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Title:
Spectral element method in structural dynamics
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Publication Information:
Singapore, SG : John Wiley & Sons, 2009
ISBN:
9780470823743

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30000010229475 TA654.15 L44 2009 Open Access Book Book
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Summary

Summary

Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields. The book consists of three key sections. In the first part, background knowledge is set up for the readers by reviewing previous work in the area and by providing the fundamentals for the spectral analysis of signals. In the second part, the theory of spectral element method is provided, focusing on how to formulate spectral element models and how to conduct spectral element analysis to obtain the dynamic responses in both frequency- and time-domains. In the last part, the applications of SEM to various structural dynamics problems are introduced, including beams, plates, pipelines, axially moving structures, rotor systems, multi-layered structures, smart structures, composite laminated structures, periodic lattice structures, blood flow, structural boundaries, joints, structural damage, and impact forces identifications, as well as the SEM-FEM hybrid method. Presents all aspects of SEM in one volume, both theory and applications Helps students and professionals master associated theories, modeling processes, and analysis methods Demonstrates where and how to apply SEM in practice Introduces real-world examples across a variety of structures Shows how models can be used to evaluate the accuracy of other solution methods Cross-checks against solutions obtained by conventional FEM and other solution methods Comes with downloadable code examples for independent practice

Spectral Element Method in Structural Dynamics can be used by graduate students of aeronautical, civil, naval architectures, mechanical, structural and biomechanical engineering. Researchers in universities, technical institutes, and industries will also find the book to be a helpful reference highlighting SEM applications to various engineering problems in areas of structural dynamics, wave propagations, and other related subjects. The book can also be used by students, professors, and researchers who want to learn more efficient and more accurate computational methods useful for their research topics from all areas of engineering, science and mathematics, including the areas of computational mechanics and numerical methods.


Author Notes

Usik Lee is a Professor of Mechanical Engineering at Inha University. He has 22 years teaching, research, and industry experience in the area of structural dynamics, and over 12 years of experience in developing and teaching spectral element methods. He has published over 100 papers in international journals and is an Associate Fellow of American Institute of Aeronautics and Astronautics and the Member of Board of the Korean Society for Railroad. Previous society and committee appointments include Secretary on the Finite Element Techniques & Computational Technologies Committee of the American Society of Mechanical Engineers (ASME), Member of Board for the Korean Society for Noise and Vibration Engineering, and Associate Editor with KSME International Journal. In addition to the societies mentioned above, he is also a member of the Korea Society of Precision Engineering, the Korean Society of Nondestructive Engineering, and the Computational Structural Engineering Institute of Korea. Lee holds a B.S. in Mechanical Engineering from Yonsei University, and an M.S. and Ph.D. in Mechanical Engineering from Stanford.


Table of Contents

Preface
Part 1 Introduction to the Spectral Element Method and Spectral Analysis of Signals
1 Introduction
1.1 Theoretical Background
1.2 Historical Background
2 Spectral Analysis of Signals
2.1 Fourier Series
2.2 Discrete Fourier Transform and the FFT
2.3 Aliasing
2.4 Leakage
2.5 Picket-Fence Effect
2.6 Zero Padding
2.7 Gibbs Phenomenon
2.8 General Procedure of DFT Processing
2.9 DFTs of Typical Functions
Part 2 Theory of Spectral Element Method
3 Methods of Spectral Element Formulation
3.1 Force-Displacement Relation Method
3.2 Variational Method
3.3 State-Vector Equation Method
3.4 Reduction from the Finite Models
4 Spectral Element Analysis Method
4.1 Formulation of Spectral Element Equation
4.2 Assembly and the Imposition of Boundary Conditions
4.3 Eigenvalue Problem and Eigensolutions
4.4 Dynamic Responses with Null Initial Conditions
4.5 Dynamic Responses with Arbitrary Initial Conditions
4.6 Dynamic Responses of Nonlinear Systems
Part 3 Applications of Spectral Element Method
5 Dynamics of Beams and Plates
5.1 Beams
5.2 Levy-Type Plates
6 Flow-Induced Vibrations of Pipelines
6.1 Theory of Pipe Dynamics
6.2 Pipelines Conveying Internal Steady Fluid
6.3 Pipelines Conveying Internal Unsteady Fluid
Appendix 6.A Finite Element Matrices Steady Fluid
Appendix 6.B Finite Element Matrices Unsteady Fluid
7 Dynamics of Axially Moving Structures
7.1 Axially Moving String
7.2 Axially Moving Bernoulli-Euler Beam
7.3 Axially Moving Timoshenko Beam
7.4 Axially Moving Thin Plates
Appendix 7.A Finite Element Matrices for Axially Moving String
Appendix 7.B Finite Element Matrices for Axially Moving Bernoulli-Euler Beam
Appendix 7.C Finite Element Matrices for Axially Moving Timoshenko Beam
Appendix 7.D Finite Element Matrices for Axially Moving Plate
8 Dynamics of Rotor Systems
8.1 Governing Equations
8.2 Spectral Element Modeling
8.3 Finite Element Model
8.4 Numerical Examples
Appendix 8.A Finite Element Matrices for the Transverse Bending Vibration
9 Dynamics of Multi-Layered Structures
9.1 Elastic-Elastic Two-Layer Beams
9.2 Elastic-Viscoelastic-elastic-Three-Layer (PCLD) Beams
Appendix 9.A Finite Element Matrices for the Elastic-Elastic Two-Layer Beam
Appendix 9.B Finite Element Matrices for the Elastic-VEM-Elastic Three-Layer Beam
10 Dynamics of Smart Structures
10.1 Elastic-Piezoelectric Two-Layer Beams
10.2 Elastic-Viscoelastic-Piezoelctric Three-Layer (ACLD) Beams
11 Dynamics of Composite Laminated Structures
11.1 Theory of Composite Mechanics
11.2 Equations of Motion for Composite Laminated Beams
11.3 Dynamics of Axial-Bending-Shear Coupled Composite Beams
11.4 Dynamics of Bending-Torsion-Shear Coupled Composite Beams
Appendix 11.A Finite Element Matrices for Axial-Bending-Shear Coupled Composite Beams
Appendix 11.B Finite Element Matrices for Bending-Torsion-Shear Coupled Composite Beams
12 Dynamics of Periodic Lattice Structures
12.1 Continuum Modeling Method
12.2 Spectral Transfer Matrix Method
13 Biomechanics: Blood Flow Analysis
13.1 Governing Equations
13.2 Spectral Element Modeling: I. Finite Element
13.3 Spectral Element Modeling: II. Semi-Infinite Element
13.4 Assembly of Spectral Elements
13.5 Finite Element Model
13.6 Numerical Examples
Appendix 13.A Finite Element Model for the 1-D Blood Flow
14 Identification of Structural Boundaries and Joints
14.1 Identification of Non-Ideal Boundary Conditions
14.2 Identification of Joints
15 Identification of Structural Damage
15.1 Spectral Element Modeling of a Damaged Structure
15.2 Theory of Damage Identification
15.3 Domain-Reduction Method
16 Other Applications
16.1 SEM-FEM Hybrid Method
16.2 Identification of Impact Forces
16.3 Other Applications
References
Index