Structural Dynamics

Yong Bai, PhD, received a doctorate from Hiroshima University in Japan and engaged in postdoctoral work in the field of ocean engineering at the Technical University of Denmark, Norwegian University of Science and Technology, and University of California at Berkeley. He has published over 100 research papers, 9 English academic treatises and 8 Chinese books on ocean engineering. He has served as a professor at the University of Stavanger, Harbin Engineering University, Zhejiang University and Southern University of Science and Technology. He has guided more than 50 graduate students and 30 doctoral students. He is currently writing a series of books for Wiley-Scrivener on pipes and pipelines, including Flexible Pipes and Flexible Pipelines, Risers, and Umbilicals. Zhao-Dong Xu, Ph.D. is a professor at the Civil Engineering School of Southeast University, serving as doctoral tutor. He earned his PhD in China, followed by a series of teaching and research positions at Xi'an Jiaotong University, Ibaraki University, North Carolina State University and the University of Illinois at Urbana-Champaign. He is the Vice President of RC & PC Key Laboratory of Education Ministry. With over 20 years of teaching and research experience on structural dynamics, he has many awards to his name, and he has published more than 200 papers on the subject.

• Preface xiAbout the Authors xiii1 Introduction 11.1 Overview of Structural Dynamics 11.2 Dynamic Loads 21.2.1 Simple Harmonic Loads 21.2.2 Nonharmonic Periodic Loads 31.2.3 Impulsive Load 31.2.4 Irregular Dynamic Load 31.3 Characteristics of a Dynamic Problem 41.3.1 Methods of Discretization 61.3.2 Lumped Mass Procedure 61.3.3 Generalized Coordinate Procedure 71.3.4 Finite Element Method 91.4 Application of Structural Dynamics 101.4.1 Application of Structural Dynamics in Civil Engineering 101.4.2 Application of Structural Dynamics in Ocean Engineering 111.4.3 Application of Structural Dynamics in Aircraft Technology 14Exercises 15References 162 Establishment of the Structural Equation of Motion 172.1 General 172.1.1 Dynamic Freedom 172.1.2 Basics of Dynamic System 18Inertia Force 18Elastic Restoring Force 19Damping Force 192.2 Formulation of the Equations of Motion 212.2.1 Direct Equilibration Using D’Alembert’s Principle 212.2.2 Principle of Virtual Displacements 232.2.3 Hamilton’s Principle 262.2.4 Lagrange’s Equations 302.3 Theory of Total Potential Energy Invariant Value of Elastic System Dynamics 322.3.1 The Main Idea of the Principle of Virtual Work 322.3.2 Derivation of the Principle of Total Potential Energy Invariant 342.4 Influence of Gravitational Forces 372.5 Influence of Support Excitation 38Exercises 39References 403 Single Degree of Freedom Systems 413.1 Response of Free Vibrations 413.1.1 Undamped Free Vibrations 433.1.2 Damped Free Vibrations 463.1.3 Damping and Its Measurement 523.2 Response to Harmonic Loading 573.2.1 Harmonic Vibration of an Undamped System 573.2.2 Harmonic Vibration of Damping System 623.2.3 Dynamic Amplification Coefficient 653.2.4 Resonance Reaction 683.2.5 Solution of Damping Ratio 703.3 Periodic Load Response 743.4 Impulsive Loading Response 803.4.1 Sine-Wave Impulse 803.4.2 Rectangular Impulse 823.4.3 Triangular Impulse 843.5 Response of Arbitrary Load 893.5.1 Duhamel Integral (Time-Domain Analysis) 893.5.2 Fourier Transform (Frequency-Domain Analysis) 953.6 Energy in Vibration 973.6.1 Energy in Free Vibration 973.6.2 Energy Dissipation of Viscous Damped System 993.6.3 Equivalent Viscous Damping 1003.6.4 Complex Damping 1033.6.5 Friction Damping 1063.7 Structural Vibration Test 1063.7.1 Introduction to Vibration Test 1063.7.2 Exciting Equipment 1073.7.3 Vibration Measuring Instrument 1103.7.4 Data Acquisition and Analysis System 1143.8 Vibration Isolation Principle 1143.8.1 Active Vibration Isolation 1143.8.2 Passive Vibration Isolation 1163.9 Structural Vibration Induced Fatigue 1213.9.1 Definition of Vibration Induced Fatigue 1213.9.2 Characteristics of Vibration Induced Fatigue 122Exercises 123References 1254 Multi-Degree of Freedom Systems 1274.1 Two Degrees of Freedom System 1284.1.1 Establishment of Motion Equation of Undamped Free Vibrations 1284.1.2 Natural Frequency and Vibration Mode Shape 1314.1.3 General Solutions of the Equations of Motion 1344.2 Free Vibrations of Undamped System 1354.2.1 Establishment of Motion Equation 1354.2.2 Vibration Shape and Its Orthogonality 1374.2.3 Generalized Mass and Generalized Stiffness 1424.3 Practical Calculation Method of Dynamic