Stochastic Dynamics of Structures

Inbunden, Engelska, 2009

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Beskrivning

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

Produktinformation

Utgivningsdatum:2009-05-15
Mått:173 x 252 x 25 mm
Vikt:857 g
Format:Inbunden
Språk:Engelska
Antal sidor:384
Förlag:John Wiley & Sons Inc
ISBN:9780470824245

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Mer om författaren

Jie Li is a Professor of Civil Engineering at Tongji University, specializing in the area of earthquake engineering and stochastic mechanics. He has worked on uncertainty quantification, response analysis, and reliability evaluation of structural systems involving randomness -- integrating both for system parameters and excitations -- for more than 15 years. He has authored six monographs and published over 200 papers in peer reviewed journals. Li holds executive positions in China's major architectural, vibration engineering, and disaster prevention societies and laboratories. He is the Editor-in-Chief of the Journal of Tongji University (Natural Science Series) and is on the editorial board of over 10 international and Chinese journals, including the International Journal of Nonlinear Mechanics and Earthquake Engineering and Engineering Vibrations. He has received a variety of national and provincial-level awards for Advancement in Science and Technology. Li holds a Ph.D. in Civil Engineering from Tongji University. Jianbing Chen is an Associate Professor of Civil Engineering at Tongji University and serves at the State Key Laboratory in Disaster Reduction in Civil Engineering. He specializes in earthquake engineering and stochastic mechanics. Awards include the MOE's National Science Award, National Excellent Doctoral Thesis, Shanghai City's Excellent Young Teacher Award, and acceptance into the MOE's Excellent Scholars Program. He holds a B.S. from Northeastern University and a Ph.D. from Tongji University, both in Civil Engineering.

