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
Autorentext
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.Inhalt
Foreword xiii
Preface xv
1 Introduction 1
1.1 Motivations and Historical Clues 1
1.2 Contents of the Book 5
2 Stochastic Processes and Random Fields 7
2.1 Random Variables 7
2.1.1 Introduction 7
2.1.2 Operations with Random Variables 8
2.1.3 Random Vectors 12
2.1.4 Decomposition of Correlation Matrix 16
2.2 Stochastic Processes 17
2.2.1 Specification of Stochastic Processes 17
2.2.2 Moment Functions of a Stochastic Process 19
2.2.3 Spectral Description of a Stochastic Process 23
2.2.4 Some Operation Rules about Expectation, Correlation and Spectrum 25
2.2.5 Karhunen-Loeve Decomposition 27
2.3 Random Fields 29
2.3.1 Basic Concepts 29
2.3.2 Correlation Structures of Random Fields 31
2.3.3 Discretization of Random Fields 32
2.3.4 Decomposition of Random Fields 34
2.4 Orthogonal Decomposition of Random Functions 36
2.4.1 Metric Spaces and Normed Linear Spaces 36
2.4.2 Hilbert Spaces and General Orthogonal Decomposition 37
2.4.3 Orthogonal Decomposition of Random Functions 40
3 Stochastic Models of Dynamic Excitations 43
3.1 General Expression of Stochastic Excitations 43
3.1.1 Dynamic Excitations and Modeling 43
3.1.2 Models of Stationary and Nonstationary Processes 44
3.1.3 Random Fourier Spectrum Model 46
3.2 Seismic Ground Motions 48
3.2.1 One-Dimensional Model 48
3.2.2 Random Field Model 50
3.2.3 Physical Stochastic Model 53
3.3 Fluctuating Wind Speed in the Boundary Layer 56
3.3.1 Structural Wind Pressure and Wind Speed 56
3.3.2 Power Spectral Density of Fluctuating Wind Speed 58
3.3.3 Random Fourier Spectrum of Fluctuating Wind Speed 60
3.3.4 Random Fourier Correlation Spectrum 63
3.4 Wind Wave and Ocean Wave Spectrum 65
3.4.1 Wind Waves and Wave Forces 65
3.4.2 Power Spectral Density of Wind Waves 68
3.4.3 Direction Spectrum 70
3.5 Orthogonal Decomposition of Random Excitations 72
3.5.1 Orthogonal Decomposition of a Stochastic Process 72
3.5.2 Hartley Orthogonal Basis Function 74
3.5.3 Orthogonal Expansion of Seismic Ground Motions 75
3.5.4 Orthogonal Expansion of Fluctuating Wind Speed Process 77
4 Stochastic Structural Analysis 79
4.1 Introductory Remarks 79
4.2 Fundamentals of Deterministic Structural Analysis 80
4.2.1 The Basic Idea of Finite-Element Analysis 80
4.2.2 Element Stiffness Matrix 81
4.2.3 Transformation of Coordinates 84
4.2.4 Static Equations 87
4.2.5 Dynamic Equations 88
4.3 Random Simulation Method 90
4.3.1 Monte Carlo Method 90
4.3.2 Sampling of Random Variables with Uniform Distribution 91
4.3.3 Sampling of Random Variables with General Probability Distribution 93
4.3.4 Random Simulation Method 95
4.3.5 Accuracy of Random Simulation Method 97
4.4 Perturbation Approach 99
4.4.1 Deterministic Perturbation 99
4.4.2 Random Perturbation 101
4.4.3 Random Matrices 102
4.4.4 Linear Expression of Random Matrices 103
4.4.5 Dynamic Response Analysis 107
4.4.6 Secular Terms Problem 110
4.5 Orthogonal Expansion Theory 113
4.5.1 Orthogonal Decomposition and Sequential Orthogonal Decomposition 113
4.5.2 Order-Expanded System Method 116
4.5.3 Proof of the Order-Expanded System Method 120
4.5.4 Dynamic Analysis 124
4.5.5 Recursive Condensation Algorithm 129
5 Random Vibration Analysis 133
5.1 Introduction 133
5.2 Moment Functions of the Responses 133
5.2.1 Response of a Sin…