS AND ROTARY INERTIA 143
6.8 OSCILLATIONS OF AN ELECTRICAL MACHINE 151
6.9 OSCILLATIONS OF A MASS ATTACHED TO A STRETCHED ELASTIC WIRE . . .
156 6.10 NONLINEAR OSCILLATOR WITH DISCONTINUITIES 162
6.11 NONLINEAR JERK EQUATIONS 168
6.12 THE MOTION OF A PARTICLE ON A ROTATING PARABOLA 173
6.13 NONLINEAR OSCILLATOR WITH DISCONTINUITIES AND FRACTIONAL-POWER
RESTORING FORCE 184
6.14 OSCILLATIONS OF A FLEXIBLE CANTILEVER BEAM WITH SUPPORT MOTION 191
6.15 THE JEFFERY-HAMEL FLOW PROBLEM 197
6.15.1 NUMERICAL EXAMPLES 206
THE OPTIMAL HOMOTOPY PERTURBATION METHOD 211
7.1 HOMOTOPY PERTURBATION METHOD 211
7.2 MODIFIED HOMOTOPY PERTURBATION METHOD 214
7.3 BASIC IDEA OF OPTIMAL HOMOTOPY PERTURBATION METHOD AND SOME
APPLICATIONS 227
7.4 A HEAT TRANSFER PROBLEM 230
7.5 THIN FILM FLOW OF A FOURTH GRADE FLUID DOWN A VERTICAL CYLINDER 234
7.6 NONLINEAR DYNAMICS OF AN ELECTRICAL MACHINE ROTOR-BEARING SYSTEM 240
7.7 A NON-CONSERVATIVE OSCILLATORY SYSTEM OF A ROTATING ELECTRICAL
MACHINE 252
THE OPTIMAL VARIATIONAL ITERATION METHOD 259
8.1 THE VARIATIONAL ITERATION METHOD AND APPLICATIONS 259
8.1.1 NONLINEAR OSCILLATOR WITH QUADRATIC AND CUBIC NONLINEARITIES 264
8.1.2 A FAMILY OF NONLINEAR DIFFERENTIAL EQUATIONS 270 8.1.3 THE DUFFING
EQUATION 271
8.2 MATHEMATICAL DESCRIPTION OF THE OPTIMAL VARIATIONAL ITERATION METHOD
275
IMAGE 3
CONTENTS XI
8.3 DUFFING-HARMONIC OSCILLATOR 275
8.4 OSCILLATIONS OF A UNIFORM CANTILEVER BEAM CARRYING AN INTERMEDIATE
LUMPED MASS AND ROTARY INERTIA 281
8.5 THIN FILM FLOW OF A FOURTH-GRADE FLUID DOWN A VERTICAL CYLINDER 286
8.6 DYNAMIC ANALYSIS OF A ROTATING ELECTRIC MACHINE 292
8.7 OSCILLATORS WITH FRACTIONAL-POWER NONLINEARITIES 297
8.8 A BOUNDARY LAYER EQUATION IN UNBOUNDED DOMAIN 305
9 OPTIMAL PARAMETRIC ITERATION METHOD 313
9.1 SHORT CONSIDERATIONS 313
9.1.1 A COMBINATION OF MICKENS AND HE ITERATION METHODS . . 315 9.1.2
AN ITERATION PROCEDURE WITH APPLICATION TO VAN DER POL OSCILLATOR 326
9.2 BASIC IDEA OF OPTIMAL PARAMETRIC ITERATION METHOD 334
9.3 THIN FILM FLOW OF A FOURTH GRADE FLUID DOWN A VERTICAL CYLINDER 335
9.4 THERMAL RADIATION ON MHD FLOW OVER A STRETCHING POROUS SHEET 338
9.5 THE OSCILLATOR WITH CUBIC AND HARMONIC RESTORING FORCE 342 9.6
OSCILLATIONS OF A UNIFORM CANTILEVER BEAM CARRYING AN INTERMEDIATE
LUMPED MASS AND ROTARY INERTIA 351
9.7 A MODIFIED VAN DER POL OSCILLATOR 356
9.8 VOLTERRA'S POPULATION MODEL 363
9.9 THOMAS-FERMI EQUATION 368
9.10 SWIRLING FLOW DOWNSTREAM OF A TURBINE RUNNER 373
9.11 LOTKA-VOLTERRA MODEL WITH THREE SPECIES 378
REFERENCES 385
INDEX 393 |
| any_adam_object | 1 |
| author | Marinca, Vasile Herisanu, Nicolae |
| author_facet | Marinca, Vasile Herisanu, Nicolae |
| author_role | aut aut |
| author_sort | Marinca, Vasile |
| author_variant | v m vm n h nh |
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| bvnumber | BV039871511 |
| classification_rvk | ZQ 5220 |
| ctrlnum | (OCoLC)740630116 (DE-599)DNB1012996352 |
| dewey-full | 620.001185 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.001185 |
| dewey-search | 620.001185 |
| dewey-sort | 3620.001185 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| isbn | 9783642227349 9783642227356 3642227341 |
| language | English |
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| physical | XI, 395 S. graph. Darst. |
| publishDate | 2011 |
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| spelling | Marinca, Vasile Verfasser aut Nonlinear dynamical systems in engineering some approximate approaches Vasile Marinca ; Nicolae Herisanu Berlin Springer 2011 XI, 395 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Technisches System (DE-588)4126276-1 gnd rswk-swf Technisches System (DE-588)4126276-1 s Nichtlineares dynamisches System (DE-588)4126142-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Herisanu, Nicolae Verfasser aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3845093&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=024730821&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marinca, Vasile Herisanu, Nicolae Nonlinear dynamical systems in engineering some approximate approaches Nichtlineares dynamisches System (DE-588)4126142-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Technisches System (DE-588)4126276-1 gnd |
| subject_GND | (DE-588)4126142-2 (DE-588)4114528-8 (DE-588)4126276-1 |
| title | Nonlinear dynamical systems in engineering some approximate approaches |
| title_auth | Nonlinear dynamical systems in engineering some approximate approaches |
| title_exact_search | Nonlinear dynamical systems in engineering some approximate approaches |
| title_full | Nonlinear dynamical systems in engineering some approximate approaches Vasile Marinca ; Nicolae Herisanu |
| title_fullStr | Nonlinear dynamical systems in engineering some approximate approaches Vasile Marinca ; Nicolae Herisanu |
| title_full_unstemmed | Nonlinear dynamical systems in engineering some approximate approaches Vasile Marinca ; Nicolae Herisanu |
| title_short | Nonlinear dynamical systems in engineering |
| title_sort | nonlinear dynamical systems in engineering some approximate approaches |
| title_sub | some approximate approaches |
| topic | Nichtlineares dynamisches System (DE-588)4126142-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Technisches System (DE-588)4126276-1 gnd |
| topic_facet | Nichtlineares dynamisches System Mathematisches Modell Technisches System |
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