Steady state behaviour of stochastically excited nonlinear dynamic systems:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Eindhoven
1999
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Eindhoven, Technische Univ., Diss., 1999 |
| Beschreibung: | XX, 164 S. graph. Darst. |
| ISBN: | 9038626010 |
Internformat
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Datensatz im Suchindex
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| adam_text | STEADY STATE BEHAVIOUR OF STOCHASTICALLY EXCITED NONLINEAR DYNAMIC
SYSTEMS PROEFSCHRIFT TER VERKRIJGING VAN DE GRAAD VAN DOCTOR AAN DE
TECHNISCHE UNIVERSITEIT EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS,
PROF.DR. M. REM, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VOOR
PROMOTIES IN HET OPENBAAR TE VERDEDIGEN OP WOENSDAG 20 OKTOBER 1999 OM
16.00 UUR DOOR NATHAN VAN DE WOUW GEBOREN TE EINDHOVEN CONTENTS ABSTRACT
XI SAMENVATTING XIII NOTATION XVII 1 INTRODUCTION 1 1.1 OBJECTIVE OF THE
THESIS 1 1.2 RESPONSE APPROXIMATION METHODS 4 1.2.1 PROBLEM DEFINITION 4
1.2.2 MONTE CARLO SIMULATION 6 1.2.3 PERTURBATION METHOD 7 1.2.4
FOKKER-PLANCK EQUATION METHOD 8 1.2.5 STOCHASTIC AVERAGING 8 1.2.6
CLOSURE TECHNIQUES 10 1.2.7 LINEARIZATION METHODS 11 1.2.8 NONLINEAR
METHODS 13 1.2.9 CONCLUDING REMARKS 14 1.3 OUTLINE OF THE THESIS 15 2
STOCHASTIC DIFFERENTIAL EQUATIONS 19 2.1 INTRODUCTION 19 2.2 STOCHASTIC
PROCESSES 19 2.2.1 WHITE NOISE 21 2.3 ITO STOCHASTIC CALCULUS 23 2.3.1
THE ITO INTEGRAL 26 2.3.2 THE ITO FORMULA 30 2.4 ITO-TAYLOR EXPANSIONS
32 2.5 NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS 36 2.5.1
TIME DISCRETE APPROXIMATION 36 2.6 SUMMARY 39 3 SIMULATED STOCHASTIC
NONLINEAR RESPONSE PHENOMENA 41 3.1 THE NONLINEAR DYNAMIC SYSTEM 42 3.2
SURVEY OF PERIODIC RESPONSE CHARACTERISTICS 43 3.3 STATISTICAL
LINEARIZATION 44 VIII CONTENTS 3.4 RESPONSE TO WHITE NOISE EXCITATION 46
3.4.1 STATISTICAL MOMENTS 47 3.4.2 - PROBABILITY DENSITY FUNCTION 49
3.4.3 POWER SPECTRAL DENSITY 51 3.5 RESPONSE TO BAND-LIMITED STOCHASTIC
EXCITATION 54 3.5.1 GENERATION OF REALISATIONS OF A BAND-LIMITED
STOCHASTIC PROCESS 54 3.5.2 APPLICATION TO THE PIECE-WISE LINEAR SYSTEM
55 3.6 RESPONSE TO NEAR-PERIODIC STOCHASTIC EXCITATION 58 3.7 DISCUSSION
64 4 EXPERIMENTAL STOCHASTIC NONLINEAR RESPONSE PHENOMENA 65 4.1 THE
NONLINEAR SYSTEM: A BASE-EXCITED BEAM WITH IMPACT 65 4.1.1 A SDOF MODEL
OF THE ELASTIC BEAM 65 4.1.2 MODELLING THE ELASTIC STOP 66 4.1.3 THE
SDOF NONLINEAR DYNAMIC MODEL 67 4.2 SURVEY OF PERIODIC RESPONSE
CHARACTERISTICS OF THE SDOF MODEL ... 68 4.3 SIMULATED STOCHASTIC
NONLINEAR RESPONSE PHENOMENA OF THE SDOF MODEL 69 4.3.1 SIMULATION
APPROACH 69 4.3.2 SIMULATION RESULTS 70 4.4 THE EXPERIMENTAL SET-UP 73
4.5 EXPERIMENTAL RESULTS 74 4.6 RESPONSE PHENOMENA OF A MDOF MODEL 77
4.6.1 A 2DOF MODEL OF THE BEAM-IMPACT SYSTEM 77 4.6.2 SURVEY OF PERIODIC
RESPONSE OF THE 2DOF MODEL 78 4.6.3 SIMULATED STOCHASTIC NONLINEAR
RESPONSE PHENOMENA OF THE 2DOF MODEL 79 4.7 DISCUSSION 82 5
HIGHER-DIMENSIONAL LINEAR APPROXIMATION 83 5.1 PROBLEM MOTIVATION 83 5.2
NON-PARAMETRIC MODELLING: SPECTRAL FACTORIZATION 85 5.2.1 ALTERNATIVE
METHODS FOR THE CONSTRUCTION OF THE TRANSFER FUNCTION 86 5.2.2
APPLICATION TO THE PIECE-WISE LINEAR SYSTEM 92 5.3 BUILDING A PARAMETRIC
MODEL 93 5.4 APPLICATION TO THE PIECE-WISE LINEAR SYSTEM 95 5.5 SYSTEM
PARAMETER VARIATION 99 5.6 DISCUSSION 101 6 NONLINEAR APPROXIMATION
USING FINITE-ORDER VOLTERRA SYSTEMS 103 6.1 INTRODUCTION 103 6.2
VOLTERRA SYSTEMS 104 6.3 BILINEARIZATION 104 6.3.1 THE BILINEARIZATION
