Linearization Methods for Stochastic Dynamic Systems

✍ Scribed by Leslaw Socha

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 392
• Category: Library

✦ Synopsis

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.

✦ Table of Contents

Introduction
References
Mathematical Preliminaries
Moments and Cumulants of Random Variables
Gaussian and Non-Gaussian Distributions
Moments and Cumulants of Stochastic Processes
Second-Order Stochastic Processes
Gaussian and Non-Gaussian Processes
Markov Processes
Diffusion Processes and Kolmogorov Equations
Wiener Process
White and Colored Noise
Integration and Differentiation Formulas of Diffusion Processes
Stochastic Differential Equations
Stochastic Stability
The Method of Fokker--Planck--Kolmogorov Equations
Bibliography Notes
References
Moment Equations for Linear Stochastic Dynamic Systems (LSDS)
Gaussian White Noise External Excitation
Gaussian White Noise External and Parametric Excitation
Gaussian Colored Noise External and Parametric Excitation
Nonstationary Gaussian External Excitation
Spectral Method
Non-Gaussian External Excitation
Bibliography Notes
References
Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS)
Moment Equations for Polynomial SDS Under Parametric and External Gaussian Excitation
Simple Closure Techniques
Non-Gaussian Closure Techniques
Bibliography Notes
References
Statistical Linearization of Stochastic Dynamic Systems Under External Excitations
Moment Criteria
Criteria in Probability Density Functions Space
Stationary Gaussian Excitations
Nonstationary Gaussian Excitations
Non-Gaussian Excitations
Bibliography Notes
References
Equivalent Linearization of Stochastic Dynamic Systems Under External Excitation
Introduction
Moment Criteria
Criteria in Probability Density Space
Criteria in Spectral Density Space
Multi-criterial Linearization Methods
Special Linearization Methods
Bibliography Notes
References
Nonlinearization Methods
Introduction
Moment Criteria
Probability Density Criteria
Application of the Generalized Stationary Potential Approach
Application of Stochastic Averaging Approach
Application of Volterra Functional Series Approach
Bibliography Notes
References
Linearization of Dynamic Systems with Stochastic Parametric Excitations
Introduction
Statistical Linearization
Equivalent Linearization
Bibliography Notes
References
Applications of Linearization Methods in Vibration Analysis of Stochastic Mechanical Structures
Introduction
Applications in Hysteretic Systems
Vibrations of Structures under Earthquake Excitations
Vibrations of Structures Under Wave Excitations
Vibrations of Structures Under Wind Excitations
Applications in Control Problems
Bibliography Notes
References
Accuracy of Linearization Methods
Theoretical Study of the Accuracy of Linearization Methods
Comparison of Linearized and Exact Response Characteristics
Comparison of Linearized and Simulated Response Characteristics
Validation of Linearization Method by Experiments
Limitations of Applicability of Linearization Methods
Bibliography Notes
References
Index