Nonlinear interactions: analytical, computational, and experimental methods
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2000
|
| Series: | Wiley series in nonlinear science
A Wiley-Interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 760 S. Ill., graph. Darst. |
| ISBN: | 0471175919 |
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| adam_text | IMAGE 1
NONLINEAR INTERACTIONS
ANALYTICAL, COMPUTATIONAL, AND EXPERIMENTAL METHODS
ALI H. NAYFEH
VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY
A WILEY-INTERSCIENCE PUBLICATION
JOHN WILEY & SONS, INC.
NEW YORK * CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO
IMAGE 2
CONTENTS
PREFACE 1 INTRODUCTION
1.1 PRELIMINARIES FROM MECHANICS 1.2 CLASSIFICATION OF NONLINEARITIES
1.3 ORDER SYMBOLS
1.4 STRAIGHTFORWARD EXPANSION AND RESONANCES 1.5 THE METHOD OF MULTIPLE
SC ALES 1.6 THE METHOD OF AVERAGING 1.7 THE TIME-A VERA GED LA GRANGIAN
AND
VIRTUAL WORK 1.8 THE METHOD OF HARMONIC BALANCE 1.9 THE METHOD OF NORMAL
FORMS 1.10 HIGHER APPROXIMATIONS
1.10.1 REAL-VALUED FORM 1.10.2 COMPLEX-VALUED FORM 1.11 COMMENTS
2 TWO-TO-ONE INTERNAL RESONANCE
V.
XV
1
1
7
8
10 13 20
23 24 25 29 30 35 37
41
IMAGE 3
VUEI CONTENTS
2.1 PHYSICAL EXAMPLES 42
2.1.1 A DOUBLE PENDULUM 43
2.1.2 A PLANAR ELASTIC PENDULUM 45
2.1.3 AUTOPARAMETRIC VIBRATION ABSORBER 46
2.1.4 SHIPS CONSTRAINED TO PITCH (HEAVE) AND ROLL 49
2.1.5 ARCHES 51
2.1.6 SURFACE WAVES IN A BASIN 54
2.1.7 CIRCULAR CYLINDRICAL SHELLS 56
2.1.8 OTHER SYSTEMS 60
2.2 FREE OSCILLATIONS 65
2.2.1 NONRESONANCE CASE 66
2.2.2 RESONANCE CASE 66
2.2.3 IMPLICATION OF INTERNAL RESONANCES ON THE LINEAR IDENTIFICATION OF
STRUCTURES 70
2.2.4 A CONTROL STRATEGY BASED ON INTERNAL RESONANCE 73
2.3 PRIMARY RESONANCE OF THE SECOND MODE 76
2.3.1 FIXED-POINT SOLUTIONS 78
2.3.2 STABILITY OF THE FIXED POINTS 80
2.3.3 SCALING OF VARIABLES 83
2.3.4 FORCE-RESPONSE CURVES 85
2.3.5 FREQUENCY-RESPONSE CURVES 92
2.3.6 DYNAMIC SOLUTIONS OF THE MODULATION EQUATIONS 96
2.3.7 A CONTROL STRATEGY BASED ON THE SATURATION PHENOMENON 109
2.4 PRIMARY RESONANCE OF THE FIRST MODE 117
2.4-1 FIXED POINTS AND THEIR STABILITY 118
2.4-2 FREQUENCY-RESPONSE CURVES 119
2.4.3 DYNAMIC MOTIONS 123
2.5 PRINCIPAL PARAMETRIC RESONANCE OF THE SECOND MODE 126
2.5.1 FIXED POINTS AND THEIR STABILITY 128
2.5.2 FORCE- AND FREQUENCY-RESPONSE CURVES 130 2.5.3 DYNAMIC SOLUTIONS
132
2.5.4 EXPERIMENTAL OBSERVATIONS WITH PRINCIPAL PARAMETRIC RESONANCE 139
IMAGE 4
CONTENTS IX
2.5.5 EXPERIMENTAL OBSERVATIONS WITH SUBHARMONIC
RESONANCE OF ORDER ONE-HALF 144
2.6 PRINCIPAL PARAMETRIC RESONANCE OF
THE FIRST MODE 148
2.6.1 FIXED POINTS AND THEIR STABUEITY 149
2.1 COMBINATION PARAMETRIC
RESONANCES 154
2.7.1 FIXED POINTS AND THEIR STABUEITY 155
2.8 INFLUENCE OF NONLINEAR DAMPING 167
2.8.1 FIXED POINTS AND THEIR STABUEITY 170
2.8.2 FORCEDIESPONSE CURVES 171
2.9 INFLUENCE OF CUBIC NONLINEARITY 177
3 ONE-TO-ONE INTERNAL RESONANCE 181
3.1 PHYSICAL EXAMPLES 182
3.1.1 THE SPHERICAL PENDULUM 182
3.1.2 TAUT STRINGS 184
3.1.3 BEAMS WITH MIDPLANE STRETCHING 188
