Contents

Cover

Preface

About the Authors

Chapter 1: Introduction

1.1 Overview of Structural Dynamics
1.2 Dynamic Loads
1.3 Characteristics of a Dynamic Problem
1.4 Application of Structural Dynamics
Exercises
References

Chapter 2: Establishment of the Structural Equation of Motion

2.1 General
2.2 Formulation of the Equations of Motion
2.3 Theory of Total Potential Energy Invariant Value of Elastic System Dynamics
2.4 Influence of Gravitational Forces
2.5 Influence of Support Excitation
Exercises
References

Chapter 3: Single Degree of Freedom Systems

3.1 Response of Free Vibrations
3.2 Response to Harmonic Loading
3.3 Periodic Load Response
3.4 Impulsive Loading Response
3.5 Response of Arbitrary Load
3.6 Energy in Vibration
3.7 Structural Vibration Test
3.8 Vibration Isolation Principle
3.9 Structural Vibration Induced Fatigue
Exercises
References

Chapter 4: Multi-Degree of Freedom System

4.1 Two Degrees of Freedom System
4.2 Free Vibrations of Undamped System
4.3 Practical Calculation Method of Dynamic Characteristics
4.4 Mode Superposition Method for Damped System
4.5 Numerical Analysis of Damping System
4.6 Stability and Accuracy Analysis of Stepwise Integration Method
Exercises
References

Chapter 5: Distributed-Parameter System

5.1 Overview
5.2 Establish Differential Equations for Motion
5.3 Free Vibration of a Beam
5.4 Orthogonality Relationships
5.5 Modal Decomposition
References

Chapter 6: Stochastic Structural Vibrations

6.1 Overview
6.2 Stochastic Process
6.3 Stochastic Response of Linear SDOF System
6.4 Stochastic Response of Linear MDOF System
6.5 Nonlinear Structural Stochastic Response Analysis
6.6 State Space Method for Structural Stochastic Response Analysis
Exercises
References

Chapter 7: Research Topics of Structural Dynamics

7.1 Analysis of Structural Seismic Response
7.2 Structural Vibration Control
7.3 Modal Analysis and Theory
7.4 Structural Dynamic Damage Identification
7.5 Nonlinear Problems of Dynamic Analysis
7.6 Sub-Structure Method
7.7 Dynamics of Offshore Structures
Exercises
References

Chapter 8: Structural Dynamics of Marine Pipeline and Riser

8.1 Overview
8.2 Environmental Conditions
8.3 Hydrodynamic Loads
8.4 Structural Response Analysis
8.5 Vortex Induced Vibrations
Exercises
References

Answers to Exercises

Index

End User License Agreement

List of Illustrations

Chapter 1

Figure 1.1 Classification of dynamic loads.
Figure 1.2 Types of dynamic load.
Figure 1.3 The difference between static and dynamic.
Figure 1.4 Schematics of lumped mass procedure.
Figure 1.5 Discretization of a simple beam by generalized coordinate procedure.

Chapter 2

Figure 2.1 Definition of degree of freedom.
Figure 2.2 Single body with SDOF dynamic system.
Figure 2.3 Dual body with 2DOF dynamic system.
Figure 2.4 Inverted Pendulum system with SDOF.
Figure 2.5 Inverted Pendulum system with 1DOF.
Figure 2.6 Single body with 1DOF dynamic system.
Figure 2.7 Influence of gravity on SDOF equilibrium.
Figure 2.8

Chapter 3

Figure 3.1 Commonly used single degree of freedom systems.
Figure 3.2 To simplify a complex structure.
Figure 3.3 Single degree of freedom system.
Figure 3.4 The response of undamped free vibration system.
Figure 3.5 Influence of different damping on free vibration motion.
Figure 3.6 Influence of different damping on free vibration motion.
Figure 3.7 Free vibration decay curve.
Figure 3.8 The curve of the dynamic amplification factor R_d of the undamped…
Figure 3.9 The dynamic response of undamped system increases with time during resonance.
Figure 3.10 A non-compact beam with a motor.
Figure 3.11 Resonance reaction time-history curve of damping system.
Figure 3.12 Amplitude-frequency characteristic curve of damping system.
Figure 3.13 Phase-frequency characteristic curve of damping system.
Figure 3.14 Simple basic dynamic system.
Figure 3.15 Calculating damping ratio on amplitude-frequency characteristic curve.
Figure 3.16 Simple dynamical system.
Figure 3.17 Displacement time-history diagram.
Figure 3.18 Sine-wave impulse.
Figure 3.19 Rectangular impulse.
Figure 3.20 Triangular impulse.
Figure 3.21 Deduction of Duhamel integral under arbitrary load.
Figure 3.22 δ function load diagram.
Figure 3.23 Viscous damping energy dissipation hysteretic curve.
Figure 3.24 Working block diagram of electromagnetic worktable.
Figure 3.25 Typical hammer and impact pulse.
Figure 3.26 Working principle of acceleration sensor.
Figure 3.27 Working principle of displacement sensor.
Figure 3.28 Single degree of freedom active vibration isolation system.
Figure 3.29 Single degree of freedom passive vibration isolation system.
Figure 3.30 Relationship of transmissibility with different frequency ratio.

