Spectral Element Method in Structural Dynamics

✍ Scribed by Usik Lee

• Publisher: Wiley
• Year: 2009
• Tongue: English
• Leaves: 468
• Edition: 1
• Category: Library

✦ Synopsis

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 applicationsHelps students and professionals master associated theories, modeling processes, and analysis methodsDemonstrates where and how to apply SEM in practiceIntroduces real-world examples across a variety of structuresShows how models can be used to evaluate the accuracy of other solution methodsCross-checks against solutions obtained by conventional FEM and other solution methodsComes with downloadable code examples for independent practiceSpectral 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.

✦ Table of Contents

Contents......Page 6
Preface......Page 12
Part One Introduction to the Spectral Element Method and Spectral Analysis of Signals......Page 15
1.1 Theoretical Background......Page 17
1.2 Historical Background......Page 22
2.1 Fourier Series......Page 25
2.2 Discrete Fourier Transform and the FFT......Page 26
2.3 Aliasing......Page 31
2.4 Leakage......Page 34
2.6 Zero Padding......Page 39
2.7 Gibbs Phenomenon......Page 43
2.8 General Procedure of DFT Processing......Page 44
2.9 DFTs of Typical Functions......Page 48
Part Two Theory of Spectral Element Method......Page 53
3.1 Force-Displacement Relation Method......Page 55
3.2 Variational Method......Page 72
3.3 State-Vector Equation Method......Page 82
3.4 Reduction from the Finite Models......Page 89
4.1 Formulation of Spectral Element Equation......Page 91
4.2 Assembly and the Imposition of Boundary Conditions......Page 96
4.3 Eigenvalue Problem and Eigensolutions......Page 97
4.4 Dynamic Responses with Null Initial Conditions......Page 100
4.5 Dynamic Responses with Arbitrary Initial Conditions......Page 103
4.6 Dynamic Responses of Nonlinear Systems......Page 118
Part Three Applications of Spectral Element Method......Page 125
5.1 Beams......Page 127
5.2 Levy-Type Plates......Page 133
6.1 Theory of Pipe Dynamics......Page 147
6.2 Pipelines Conveying Internal Steady Fluid......Page 152
6.3 Pipelines Conveying Internal Unsteady Fluid......Page 160
7.1 Axially Moving String......Page 177
7.2 Axially Moving Bernoulli–Euler Beam......Page 186
7.3 Axially Moving Timoshenko Beam......Page 195
7.4 Axially Moving Thin Plates......Page 206
8.1 Governing Equations......Page 233
8.2 Spectral Element Modeling......Page 242
8.3 Finite Element Model......Page 256
8.4 Numerical Examples Example 8.1 Spinning Shaft without Disks......Page 263
9.1 Elastic–Elastic Two-Layer Beams......Page 269
9.2 Elastic–Viscoelastic–elastic Three-Layer (PCLD) Beams......Page 283
10.1 Elastic–Piezoelectric Two-Layer Beams......Page 307
10.2 Elastic–Viscoelastic–Piezoelectric Three-Layer (ACLD) Beams......Page 319
11.1 Theory of Composite Mechanics......Page 333
11.2 Equations of Motion for Composite Laminated Beams......Page 338
11.3 Dynamics of Axial–Bending–Shear Coupled Composite Beams......Page 344
11.4 Dynamics of Bending–Torsion–Shear Coupled Composite Beams......Page 353
12.1 Continuum Modeling Method......Page 369
12.2 Spectral Transfer Matrix Method......Page 379
13.1 Governing Equations......Page 387
13.2 Spectral Element Modeling: I. Finite Element......Page 390
13.3 Spectral Element Modeling: II. Semi-Infinit Element......Page 398
13.4 Assembly of Spectral Elements......Page 399
13.5 Finite Element Model......Page 400
13.6 Numerical Examples Example 13.1......Page 402
14.1 Identificatio of Non-Ideal Boundary Conditions......Page 407
14.2 Identificatio of Joints......Page 418
15.1 Spectral Element Modeling of a Damaged Structure......Page 427
15.2 Theory of Damage Identificatio......Page 430
15.3 Domain-Reduction Method......Page 439
16.1 SEM–FEM Hybrid Method......Page 443
16.2 Identi cation of Impact Forces......Page 448
16.3 Other Applications......Page 453
References......Page 455
Index......Page 463

✦ Subjects

Механика;Строительная механика;Динамика и устойчивость сооружений;