Spectral Element Method in Structural Dynamics

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.

Autorentext
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.

Zusammenfassung
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.

Inhalt
Preface. Part One 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 Two 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 Three 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 BernoulliEuler 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 BernoulliEuler Beam.

Appendix 7.C: Finite Elemen…