Innehållsförteckning

Foreword xiiiPreface xv1 Introduction 11.1 Motivations and Historical Clues 11.2 Contents of the Book 52 Stochastic Processes and Random Fields 72.1 Random Variables 72.1.1 Introduction 72.1.2 Operations with Random Variables 82.1.3 Random Vectors 122.1.4 Decomposition of Correlation Matrix 162.2 Stochastic Processes 172.2.1 Specification of Stochastic Processes 172.2.2 Moment Functions of a Stochastic Process 192.2.3 Spectral Description of a Stochastic Process 232.2.4 Some Operation Rules about Expectation, Correlation and Spectrum 252.2.5 Karhunen–Loeve Decomposition 272.3 Random Fields 292.3.1 Basic Concepts 292.3.2 Correlation Structures of Random Fields 312.3.3 Discretization of Random Fields 322.3.4 Decomposition of Random Fields 342.4 Orthogonal Decomposition of Random Functions 362.4.1 Metric Spaces and Normed Linear Spaces 362.4.2 Hilbert Spaces and General Orthogonal Decomposition 372.4.3 Orthogonal Decomposition of Random Functions 403 Stochastic Models of Dynamic Excitations 433.1 General Expression of Stochastic Excitations 433.1.1 Dynamic Excitations and Modeling 433.1.2 Models of Stationary and Nonstationary Processes 443.1.3 Random Fourier Spectrum Model 463.2 Seismic Ground Motions 483.2.1 One-Dimensional Model 483.2.2 Random Field Model 503.2.3 Physical Stochastic Model 533.3 Fluctuating Wind Speed in the Boundary Layer 563.3.1 Structural Wind Pressure and Wind Speed 563.3.2 Power Spectral Density of Fluctuating Wind Speed 583.3.3 Random Fourier Spectrum of Fluctuating Wind Speed 603.3.4 Random Fourier Correlation Spectrum 633.4 Wind Wave and Ocean Wave Spectrum 653.4.1 Wind Waves and Wave Forces 653.4.2 Power Spectral Density of Wind Waves 683.4.3 Direction Spectrum 703.5 Orthogonal Decomposition of Random Excitations 723.5.1 Orthogonal Decomposition of a Stochastic Process 723.5.2 Hartley Orthogonal Basis Function 743.5.3 Orthogonal Expansion of Seismic Ground Motions 753.5.4 Orthogonal Expansion of Fluctuating Wind Speed Process 774 Stochastic Structural Analysis 794.1 Introductory Remarks 794.2 Fundamentals of Deterministic Structural Analysis 804.2.1 The Basic Idea of Finite-Element Analysis 804.2.2 Element Stiffness Matrix 814.2.3 Transformation of Coordinates 844.2.4 Static Equations 874.2.5 Dynamic Equations 884.3 Random Simulation Method 904.3.1 Monte Carlo Method 904.3.2 Sampling of Random Variables with Uniform Distribution 914.3.3 Sampling of Random Variables with General Probability Distribution 934.3.4 Random Simulation Method 954.3.5 Accuracy of Random Simulation Method 974.4 Perturbation Approach 994.4.1 Deterministic Perturbation 994.4.2 Random Perturbation 1014.4.3 Random Matrices 1024.4.4 Linear Expression of Random Matrices 1034.4.5 Dynamic Response Analysis 1074.4.6 Secular Terms Problem 1104.5 Orthogonal Expansion Theory 1134.5.1 Orthogonal Decomposition and Sequential Orthogonal Decomposition 1134.5.2 Order-Expanded System Method 1164.5.3 Proof of the Order-Expanded System Method 1204.5.4 Dynamic Analysis 1244.5.5 Recursive Condensation Algorithm 1295 Random Vibration Analysis 1335.1 Introduction 1335.2 Moment Functions of the Responses 1335.2.1 Response of a Single-Degree-of-Freedom System in the Time Domain 1345.2.2 Response of MDOF Systems in the Time Domain 1405.3 Power Spectral Density Analysis 1465.3.1 Frequency Response Function and Power Spectral Density 1465.3.2 Evolutionary Spectral Analysis 1565.4 Pseudo-Excitation Method 1605.4.1 Pseudo-Excitation Method for Stationary Stochastic Response Analysis 1615.4.2 Pseudo-Excitation Method for Evolutionary Stochastic Response Analysis 1635.4.3 Notes on Sections 5.2–5.4 1645.5 Statistical Linearization 1645.5.1 Statistical Linearization Approximation 1645.5.2 Random Vibrations of Hysteretic Structures 1675.5.3 Notes on Arguments and Some Special Issues 1715.6 Fokker–Planck–Kolmogorov Equation 1745.6.1 Stochastic Differential Equation 1745.6.2 Fokker–Planck–Kolmogorov Equation 1815.6.3 Solution to the Fokker–Planck–Kolmogorov Equation 1846 Probability Density Evolution Analysis: Theory 1916.1 Introduction 1916.2 The Principle of Preservation of Probability 1926.2.1 Functions of Random Variables and their Probability Density Function Revisited 1926.2.2 The Principle of Preservation of Probability 1956.3 Markovian Systems and State Space Description: Liouville and Fokker–Planck–Kolmogorov Equations 1986.3.1 The Liouville Equation 1986.3.2 Fokker–Planck–Kolmogorov Equation Revisited 2046.4 Dostupov–Pugachev Equation 2096.4.1 From Equation of Motion to