Stochastic Dynamics of Structures

Preface.

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.

Index.