3.1.4 BEAMS WITHOUT MIDPLANE STRETCHING 191
3.1.5 THIN RECTANGULAR PLATES 200
3.1.6 CIRCULAR CYLINDRICAL SHELLS 205
3.1.7 THIN CIRCULAR PLATES 211
3.1.8 ROTATING DISKS 218
3.1.9 VIBRATION ABSORBERS 224
3.1.10 AN ISOTROPIE PANEL IN A SUPERSONIC
AIRSTREAM 230
3.1.11 OTHER SYSTEMS 234
3.2 RESPONSE OF TAUT STRINGS TO
PRIMARY RESONANCES 240
3.2.1 EQUUEIBRIUM SOLUTIONS AND THEIR STABUEITY 241
3.2.2 DYNAMIC SOLUTIONS 248
3.3 PRIMARY RESONANCES IN CYLINDRICAL
SHELLS 261
3.4 PRIMARY RESONANCES OF SURFACE
WAVES 270
3.4-1 EXPERIMENTAL RESULTS 270
3.4.2 THEORETICAL RESULTS 275
3.5 PRIMARY RESONANCE IN CANTILEVER
BEAMS 281
3.5.1 MODULATION EQUATIONS
IMAGE 5
X CONTENTS
3.5.2 THEORETICAL RESULTS 285
3.5.3 EXPERIMENTS 291
3.6 PRINCIPAL PARAMETRIC RESONANCE IN A NONSEMISIMPLE SYSTEM 297
3.6.1 MODULATION EQUATIONS 297
3.6.2 EQUILIBRIUM SOLUTIONS AND THEIR STABILITY 300 3.6.3 DYNAMIC
SOLUTIONS 304
3.7 FUNDAMENTAL PARAMETRIC RESONANCE IN A NONSEMISIMPLE SYSTEM 307
3.7.1 MODULATION EQUATIONS 307
3.7.2 EQUILIBRIUM SOLUTIONS 311
3.7.3 DYNAMIC SOLUTIONS 314
3.8 COMBINATION PARAMETRIC RESONANCE IN A NONSEMISIMPLE SYSTEM 320
3.8.1 MODULATION EQUATIONS 321
3.8.2 EQUILIBRIUM SOLUTIONS 324
3.8.3 DYNAMIC SOLUTIONS 326
3.9 COMBINED PARAMETRIC AND EXTERNAL EXCITATIONS 333
3.9.1 MODULATION EQUATIONS 334
3.9.2 EQUILIBRIUM SOLUTIONS 340
3.9.3 EXPERIMENTS 342
THREE- TO- ONE INTERNAL RESONANCE 34 7
4.1 PHYSICAL EXAMPLES 347
4-1.1 A DOUBLE PENDULUM WITH A MOVING SUPPORT 347
4.1.2 A HINGED-FIXED BEAM 353
4-1.3 LONGITUDINAL VIBRATIONS OF BEAMS 363
4-1-4 CLAMPED-CLAMPED BUCKLED BEAMS 369
4.1.5 OTHER SYSTEMS 377
4.2 PRIMARY RESONANCE OF THE FIRST MODE 379
4-2.1 EQUILIBRIUM SOLUTIONS 381
4-2.2 DYNAMIC SOLUTIONS 383
4-3 PRIMARY RESONANCE OF THE SECOND MODE 392
4-3.1 EQUILIBRIUM SOLUTIONS 394
4-3.2 DYNAMIC SOLUTIONS 396
IMAGE 6
CONTENTS
XI
44 PRINCIPAL PARAMETRIC RESONANCE OF
THE FIRST MODE 398
4-4-1 EQUILIBRIUM SOLUTIONS AND THEIR STABILITY 399 4-4-2 DYNAMIC
SOLUTIONS 400
4-5 PRINCIPAL PARAMETRIC RESONANCE OF THE SECOND MODE 402
4-5.1 EQUILIBRIUM SOLUTIONS AND THEIR STABILITY 403 4-5.2 DYNAMIC
SOLUTIONS 404
4.6 COMBINATION PARAMETRIC RESONANCE OF THE ADDITIVE TYPE 410
4.6.I EQUILIBRIUM SOLUTIONS AND THEIR STABILITY 4H 4-6.2 DYNAMIC
SOLUTIONS 41%
5 COMBINATION RESONANCES 411
5.1 EXPERIMENTS 421
5.1.1 COMBINATION PARAMETRIC RESONANCE IN A CANTILEVER BEAM 421
5.1.2 COMBINATION EXTERNAL RESONANCES IN A PORTAL FRAME 422
5.1.3 COMBINATION RESONANCE OF THE ADDITIVE TYPE IN A COMPOSITE PLATE
425
5.1.4 SUBCOMBINATION RESONANCE IN A COMPOSITE PLATE 428
5.1.5 COMBINATION INTERNAL RESONANCE IN A TWO-BEAM-MASS STRUCTURE 432
5.1.6 COMBINATION INTERNAL RESONANCE IN A T-SHAPED STRUCTURE 434
5.1.7 SUBCOMBINATION INTERNAL RESONANCE IN A COMPOSITE PLATE 44%
5.2 COMBINATION PARAMETRIC RESONANCE 446 5.2.1 MODULATION EQUATIONS 448
5.2.2 FIXED POINTS AND THEIR STABILITY 452
5.3 EXTERNAL SUBCOMBINATION RESONANCE 456
5.3.1 MODULATION EQUATIONS 457
5.3.2 FIXED POINTS AND THEIR STABILITY 459
5.4 COMBINATION INTERNAL RESONANCE 464