Chapter 4

Figure 4.1 Multiple degree of freedom system with one point.
Figure 4.2 Multi-degree of freedom system.
Figure 4.3 Establishment of the equation of motion by elasticity method.
Figure 4.4 Dynamic balance of two degrees of freedom system.
Figure 4.5 The physical meaning of the stiffness factor.
Figure 4.6 Five degrees of freedom of system.
Figure 4.7 The reciprocity theorem of work.
Figure 4.8 Two-layer shear frame structure and vibration mode.
Figure 4.9 Three-particle simply support beam structure.
Figure 4.10 Unequal height single story plant.
Figure 4.11 Simplified calculation of simply supported beam.
Figure 4.12 Simplified calculation of the beam with concentrated mass.
Figure 4.13 Cantilever beam structure.
Figure 4.14 Simple support beam structure.
Figure 4.15 The constant average acceleration method.
Figure 4.16 Schematic diagram of linear acceleration.
Figure 4.17 Comparison of three basic assumptions for acceleration.
Figure 4.18 The basic assumptions of the acceleration method of the Wilson-θ…
Figure 4.19 External load excitation diagram.

Chapter 5

Figure 5.1 (a) Transverse vibration of a beam; the transverse displacement is v(x,t)…
Figure 5.2 Free body diagram of the beam in presence of an axial preload N.
Figure 5.3 Bar subjected to dynamic axial deformations: (a) bar properties and coordinates;…
Figure 5.4 Simply supported beam. (a) boundary conditions. (b) Mode shapes.
Figure 5.5 Free-free beam. The solutions of the equation cosμ = (coshµ)^–1…
Figure 5.6 Free-free beam. (a) Boundary conditions (b) Mode shapes (rigid body modes and flexible…
Figure 5.7 Simple beam-vibration analysis: (a) basic properties of simple beam; (b) first…

Chapter 6

Figure 6.1 Classification of stochastic vibration problems.
Figure 6.2 Sample function of stochastic process.
Figure 6.3 Unilateral and bilateral spectral density of stationary process.
Figure 6.4 Spectral density and sample function of narrowband process.
Figure 6.5 Spectral density and sample function of broadband process.
Figure 6.6 Filtered stationary white noise model.
Figure 6.7 Filtered white noise model and improved filtered white noise model.
Figure 6.8 Power spectrum of acceleration of strong earthquake filtered by multiple layer.
Figure 6.9 Time envelope function of quasi-stationary process.
Figure 6.10 Calculation diagram of single-layer structure.
Figure 6.11 Multi-layer shear structure under the action of seism.
Figure 6.12 Large-span structure under the action of seism.

Chapter 7

Figure 7.1 Acceleration records of El-Centro ground motion.
Figure 7.2 The process of calculating the accelerationg response spectrum.
Figure 7.3 El-Centro seismic wave acceleration response spectrum.
Figure 7.4 Earthquake impact coefficient α curve.
Figure 7.5 Bottom shearing force method illustration.
Figure 7.6 Two-story reinforced concrete frame structure.
Figure 7.7 Interlayer shearing force illustration.
Figure 7.8 Viscoelastic dampers illustration.
Figure 7.9 Rubber isolation bearing illustration.
Figure 7.10 Rubber isolation bearing illustration model.
Figure 7.11 Resilience-displacement curve of rubber isolation bearing.
Figure 7.12 Several calculation models of isolated structures.
Figure 7.13 Three modes of magneto-rheological damper.
Figure 7.14 Magneto-rheological damper commonly used in building structure shock absorption.
Figure 7.15 MDOF system.
Figure 7.16 Two different spring models.
Figure 7.17 Hysteretic curve of reinforced concrete beams.
Figure 7.18 Two commonly used resilience models.
Figure 7.19 The mass steel wire system which has geometric nonlinearity.
Figure 7.20 P – Δ effect of single particle system.

