Linearization methods for stochastic dynamic systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Medienkombination Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Lecture notes in physics
730 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XI, 383 S. graph. Darst. |
| ISBN: | 9783540729969 |
Internformat
MARC
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| 300 | |a XI, 383 S. |b graph. Darst. | ||
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| 650 | 0 | 7 | |a Linearisierung |0 (DE-588)4199872-8 |2 gnd |9 rswk-swf |
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| 689 | 1 | 2 | |a Linearisierung |0 (DE-588)4199872-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804137346611806208 |
|---|---|
| adam_text | Contents
1
Introduction
............................................... 1
References
.................................................. 5
2
Mathematical Preliminaries
................................ 7
2.1
Moments and
Cumulants
of Random Variables
..................................... 7
2.2
Gaussian and Non-Gaussian Distributions
.................. 9
2.3
Moments and
Cumulants
of Stochastic Processes
............ 11
2.4
Second-Order Stochastic Processes
......................... 13
2.5
Gaussian and Non-Gaussian Processes
..................... 20
2.6
Markov Processes
....................................... 23
2.7
Diffusion Processes and Kolmogorov Equations
.............. 25
2.8
Wiener Process
......................................... 27
2.9
White and Colored Noise
................................. 29
2.10
Integration and Differentiation Formulas of Diffusion Processes
31
2.11
Stochastic Differential Equations
.......................... 35
2.12
Stochastic Stability
...................................... 43
2.13
The Method of
Fokker
Planck Kolmogorov Equations
....... 48
Bibliography Notes
........................................... 55
References
.................................................. 56
3
Moment Equations for Linear Stochastic Dynamic
Systems (LSDS)
........................................... 59
3.1
Gaussian White Noise External Excitation
.................. 60
3.2
Gaussian White Noise External and Parametric Excitation
... 61
3.3
Gaussian Colored Noise External and Parametric Excitation
. . 63
3.4
Nonstationary Gaussian External Excitation
................ 65
3.5
Spectral Method
........................................ 69
3.6
Non-Gaussian External Excitation
......................... 74
Bibliography Notes
........................................... 79
References
.................................................. 80
Moment Equations for Nonlinear Stochastic Dynamic
Systems (NSDS)
........................................... 85
4.1
Moment Equations for Polynomial
SDS
Under Parametric
and External Gaussian Excitation
......................... 86
4.2
Simple Closure Techniques
................................ 94
4.3
Non-Gaussian Closure Techniques
......................... 96
Bibliography Notes
...........................................100
References
..................................................100
Statistical Linearization of Stochastic Dynamic Systems
Under External Excitations
................................103
5.1
Moment Criteria
........................................103
5.2
Criteria in Probability Density Functions Space
.............118
5.3
Stationary Gaussian Excitations
...........................123
5.4
Nonstationary Gaussian Excitations
.......................125
5.5
Non-Gaussian Excitations
................................132
Bibliography Notes
...........................................137
References
..................................................142
Equivalent Linearization of Stochastic Dynamic Systems
Under External Excitation
.................................147
6.1
Introduction
............................................147
(¡.2
Moment Criteria
........................................147
6.3
Criteria in Probability Density Space
......................167
6.4
Criteria in Spectral Density Space
.........................174
6.5
Multi-criterial Linearization Methods
......................187
6.6
Special Linearization Methods
............................194
Bibliography Notes
...........................................201
References
..................................................204
Nonlinearization Methods
.................................211
7.1
Introduction
............................................211
7.2
Moment Criteria
........................................214
7.3
Probability Density Criteria
..............................226
7.4
Application of the Generalized Stationary Potential Approach
. 229
7.5
Application of Stochastic Averaging Approach
..............235
7.6
Application of Volterra Functional Series Approach
..........240
Bibliography Notes
...........................................246
References
..................................................247
Linearization of Dynamic Systems with Stochastic
Parametric Excitations
....................................251
8.1
Introduction
............................................251
8.2
Statistical Linearization
..................................251
8.3
Equivalent Linearization
..................................258
Bibliography Notes
...........................................278
References
..................................................279
9
Applications of Linearization Methods in Vibration
Analysis of Stochastic Mechanical Structures
..............281
9.1
Introduction
............................................