5.4-1 MODULATION EQUATIONS 465
5-4-2 FIXED POINTS AND THEIR STABILITY 466
5-4-3 FORCE-RESPONSE CURVES 4*70
IMAGE 7
XUE CONTENTS
5.4-4 FREQUENCY-RESPONSE CURVES 471
5.5 SUBCOMBINATION INTERNAL RESONANCE IN A CANTILEVER BEAM 41%
5.5.1 MODULATION EQUATIONS 474
5.5.2 FIXED POINTS AND THEIR STABILITY 476
5.6 COMBINATION INTERNAL RESONANCE IN CIRCULAR PLATES 482
5.6.1 DISCRETIZATION 4%4-
5.6.2 MODULATION EQUATIONS 487
5.6.3 FIXED POINTS AND THEIR STABILITY 489
S YSTEMS WITH WIDEL Y SPA CED MODES 495
6.1 EXPERIMENTAL RESULTS 497
6.1.1 A PARAMETRICALLY EXCITED CANTILEVER BEAM 497 6.1.2 A TRANSVERSELY
EXCITED CANTILEVER BEAM 503 6.1.3 FRAMES 503
6.1.4 COMPOSITE PLATES 505
6.1.5 AN EXTERNALLY EXCITED CIRCULAR ROD 507
6.2 ANALYSIS OF AN EXTERNALLY EXCITED SYSTEM 513
6.2.1 METHOD OF AVERAGING 515
6.2.2 METHOD OF MULTIPLE SCALES 516
6.2.3 THE METHOD OF NORMAL FORMS 518
6.2.4 FIXED POINTS AND THEIR STABILITY 520
6.2.5 DYNAMIC SOLUTIONS 523
6.3 ANALYSIS OF A PARAMETRICALLY
EXCITED SYSTEM 526
6.3.1 MODULATION EQUATIONS 527
6.3.2 FIXED POINTS AND THEIR STABILITY 529
6.3.3 DYNAMIC SOLUTIONS 531
6.4 APPLICATION TO CANTILEVER METALLIC BEAMS 542
6.4-1 PROBLEM FORMULATION 543
6.4-2 INTERACTION BETWEEN TWO BENDING MODES IN THE Y-DIRECTION 545
6-4-3 INTERACTION BETWEEN TWO BENDING MODES IN ORTHOGONAL DIRECTIONS 547
6-4-4 INTERACTION BETWEEN A BENDING AND A TORSIONAL MODE 550
IMAGE 8
CONTENTS XUEI
6.4-5 INTERACTION AMONG FOUR BENDING MODES
IN A CIRCULAR ROD 554
7 MULTIPLE INTERNAL RESONANCES 557
7.1 MULTIPLE TWO-TO-ONE AUTOPARAMETRIC RESONANCES 561
7.1.1 MODULATION EQUATIONS 561
7.1.2 FIXED POINTS AND THEIR STABILITY 564
7.1.3 BIFURCATION ANALYSIS OF THE FIXED-POINT SOLUTIONS 567
7.1.4 DYNAMIC SOLUTIONS 572
7.2 SUSPENDED HOMOGENEOUS ELASTIC CABLES 575
7.2.1 PROBLEM FORMULATION 575
7.2.2 MODULATION EQUATIONS 579
7.2.3 BIFURCATION ANALYSIS 590
8 NONLINEAR NORMAL MODES 599
8.1 CONCEPT OF NONLINEAR NORMAL MODES 599
8.1.1 INVARIANT-MANIFOLD APPROACH TO NONLINEAR NORMAL MODES 603
8.1.2 AN ENERGY-BASED APPROACH TO NONLINEAR NORMAL MODES 606
8.1.3 COMMENTS 607
8.2 A SYMMETRIC 2D0F SYSTEM 609
8.2.1 SIMILAR NONLINEAR NORMAL MODES 610
8.2.2 PERIODIC SOLUTIONS BY THE METHOD OF MULTIPLE SCALES 614
8.2.3 COMMENTS 618
8.3 AN ASYMMETRIC 2D0F SYSTEM 618
8.3.1 SIMILAR NONLINEAR NORMAL MODES 619
8.3.2 PERIODIC SOLUTIONS BY THE METHOD OF MULTIPLE SCALES 619
8.4 CUBIC AND QUINTIC NONLINEARITIES 625
8.4-1 SYMMETRIE CASE 626
8.4-2 UNSYMMETRIC CASE 627
8.5 QUADRATIC AND CUBIC NONLINEARITIES 629
8.5.1 SIMILAR NONLINEAR NORMAL MODES 629
IMAGE 9
*
XIV CONTENTS
8.5.2 PERIODIC SOLUTIONS BY THE METHOD OF MULTIPLE SCALES 630
8.5.3 COMMENTS 633
8.6 MULTI-DEGREE-OF-FREEDOM SYSTEMS 633
8.6.1 REAL-VARIABLE INVARIANT-MANIFOLD APPROACH 634
8.6.2 COMPLEX-VARIABLE INVARIANT-MANIFOLD APPROACH 636
8.6.3 THE METHOD OF MULTIPLE SCALES 639
8.7 SYSTEMS WITH INTERNAL RESONANCE 641
8.7.1 METHOD OF SOLUTION 642
8.7.2 ONE-TO-ONE INTERNAL RESONANCE 646
8.7.3 THREE-TO-ONE INTERNAL RESONANCE 651
8.8 CONTINUOUS SYSTEMS 653