Chapter 8

Figure 8.1 Uses of offshore pipelines and risers.
Figure 8.2 Regular long-crested waves.
Figure 8.3 Random long-crested waves.
Figure 8.4 Wave spectrum.
Figure 8.5 2048s zero mean wave amplitude time realization.
Figure 8.6 Frequency domain and time domain representation of long-crested waves.
Figure 8.7 Example Hm0 – Tp contour lines.
Figure 8.8 Flow field around pipe.
Figure 8.9 Fluid drag and inertia forces acting on a pipe section.
Figure 8.10 CL in shear and shear-free flow for 103< Re < 30 x 104.
Figure 8.11 Sketch of the riser system.
Figure 8.12 Element defintion for a finite element idealization of a vertical riser.
Figure 8.13 Vibrations of a cylinder submitted to vortex shedding.
Figure 8.14 Typical pipeline spans.
Figure 8.15 Vertical riser eigenmodes.
Figure 8.16 Flow regimes for smooth circular cylinders.
Figure 8.17 Relation between the Strouhal Number and Reynolds Number.
Figure 8.18 A schematic model of a 2-D freely oscillating rigid cylinder.
Figure 8.19 A schematic model of a spring mounted rigid cylinder undergoing two-dimensional…
Figure 8.20 Layout of the experiments (left); the vacuum tank (on the top of the structure)…
Figure 8.21 The modal shape up to transverse forth mode.
Figure 8.22 Vibration response of the riser. The cross-flow instantaneous deflected shapes of…

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Library of Congress Cataloging-in-Publication Data

ISBN 978-1-119-60560-7

Preface

Dynamic problems of structures are ubiquitous in research. Therefore, it is very important for students majoring in civil engineering, mechanical engineering, aircraft engineering and ocean engineering to systematically grasp the basic concepts, calculation principles and calculation methods of structural dynamics. This book focuses on the basic theories and concepts, as well as the application and background of theories and concepts in engineering. Since the basic principles and methods of dynamics are applied to other various engineering fields, this book can also be used as a reference for undergraduate and graduate students in other majors.

The main contents include basic theory of dynamics, establishment of equation of motion, single degree of freedom systems, multi-degree of freedom systems, distributed-parameter systems, stochastic structural vibrations, research projects of structural dynamics, and structural dynamics of marine pipeline and riser.

This book was co-authored by Professor Yong Bai of Southern University of Science and Technology and Professor Zhao-Dong Xu of Southeast University. The authors would like to appreciate Dr. Yong Bai’s and Dr. Zhao-Dong Xu’s graduate students and postdoctoral fellows who provided the initial technical writing. The students in Southern University of Science and Technology are Ms. Xinyu Sun (Chapters 1 & 3), Mr. Jiannan Zhao (Chapters 2 & 4), Mr. Zhao Wang (Chapters 5, 6, & 7), and Mr. Wei Qin (Chapter 8). The students in Southeast University are Mr. Yanwei Xu (Chapter 1 and proofread all), Mr. Hao Hu (Chapter 3), Mr. Yun Yang (Chapter 6), Mr. Shi Chen (Chapter 7), and Mr. Qiangqiang Li (proofread all). The students in Xi’an University of Architecture and Technology are Mr. Zefeng He (Chapter 3), Mr. Zhenhua He (Chapter 4), and Ms. Tian Zhang (proofread all). Thanks to all persons involved in reviewing the book.

About the Authors

Professor Bai received a doctorate from Hiroshima University in Japan and engaged in postdoctoral work in the field of ocean engineering in 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. Bai served as a professor at University of Stavanger, Harbin Engineering University, Zhejiang University and Southern University of Science and Technology. He guided more than 50 graduate students and 30 doctoral students.

Professor Bai has a wealth of engineering experience and management skills. He worked in Det Norske Veritas, American Bureau of Shipping, JP KENNY Company in Norway, Shell E & P Company and MCS in the United States. He has presided over dozens of large projects in the field of ship structures, submarine pipelines and risers, design analysis and risk assessment of offshore platforms. Bai put forward the design concept of buckling and ultimate load carrying capacity of deepwater submarine pipelines. He improved the design methods, analytical tools and design standards of marine pipelines and reached the international leading level. He significantly improved the design methodology and criteria for subsea pipelines and risers such as ultimate strength design, use of risk and reliability methods.

He contributed to subsea technology by publishing many papers and a recognized book entitled Subsea Engineering Handbook and promoted limit-state design and use of risk and reliability by teaching at universities and publishing a book entitled Marine Structural Design.

Professor Zhao-Dong Xu is the professor at the Civil Engineering School of Southeast University, serving as doctoral tutor. His major research fields are Anti-earthquake of Structures, Structural Control and Health Monitoring, Smart Material and Structures. Professor Xu got his Ph.D. in China, followed by a series of teaching and research positions at Xi’an Jiaotong University, Ibaraki University, North Carolina State University and University of Illinois at Urbana-Champaign. He is the Vice President of RC & PC Key Laboratory of Education Ministry. He has also been Changjiang Scholar Distinguished Professor and the National Science Fund for Distinguished Young Scholars in China.

Professor Xu engaged in teaching and research on structural dynamics for more than 20 years. He has published more than 200 papers on the subject of structure dynamics research, numerical analysis and application of civil engineering, etc. He has been honored with many awards—the 43rd Geneva International Patents Exhibition Gold Award, the Second Award of National Award for Technological Invention in China, the Top Award of Chinese Building Materials Technology Invention, etc. He has completed many significant research projects in the areas of structural vibration control and structural health monitoring, and many research outcomes have been utilized in major real applications.