281
9.2
Applications in Hysteretic Systems
........................282
9.3
Vibrations of Structures
under Earthquake Excitations
.............................293
9.4
Vibrations of Structures Under Wave Excitations
............303
9.5
Vibrations of Structures Under Wind Excitations
............307
9.6
Applications in Control Problems
..........................308
Bibliography Notes
...........................................
32^
References
..................................................
10
Accuracy of Linearization Methods
........................341
10.1
Theoretical Study of the Accuracy of Linearization Methods
. . 341
10.2
Comparison of Linearized and Exact, Response Characteristics
353
10.3
Comparison of Linearized and Simulated Response
Characteristics
..........................................^50
10.4
Validation of Linearization Method by Experiments
..........359
10.5
Limitations of Applicability of Linearization Methods
........365
Bibliography Notes
...........................................
367
References
..................................................
370
Index
..........................................................
377
|
| adam_txt |
Contents
1
Introduction
. 1
References
. 5
2
Mathematical Preliminaries
. 7
2.1
Moments and
Cumulants
of Random Variables
. 7
2.2
Gaussian and Non-Gaussian Distributions
. 9
2.3
Moments and
Cumulants
of Stochastic Processes
. 11
2.4
Second-Order Stochastic Processes
. 13
2.5
Gaussian and Non-Gaussian Processes
. 20
2.6
Markov Processes
. 23
2.7
Diffusion Processes and Kolmogorov Equations
. 25
2.8
Wiener Process
. 27
2.9
White and Colored Noise
. 29
2.10
Integration and Differentiation Formulas of Diffusion Processes
31
2.11
Stochastic Differential Equations
. 35
2.12
Stochastic Stability
. 43
2.13
The Method of
Fokker
Planck Kolmogorov Equations
. 48
Bibliography Notes
. 55
References
. 56
3
Moment Equations for Linear Stochastic Dynamic
Systems (LSDS)
. 59
3.1
Gaussian White Noise External Excitation
. 60
3.2
Gaussian White Noise External and Parametric Excitation
. 61
3.3
Gaussian Colored Noise External and Parametric Excitation
. . 63
3.4
Nonstationary Gaussian External Excitation
. 65
3.5
Spectral Method
. 69
3.6
Non-Gaussian External Excitation
. 74
Bibliography Notes
. 79
References
. 80
Moment Equations for Nonlinear Stochastic Dynamic
Systems (NSDS)
. 85
4.1
Moment Equations for Polynomial
SDS
Under Parametric
and External Gaussian Excitation
. 86
4.2
Simple Closure Techniques
. 94
4.3
Non-Gaussian Closure Techniques
. 96
Bibliography Notes
.100
References
.100
Statistical Linearization of Stochastic Dynamic Systems
Under External Excitations
.103
5.1
Moment Criteria
.103
5.2
Criteria in Probability Density Functions Space
.118
5.3
Stationary Gaussian Excitations
.123
5.4
Nonstationary Gaussian Excitations
.125
5.5
Non-Gaussian Excitations
.132
Bibliography Notes
.137
References
.142
Equivalent Linearization of Stochastic Dynamic Systems
Under External Excitation
.147
6.1
Introduction
.147
(¡.2
Moment Criteria
.147
6.3
Criteria in Probability Density Space
.167
6.4
Criteria in Spectral Density Space
.174
6.5
Multi-criterial Linearization Methods
.187
6.6
Special Linearization Methods
.194
Bibliography Notes
.201
References
.204
Nonlinearization Methods
.211
7.1
Introduction
.211
7.2
Moment Criteria
.214
7.3
Probability Density Criteria
.226
7.4
Application of the Generalized Stationary Potential Approach
. 229
7.5
Application of Stochastic Averaging Approach
.235
7.6
Application of Volterra Functional Series Approach
.240
Bibliography Notes
.246
References
.247
Linearization of Dynamic Systems with Stochastic
Parametric Excitations
.251
8.1
Introduction
.251
8.2
Statistical Linearization
.251
8.3
Equivalent Linearization
.258
Bibliography Notes
.278
References
.279
9
Applications of Linearization Methods in Vibration
Analysis of Stochastic Mechanical Structures
.281
9.1
Introduction
.
