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Stochastic Dynamics of Structures

Stochastic Dynamics of Structures

Jie Li, Jianbing Chen

ISBN: 978-0-470-82425-2

Jul 2009

384 pages



In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures.

Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters.

"The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution."
A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA

"The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field."
Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA



1 Introduction.

1.1 Motivations and Historical Clues.

1.2 Contents of the Book.

2 Stochastic Processes and Random Fields.

2.1 Random Variables.

2.2 Stochastic Processes.

2.3 Random Fields.

2.4 Orthogonal Decomposition of Random Functions.

3 Stochastic Models of Dynamic Excitations.

3.1 General Expression of Stochastic Excitations.

3.2 Seismic Ground Motions.

3.3 Fluctuating Wind Speed in the Boundary Layer.

3.4 Wind Wave and Ocean Wave Spectrum.

3.5 Orthogonal Decomposition of Random Excitations.

4 Stochastic Structural Analysis.

4.1 Introductory Remarks.

4.2 Fundamentals of Deterministic Structural Analysis.

4.3 Random Simulation Method.

4.4 Perturbation Approach.

4.5 Orthogonal Expansion Theory.

5 Random Vibration Analysis.

5.1 Introduction.

5.2 Moment Functions of the Responses.

5.3 Power Spectral Density Analysis.

5.4 Pseudo-Excitation Method.

5.5 Statistical Linearization.

5.6 Fokker?Planck?Kolmogorov Equation.

6 Probability Density Evolution Analysis: Theory.

6.1 Introduction.

6.2 The Principle of Preservation of Probability.

6.3 Markovian Systems and State Space Description: Liouville and Fokker?Planck?Kolmogorov Equations.

6.4 Dostupov?Pugachev Equation.

6.5 The Generalized Density Evolution Equation.

6.6 Solution of the Generalized Density Evolution Equation.

7 Probability Density Evolution Analysis: Numerical Methods.

7.1 Numerical Solution of First-Order Partial Differential Equation.

7.2 Representative Point Sets and Assigned Probabilities.

7.3 Strategy for Generating Basic Point Sets.

7.4 Density-Related Transformation.

7.5 Stochastic Response Analysis of Nonlinear MDOF Structures.

8 Dynamic Reliability of Structures.

8.1 Fundamentals of Structural Reliability Analysis.

8.2 Dynamic Reliability Analysis: First-Passage Probability Based on Excursion Assumption.

8.3 Dynamic Reliability Analysis: Generalized Density Evolution Equation-Based Approach.

8.4 Structural System Reliability.

9 Optimal Control of Stochastic Systems.

9.1 Introduction.

9.2 Optimal Control of Deterministic Systems.

9.3 Stochastic Optimal Control.

9.4 Reliability-Based Control of Structural Systems.

Appendix A: Dirac Delta Function.

A.1 Definition.

A.2 Integration and Differentiation.

A.3 Common Physical Backgrounds.

Appendix B: Orthogonal Polynomials.

B.1 Basic Concepts.

B.2 Common Orthogonal Polynomials.

Appendix C: Relationship between Power Spectral Density and Random Fourier Spectrum.

C.1 Spectra via Sample Fourier Transform.

C.2 Spectra via One-sided Finite Fourier Transform.

Appendix D: Orthonormal Base Vectors.

Appendix E: Probability in a Hyperball.

E.1 The Case s is Even.

E.2 The Case s is Odd.

E.3 Monotonic Features of F(r, s).

Appendix F: Spectral Moments.

Appendix G: Generator Vectors in the Number Theoretical Method.

References and Bibliography.