8.8.1 HARMONIE-BALANCE METHODS 654
8.8.2 DISCRETIZATION METHODS 655
8.8.3 DIRECT APPROACHES 657
8.9 A BEAM ON A NONLINEAR FOUNDATION 662
8.9.1 THE METHOD OF MULTIPLE SCALES 663
8.9.2 THE METHOD OF NORMAL FORMS 665
8.9.3 THE METHOD OF SHAW AND PIERRE 666
8.9.4 THE METHOD OF KING AND VAKAKIS 670
8.10 NONLINEAR BOUNDARY CONDITIONS 672
8.10.1 THE METHOD OF MULTIPLE SCALES 672
8.10.2 THE METHOD OF NORMAL FORMS 673
8.10.3 THE METHOD OF SHAW AND PIERRE 675
8.10.4 THE METHOD OF KING AND VAKAKIS 677
8.11 THE CASE OF INTERNAL RESONANCE 679
8.11.1 THE METHOD OF MULTIPLE SCALES 679
8.11.2 THE METHOD OF NORMAL FORMS 681
BIBLIOGRAPHY 685
S UEB JE CT INDEX 749
|
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| indexdate | 2024-07-09T18:43:20Z |
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| isbn | 0471175919 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009065862 |
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| physical | XIX, 760 S. Ill., graph. Darst. |
| publishDate | 2000 |
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| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in nonlinear science A Wiley-Interscience publication |
| spelling | Nayfeh, Ali Hasan 1933-2017 Verfasser (DE-588)151240388 aut Nonlinear interactions analytical, computational, and experimental methods Ali H. Nayfeh New York [u.a.] Wiley 2000 XIX, 760 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in nonlinear science A Wiley-Interscience publication Nonlinear mechanics Nonlinear theories Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009065862&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nayfeh, Ali Hasan 1933-2017 Nonlinear interactions analytical, computational, and experimental methods Nonlinear mechanics Nonlinear theories Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| subject_GND | (DE-588)4126142-2 |
| title | Nonlinear interactions analytical, computational, and experimental methods |
| title_auth | Nonlinear interactions analytical, computational, and experimental methods |
| title_exact_search | Nonlinear interactions analytical, computational, and experimental methods |
| title_full | Nonlinear interactions analytical, computational, and experimental methods Ali H. Nayfeh |
| title_fullStr | Nonlinear interactions analytical, computational, and experimental methods Ali H. Nayfeh |
| title_full_unstemmed | Nonlinear interactions analytical, computational, and experimental methods Ali H. Nayfeh |
| title_short | Nonlinear interactions |
| title_sort | nonlinear interactions analytical computational and experimental methods |
| title_sub | analytical, computational, and experimental methods |
| topic | Nonlinear mechanics Nonlinear theories Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| topic_facet | Nonlinear mechanics Nonlinear theories Nichtlineares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009065862&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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