Fundamentals of Structural Dynamics

1st Edition - June 8, 2021
Authors: Zhihui Zhou, Ying Wen, Chenzhi Cai, Qingyuan Zeng
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 2 3 7 0 4 - 5
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 2 3 7 0 5 - 2

Dynamics of Structural Dynamics explains foundational concepts and principles surrounding the theory of vibrations and gives equations of motion for complex systems. The book pres… Read more

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Dynamics of Structural Dynamics explains foundational concepts and principles surrounding the theory of vibrations and gives equations of motion for complex systems. The book presents classical vibration theory in a clear and systematic way, detailing original work on vehicle-bridge interactions and wind effects on bridges. Chapters give an overview of structural vibrations, including how to formulate equations of motion, vibration analysis of a single-degree-of-freedom system, a multi-degree-of-freedom system, and a continuous system, the approximate calculation of natural frequencies and modal shapes, and step-by-step integration methods. Each chapter includes extensive practical examples and problems.

This volume presents the foundational knowledge engineers need to understand and work with structural vibrations, also including the latest contributions of a globally leading research group on vehicle-bridge interactions and wind effects on bridges.

1 Overview of Structural Vibrations

1.1 Objectives

1.2 Characteristics of Structural Vibrations

1.3 Classification of Vibrations

1.4 Some typical issues in structural vibrations

1.5 Main Tasks of the Response analysis
Problems

2 Formulation of equations of motion

2.1 System constraints

2.2 Description of structural vibrating configuration

2.3 Direct balance method

2.4 Principle of virtual displacements

2.5 Lagrange’s Equations

2.6 Hamilton’s Principle

2.7 Principle of Total Potential Energy with Stationary Value in Elastic System Dynamics

2.8 “Set in right position” rule for formulating system matrices and computer programs
Problems

3 Vibration Analysis of Single-Degree-of-Freedom System

3.1 Free vibrations

3.2 Responses of Single degree of freedom system to harmonic loading

3.3 Vibrations caused by base motion and vibration isolation

3.4 Introductions to the damping theory

3.5 Determination of the viscos-damping ratio by experimental method

3.6 Response of a single degree of freedom system to periodic loading

3.7 Response of a single degree of freedom system to impulsive loading

3.8 Time integration analysis for dynamic responses
Problems

4 Vibration Analysis of Multi-Degree-of-Freedom System

4.1 The dynamic characteristics of the system.

4.2 Modal expansion and normalized equations of motion for multi-degree-of-freedom systems

4.3 Free vibration responses of undamped systems

4.4 Response of damped system to arbitrary dynamic loads

4.5 Response of undamped system to arbitrary dynamic loads
Problems

5 Vibration analysis of continuous system (straight beam)

5.1 Equations of motion for undamped straight beam in bending

5.2 Modal expansion techniques and the orthogonality of modal shapes for linear vibrations of straight beam

5.3 Free transverse vibrations of undamped straight beam

5.4 Forced flexural vibrations of undamped straight beam

5.5 Forced flexural vibrations of damped straight beam
Problems

6 Approximate calculation of natural frequencies and modal shapes

6.1 Rayleigh energy method

6.2 Rayleigh-Ritz method

6.3 Stodola-Vianello method

6.4 Subspace iteration method

6.5 Degree of freedom reduction in vibration analysis
Problems

7 Step-by step integration methods

7.1 Basic concepts of methods

7.2 Linear acceleration method

7.3 The Wilson- Method

7.4 The Newmark-β method

7.5 Stability and accuracy analysis of the step-by-step integration methods
Problems

Zhihui Zhou

Zhihui Zhou is an Associate Professor in the School of Civil Engineering at Central South University in China. His research focuses on train derailment and vibration analysis. He has led several research projects, including on the safe operation of high-speed trains over railway bridges, and the safety of long-span cable-stayed bridge trains. He holds a PhD in Bridge and Tunnel Engineering, and has published over 30 papers, and two monographs.

Affiliations and expertise

Associate Professor, School of Civil Engineering, Central South University, China

Ying Wen

Dr Ying Wen was employed in the School of Civil Engineering, CSU, after obtaining his Ph.D. degree in 2010, and he was promoted to be the associate professor in 2012. He took up the research associate in the Department of Civil and Structural Engineering, The Hong Kong Polytechnic University in 2011. In 2014, Dr Wen was invited to visit the Department of Aerospace and Mechanical Engineering, University of Southern California, for a collaborative research on the problem of moving loads on structures. After he returned to CSU in 2015, Dr Wen was appointed as the vice director of the Key Laboratory of Engineering Structures of Heavy-haul Railway, Ministry of Education. Dr Wen has interest in fields of various structural dynamics and stability, especially nonlinear mechanics of long span bridges and their dynamic stability under moving trains. Dr Wen has published more than 20 journal papers, one of which is listed as Top 25 Hottest articles published in ‘Finite Elements in Analysis & Design’. He also published three Chinese monographs about statics and dynamics of structures as a co-author. Dr Wen obtained the awards of the Science and Technology Progress of Hunan Province (2006) and Zhejiang Province (2011).

Affiliations and expertise

vice director of the Key Laboratory of Engineering Structures of Heavy-haul Railway, Ministry of Education, Changsha, China

Chenzhi Cai

Dr Chenzhi Cai received his BS degree in civil engineering and MS degree in road and railway engineering from CSU in 2011 and 2015, respectively. He graduated from The Hong Kong Polytechnic University with a Ph.D. degree in civil engineering in 2018 and joined the Department of Bridge Engineering as well as the Wind Tunnel Laboratory of CSU as an associate professor later this year. Dr Cai’s main research interests are the fields of noise and vibration control, high-speed railway bridge/elevated subway system, and the train-induced ground vibration isolation. He has participated in several research projects funded by the Hong Kong government and has also received research funding from National Natural Science Foundation of China and Hunan Provincial Natural Science Foundation of China. Dr Cai has published more than 20 papers in international journals, and some of his work is under consideration of acceptance by UK CIBSE Guide.

Affiliations and expertise

Associate Professor, Department of Bridge Engineering and the Wind Tunnel Laboratory, School of Civil Engineering, Central South University, Changsha, China

Qingyuan Zeng

Prof. Qingyuan Zeng is a distinguished scientist on bridge engineering in Central South University. He obtained his BS and MS degrees from the Department of Civil Engineering, Nanchang University and Department of Engineering Mechanics, Tsinghua University, in 1950 and 1956, respectively. He was elected as the member of Chinese Academy of Engineering in 1999 for his great contributions to local-global interactive buckling behavior of long-span bridge structures, train-bridge interaction dynamics and the basic theory of train derailment. He presented the principle of total potential energy with a stationary value in elastic system dynamics and the ‘set-in-right-position’ rule for assembling system matrices, which is a significant improvement of classical theory of structural dynamics and finite element method. Prof. Zeng has an international reputation for his originality in the transverse vibration mechanism and time-varying analysis method of train-bridge system. He has authored and co-authored more than 100 journal papers, 3 monographs and 3 textbooks. He received numerous awards, including State Science and Technology Progress Award, Distinguished Achievement Award for Railway Science and Technology from Zhan Tianyou Development Foundation, and Honorary Member Award from the China Railway Society. He has supervised more than 16 MS students and 30 Ph.D. students in the past three decades.

Affiliations and expertise

Distinguished Scientist on Bridge Engineering, Central South University, Changsha, China