Characteristics 1464.3.1 Dunkerley Formula 1474.3.2 Rayleigh Energy Method 1504.3.3 Ritz Method 1564.3.4 Matrix Iteration Method 1604.3.5 Subspace Iteration Method 1674.4 Mode Superposition Method for Damped System 1724.4.1 Coordinate Coupling and Regular Coordinates 1734.4.2 Damping Assumptions 1744.4.3 Mode Superposition Method 1794.5 Numerical Analysis of Damping System 1854.5.1 Central Difference Method 1864.5.2 Average Constant Acceleration Method 1874.5.3 Linear Acceleration Method 1914.5.4 Newmark-β Method 1934.5.5 Wilson-θ Method 1954.6 Stability and Accuracy Analysis of Stepwise Integration Method 1994.6.1 Stability Analysis of Algorithm Solutions 2024.6.2 Accuracy Analysis of Algorithm Solutions 202Exercises 203References 2055 Distributed-Parameter System 2075.1 Overview 2075.2 Establish Differential Equations for Motion 2085.2.1 Euler-Bernoulli Beam 2085.2.2 Beam with Axial Pressures 2105.2.3 Beam Flexure with Viscous Damping 2115.2.4 Beam Axial Deformations without Damping 2115.3 Free Vibration of a Beam 2135.3.1 Decoupling the Boundary Conditions 2145.3.2 Simply Supported Beam 2155.3.3 Free-Free Beam 2175.4 Orthogonality Relationships 2215.5 Modal Decomposition 223References 2256 Stochastic Structural Vibrations 2276.1 Overview 2276.2 Stochastic Process 2306.2.1 Concept of Stochastic Process 2306.2.2 Probability Description of Stochastic Processes 2326.2.3 The Numerical Characteristics of Stochastic Processes 2346.2.4 Stationary Stochastic Process 2486.2.5 Several Important Stochastic Processes 2516.2.6 Stochastic Model of Seismic Ground Motion 2536.3 Stochastic Response of Linear SDOF System 2606.3.1 Time-Domain Analysis Method 2606.3.2 Frequency-Domain Analysis Method 2636.3.3 Cross-Correlation Function and Cross-Spectral Density of Excitation and Response 2666.3.4 Fatigue Predictions for Narrowband Systems 2706.4 Stochastic Response of Linear MDOF System 2716.4.1 Direct Method 2726.4.2 Vibration Mode Superposition Method 2806.5 Nonlinear Structural Stochastic Response Analysis 2916.5.1 Perturbation Method 2926.5.2 Equivalent Linearization Method 2946.6 State Space Method for Structural Stochastic Response Analysis 2976.6.1 Basic Concept of State Space 2986.6.2 SDOF System 2996.6.3 MDOF System 302Exercises 304References 3047 Research Topics of Structural Dynamics 3057.1 Analysis of Structural Seismic Response 3057.1.1 Brief Introduction to the Calculation Method 3077.1.2 Horizontal Seismic Action of SDOF Elastic System 3087.1.3 Seismic Response Spectrum 3107.1.4 Vibration Mode Decomposition Method 3147.1.5 Bottom Shearing Force Method 3177.2 Structural Vibration Control 3237.2.1 Concept and Classification 3237.2.2 Vibration Reduction Technology of Viscoelastic Dampers 3257.2.3 Rubber Base Isolation Technology 3327.2.4 Vibration Reduction Technology of Magneto-Rheological Damper 3377.3 Modal Analysis and Theory 3417.3.1 Modal Parameters 3427.3.2 Real Modal Analysis 3447.3.3 Complex Modal Analysis 3457.4 Structural Dynamic Damage Identification 3507.4.1 Frequency Base Damage Identification Method 3507.4.2 Modal Base Damage Identification Method 3517.4.3 Damage Identification Method Based on Stiffness Variation 3547.4.4 Damage Identification Method Based on Flexibility Change 3557.4.5 Energy-Based Damage Identification Method 3567.4.6 Prospects for Research on Dynamic Damage Identification 3577.5 Nonlinear Problems of Dynamic Analysis 3587.5.1 Physical Nonlinearity Problems in Dynamic Analysis 3597.5.2 Geometric Nonlinearity Problems in Dynamic Analysis 3627.6 Sub-Structure Method 3657.6.1 Finite Element Analysis of Sub-Structure Method 3657.6.2 Damage Identification by Sub-Structure Method 3687.7 Dynamics of Offshore Structures 3697.7.1 Descriptions of Offshore Waves 3707.7.2 Introduction to Wave Spectra 3707.7.3 Frequency Domain Analysis 371Exercises 373References 3738 Structural Dynamics of Marine Pipeline and Riser 3758.1 Overview 3758.2 Environmental Conditions 3768.2.1 General 3768.2.2 Linear Wave Theory 3778.2.3 Nonlinear Wave Theory 3848.2.4 Current 3848.3 Hydrodynamic Loads 3868.3.1 Hydrodynamic Drag and Inertia Forces 3868.3.2 Hydrodynamic Lift Forces 3908.4 Structural Response Analysis 3928.4.1 Global Deformation Due to Environmental Loads 3928.4.2 Mass Matrices 3948.4.3 Stiffness Matrices 3978.4.4 Damping Matrices 3998.4.5 Riser Deformation 4008.5 Vortex Induced Vibrations 4018.5.1 Introduction 4018.5.2 Analysis of Vortex-Induced Vibration 4048.5.3 Harmonic Model 4068.5.4 Wake Oscillator Model 409Exercises 415References 415Answers to Exercises 417Index 443