TECHNIQUE 105 6.3.2 INPUT-OUTPUT RELATION FOR BILINEAR STATE EQUATIONS
107 6.4 STATISTICAL BILINEARIZATION: APPLICATION TO THE PIECE-WISE
LINEAR SYSTEM 107 6.5 RESULTS 110 CONTENTS IX 6.6 DISCUSSION 113 7
CONCLUSIONS, DISCUSSION AND RECOMMENDATIONS 115 7.1 CONCLUSIONS AND
DISCUSSION 115 7.2 RECOMMENDATIONS 120 A THE MOMENT EQUATIONS 123 B
REMAINDER OF THE SECOND-ORDER ITO-TAYLOR EXPANSION 125 C EVALUATION OF
THE EXPECTED VALUES OF NONLINEAR FUNCTIONS FOR STATISTICAL LINEARIZATION
127 D HERTZIAN CONTACT AND HYSTERESIS DAMPING 129 D.I THE HERTZIAN
CONTACT FORCE LAW 129 D.2 HYSTERESIS DAMPING 133 D.3 ESTIMATION OF THE
HERTZIAN CONTACT PARAMETER KB AND THE COEFFICIENT OF RESTITUTION E 136 E
SPECIFICATIONS OF THE COMPONENTS OF THE EXPERIMENTAL SET-UP 139 E.I
COMPONENTS OF THE EXPERIMENTAL SET-UP 139 E.2 MEASURING EQUIPMENT 141 F
MDOF MODEL OF THE BEAM-IMPACT SYSTEM 143 F.I APPLICATION OF THE METHOD
OF RAYLEIGH-RITZ 143 F.2 MODELLING OF THE DAMPING OF THE ELASTIC BEAM
147 F.3 A 2DOF MODEL OF THE BEAM-IMPACT SYSTEM 147 G SOME NUMERICAL
ASPECTS OF THE SPECTRAL FACTORIZATION APPROACH BASED ON POTENTIAL THEORY
149 H DETERMINATION OF THE SECOND-ORDER SYMMETRIC TRANSFER FUNCTION 151
I EVALUATION OF THE EXPECTED VALUES OF NONLINEAR FUNCTIONS FOR
STATISTICAL BILINEARIZATION 155 BIBLIOGRAPHY 157 ACKNOWLEDGEMENTS 165
CURRICULUM VITAE 167
|
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| isbn | 9038626010 |
| language | English |
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| physical | XX, 164 S. graph. Darst. |
| publishDate | 1999 |
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| spelling | Wouw, Nathan van de Verfasser aut Steady state behaviour of stochastically excited nonlinear dynamic systems door Nathan van de Wouw Eindhoven 1999 XX, 164 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Eindhoven, Technische Univ., Diss., 1999 Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Stochastische Anregung (DE-588)4605452-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineares dynamisches System (DE-588)4126142-2 s Stochastische Anregung (DE-588)4605452-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008874362&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wouw, Nathan van de Steady state behaviour of stochastically excited nonlinear dynamic systems Nichtlineares dynamisches System (DE-588)4126142-2 gnd Stochastische Anregung (DE-588)4605452-2 gnd |
| subject_GND | (DE-588)4126142-2 (DE-588)4605452-2 (DE-588)4113937-9 |
| title | Steady state behaviour of stochastically excited nonlinear dynamic systems |
| title_auth | Steady state behaviour of stochastically excited nonlinear dynamic systems |
| title_exact_search | Steady state behaviour of stochastically excited nonlinear dynamic systems |
| title_full | Steady state behaviour of stochastically excited nonlinear dynamic systems door Nathan van de Wouw |
| title_fullStr | Steady state behaviour of stochastically excited nonlinear dynamic systems door Nathan van de Wouw |
| title_full_unstemmed | Steady state behaviour of stochastically excited nonlinear dynamic systems door Nathan van de Wouw |
| title_short | Steady state behaviour of stochastically excited nonlinear dynamic systems |
| title_sort | steady state behaviour of stochastically excited nonlinear dynamic systems |
| topic | Nichtlineares dynamisches System (DE-588)4126142-2 gnd Stochastische Anregung (DE-588)4605452-2 gnd |
| topic_facet | Nichtlineares dynamisches System Stochastische Anregung Hochschulschrift |
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