281
9.2
Applications in Hysteretic Systems
.282
9.3
Vibrations of Structures
under Earthquake Excitations
.293
9.4
Vibrations of Structures Under Wave Excitations
.303
9.5
Vibrations of Structures Under Wind Excitations
.307
9.6
Applications in Control Problems
.308
Bibliography Notes
.
32^
References
.
10
Accuracy of Linearization Methods
.341
10.1
Theoretical Study of the Accuracy of Linearization Methods
. . 341
10.2
Comparison of Linearized and Exact, Response Characteristics
353
10.3
Comparison of Linearized and Simulated Response
Characteristics
.^50
10.4
Validation of Linearization Method by Experiments
.359
10.5
Limitations of Applicability of Linearization Methods
.365
Bibliography Notes
.
367
References
.
370
Index
.
377 |
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| id | DE-604.BV023092814 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:41:43Z |
| indexdate | 2024-07-09T21:10:50Z |
| institution | BVB |
| isbn | 9783540729969 |
| language | English |
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| physical | XI, 383 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | Springer |
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| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Socha, Lesław Verfasser (DE-588)134046633 aut Linearization methods for stochastic dynamic systems L. Socha Berlin [u.a.] Springer 2008 XI, 383 S. graph. Darst. Lecture notes in physics 730 Literaturangaben Stochastisches dynamisches System (DE-588)4305316-6 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Linearisierung (DE-588)4199872-8 gnd rswk-swf Schwingungssystem (DE-588)4180568-9 gnd rswk-swf Stochastisches dynamisches System (DE-588)4305316-6 s Linearisierung (DE-588)4199872-8 s DE-604 Schwingungssystem (DE-588)4180568-9 s Stochastisches Modell (DE-588)4057633-4 s Lecture notes in physics 730 (DE-604)BV000003166 730 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016295658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Socha, Lesław Linearization methods for stochastic dynamic systems Lecture notes in physics Stochastisches dynamisches System (DE-588)4305316-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd Linearisierung (DE-588)4199872-8 gnd Schwingungssystem (DE-588)4180568-9 gnd |
| subject_GND | (DE-588)4305316-6 (DE-588)4057633-4 (DE-588)4199872-8 (DE-588)4180568-9 |
| title | Linearization methods for stochastic dynamic systems |
| title_auth | Linearization methods for stochastic dynamic systems |
| title_exact_search | Linearization methods for stochastic dynamic systems |
| title_exact_search_txtP | Linearization methods for stochastic dynamic systems |
| title_full | Linearization methods for stochastic dynamic systems L. Socha |
| title_fullStr | Linearization methods for stochastic dynamic systems L. Socha |
| title_full_unstemmed | Linearization methods for stochastic dynamic systems L. Socha |
| title_short | Linearization methods for stochastic dynamic systems |
| title_sort | linearization methods for stochastic dynamic systems |
| topic | Stochastisches dynamisches System (DE-588)4305316-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd Linearisierung (DE-588)4199872-8 gnd Schwingungssystem (DE-588)4180568-9 gnd |
| topic_facet | Stochastisches dynamisches System Stochastisches Modell Linearisierung Schwingungssystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016295658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT sochalesław linearizationmethodsforstochasticdynamicsystems |