Linearization methods for stochastic dynamic systems / L. Socha.

By: Socha, Lesław
Material type: TextTextSeries: Lecture notes in physics: 730.Publisher: Berlin ; New York : Springer Verlag, ©2008Description: 1 online resource (viii, 383 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540729969; 3540729968; 9783540729976; 3540729976; 6611139109; 9786611139100Subject(s): Stochastic processes | Differential equations, Linear | Stochastic processes | Differential equations, Linear | Physique | Differential equations, Linear | Stochastic processesGenre/Form: Electronic books. Additional physical formats: Linearization methods for stochastic dynamic systems.DDC classification: 519.2 LOC classification: QA274 | .S625 2008Other classification: O211. 6 Online resources: Click here to access online
Contents:
Mathematical Preliminaries -- Moment Equations for Linear Stochastic Dynamic Systems (LSDS) -- Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS) -- Statistical Linearization of Stochastic Dynamic Systems Under External Excitations -- Equivalent Linearization of Stochastic Dynamic Systems Under External Excitation -- Nonlinearization Methods -- Linearization of Dynamic Systems with Stochastic Parametric Excitations -- Applications of Linearization Methods in Vibration Analysis of Stochastic Mechanical Structures -- Accuracy of Linearization Methods.
Summary: For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. The aim of this book is to give a systematic introduction to and overview of the relatively simple and popular linearization methods available. The scope is limited to models with continous external and parametric excitations, yet these cover the majority of known approaches. The book contains an application chapter with emphasis on vibration analysis of stochastic mechanical structures as well as a chapter devoted to the assessment of the accuracy of the theoretical methods presented, both with respect to numerical and to experimental studies. The material derives partly from graduate course notes developed by the author for courses and seminars over the past 20 years.
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Includes bibliographical references and index.

Mathematical Preliminaries -- Moment Equations for Linear Stochastic Dynamic Systems (LSDS) -- Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS) -- Statistical Linearization of Stochastic Dynamic Systems Under External Excitations -- Equivalent Linearization of Stochastic Dynamic Systems Under External Excitation -- Nonlinearization Methods -- Linearization of Dynamic Systems with Stochastic Parametric Excitations -- Applications of Linearization Methods in Vibration Analysis of Stochastic Mechanical Structures -- Accuracy of Linearization Methods.

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. The aim of this book is to give a systematic introduction to and overview of the relatively simple and popular linearization methods available. The scope is limited to models with continous external and parametric excitations, yet these cover the majority of known approaches. The book contains an application chapter with emphasis on vibration analysis of stochastic mechanical structures as well as a chapter devoted to the assessment of the accuracy of the theoretical methods presented, both with respect to numerical and to experimental studies. The material derives partly from graduate course notes developed by the author for courses and seminars over the past 20 years.

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