
Spectral Element Method in Structural Dynamics
Lee, Usik

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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 timedomains. In the last part, the applications of SEM to various structural dynamics problems are introduced, including beams, plates, pipelines, axially moving structures, rotor systems, multilayered structures, smart structures, composite laminated structures, periodic lattice structures, blood flow, structural boundaries, joints, structural damage, and impact forces identifications, as well as the SEMFEM 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 realworld examples across a variety of structures Shows how models can be used to evaluate the accuracy of other solution methods Crosschecks 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.

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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 PicketFence 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 ForceDisplacement Relation Method.
3.2 Variational Method.
3.3 StateVector 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 LevyType Plates.
6 FlowInduced 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 MultiLayered Structures.
9.1 Elastic–Elastic TwoLayer Beams.
9.2 Elastic–Viscoelastic–elastic–ThreeLayer (PCLD) Beams.
Appendix 9.A: Finite Element Matrices for the Elastic–Elastic TwoLayer Beam.
Appendix 9.B: Finite Element Matrices for the Elastic–VEM–Elastic ThreeLayer Beam.
10 Dynamics of Smart Structures.
10.1 Elastic–Piezoelectric TwoLayer Beams.
10.2 Elastic–Viscoelastic–Piezoelctric ThreeLayer (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. SemiInfinite Element.
13.4 Assembly of Spectral Elements.
13.5 Finite Element Model.
13.6 Numerical Examples.
Appendix 13.A: Finite Element Model for the 1D Blood Flow.
14 Identification of Structural Boundaries and Joints.
14.1 Identification of NonIdeal 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 DomainReduction Method.
16 Other Applications.
16.1 SEM–FEM Hybrid Method.
16.2 Identification of Impact Forces.
16.3 Other Applications.
References.
Index.