Random State Equation 2096.4.2 The Dostupov–Pugachev Equation 2106.5 The Generalized Density Evolution Equation 2136.5.1 Derivation of the Generalized Density Evolution Equation 2136.5.2 Linear Systems: Uncoupling of the Dostupov–Pugachev Equation 2176.5.3 Initial and Boundary Conditions 2196.5.4 Physical Sense of the Generalized Density Evolution Equation 2196.6 Solution of the Generalized Density Evolution Equation 2216.6.1 Analytical Solution 2216.6.2 Numerical Solving Flow of the Generalized Density Evolution Equation 2267 Probability Density Evolution Analysis: Numerical Methods 2317.1 Numerical Solution of First-Order Partial Differential Equation 2317.1.1 The Finite-Difference Method 2317.1.2 Dissipation, Dispersion and Total Variation Diminishing Schemes 2407.2 Representative Point Sets and Assigned Probabilities 2517.2.1 Sphere Packings, Covering and Partition of Space 2517.2.2 Representative Point Sets and Assigned Probabilities 2567.2.3 First- and Second-Order Discrepancies of Point Sets 2607.2.4 Two-Step Procedure of Constructing Representative Points 2617.3 Strategy for Generating Basic Point Sets 2627.3.1 From Sphere Packings: Tangent Sphere Method 2627.3.2 From Thinnest Covering: Lattices Approach 2667.3.3 Number Theoretical Method 2707.4 Density-Related Transformation 2727.4.1 Affine Transformation 2727.4.2 Density-Related Transformation 2737.4.3 Radial Decay Distribution: Spherical Sieving and Expansion–Contraction Transformation 2747.5 Stochastic Response Analysis of Nonlinear MDOF Structures 2787.5.1 Responses of Nonlinear Stochastic Structures 2787.5.2 Stochastic Seismic Response of Nonlinear Structures 2828 Dynamic Reliability of Structures 2858.1 Fundamentals of Structural Reliability Analysis 2858.1.1 Structural Reliability 2858.1.2 Dynamic Reliability Analysis of Structures 2868.1.3 Global Reliability of Structures 2878.2 Dynamic Reliability Analysis: First-Passage Probability Based on Excursion Assumption 2888.2.1 Excursion Rates 2888.2.2 Excursion Assumption and First-Passage Probability 2908.2.3 First-Passage Probability Considering Random Thresholds 2928.2.4 Pseudo-Static Analysis Method 2938.3 Dynamic Reliability Analysis: Generalized Density Evolution Equation-Based Approach 2958.3.1 Absorbing Boundary Condition Method 2958.3.2 Extreme-Value Distribution of the Stochastic Dynamical Response 2968.3.3 Extreme-Value Distribution-based Dynamical Reliability Evaluation of Stochastic Systems 2998.4 Structural System Reliability 3008.4.1 Equivalent Extreme-Value Event 3008.4.2 Inherent Correlation Property of Equivalent Extreme-Value Event 3048.4.3 Differences between the Equivalent Extreme-Value Event and the Weakest Link Assumption 3058.4.4 Evaluation of Structural System Reliability 3089 Optimal Control of Stochastic Systems 3139.1 Introduction 3139.2 Optimal Control of Deterministic Systems 3159.2.1 Optimal Control of Structural Systems 3159.2.2 Linear Quadratic Control 3189.2.3 The Minimum Principle and Hamilton–Jacobi-Bellman Equation 3209.3 Stochastic Optimal Control 3259.3.1 Stochastic Optimal Control of Nonlinear Systems: Classical Theory 3259.3.2 Linear Quadratic Gaussian Control 3289.3.3 Probability Density Evolution Analysis of Stochastic Optimal Control Systems 3309.4 Reliability-Based Control of Structural Systems 3389.4.1 Reliability of Controlled Structural Systems 3389.4.2 Determination of Control Criterion 340Appendix A: Dirac Delta Function 343A.1 Definition 343A.2 Integration and Differentiation 344A.3 Common Physical Backgrounds 346A.3.1 Probability Distribution of Discrete Random Variables 346A.3.2 Concentrated and Distributed Loads 347A.3.3 Unit Impulse Function 347A.3.4 Unit Harmonic Function 348Appendix B: Orthogonal Polynomials 349B.1 Basic Concepts 349B.2 Common Orthogonal Polynomials 351B.2.1 Hermite Polynomials Hen (x) 351B.2.2 Legendre Polynomials Pn (x) 352B.2.3 Gegenbauer Polynomials Cn(α) (x) 354Appendix C: Relationship between Power Spectral Density and Random Fourier Spectrum 355C.1 Spectra via Sample Fourier Transform 355C.2 Spectra via One-sided Finite Fourier Transform 357Appendix D: Orthonormal Base Vectors 361Appendix E: Probability in a Hyperball 377E.1 The Case s is Even 378E.2 The Case s is Odd 378E.3 Monotonic Features of F(r, s) 380E.3.1 Monotonic Feature of F(r, s) with Respect to the Radius r 380E.3.2 Monotonic Feature of F(r, s) with Respect to the Dimensions 381Appendix F: Spectral Moments 383Appendix G: Generator Vectors in the Number Theoretical Method 385References and Bibliography 391Index 405