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E-grāmata: Spectral Element Method in Structural Dynamics

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(Inha University, Korea)
  • Formāts: PDF+DRM
  • Izdošanas datums: 31-Jul-2009
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9780470823750
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Spectral Element Method in Structural DynamicsPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 31-Jul-2009
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9780470823750
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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 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.

Preface xi
Part One Introduction to the Spectral Element Method and Spectral Analysis of Signals 1
1 Introduction
3
1.1 Theoretical Background
3
1.1.1 Finite Element Method
3
1.1.2 Dynamic Stiffness Method
4
1.1.3 Spectral Analysis Method
4
1.1.4 Spectral Element Method
5
1.1.5 Advantages and Disadvantages of SEM
6
1.2 Historical Background
8
2 Spectral Analysis of Signals
11
2.1 Fourier Series
11
2.2 Discrete Fourier Transform and the FFT
12
2.2.1 Discrete Fourier Transform (DFT)
12
2.2.2 Fast Fourier Transform (FFT)
16
2.3 Aliasing
17
2.3.1 Aliasing Error
17
2.3.2 Remedy for Aliasing
20
2.4 Leakage
20
2.4.1 Leakage Error
20
2.4.2 Artificial Damping
23
2.5 Picket-Fence Effect
25
2.6 Zero Padding
25
2.6.1 Improving Interpolation in the Transformed Domain
26
2.6.2 Remedy for Wraparound Error
27
2.7 Gibbs Phenomenon
29
2.8 General Procedure of DFT Processing
30
2.9 DFTs of Typical Functions
34
2.9.1 Product of Two Functions
34
2.9.2 Derivative of a Function
36
2.9.3 Other Typical Functions
36
Part Two Theory of Spectral Element Method 39
3 Methods of Spectral Element Formulation
41
3.1 Force-Displacement Relation Method
41
3.2 Variational Method
58
3.3 State-Vector Equation Method
68
3.4 Reduction from the Finite Models
75
4 Spectral Element Analysis Method
77
4.1 Formulation of Spectral Element Equation
77
4.1.1 Computation of Wavenumbers and Wavemodes
79
4.1.2 Computation of Spectral Nodal Forces
81
4.2 Assembly and the Imposition of Boundary Conditions
82
4.3 Eigenvalue Problem and Eigensolutions
83
4.4 Dynamic Responses with Null Initial Conditions
86
4.4.1 Frequency-Domain and Time-Domain Responses
86
4.4.2 Equivalence between Spectral Element Equation and Convolution Integral
87
4.5 Dynamic Responses with Arbitrary Initial Conditions
89
4.5.1 Discrete Systems with Arbitrary Initial Conditions
90
4.5.2 Continuous Systems with Arbitrary Initial Conditions
99
4.6 Dynamic Responses of Nonlinear Systems
104
4.6.1 Discrete Systems with Arbitrary Initial Conditions
105
4.6.2 Continuous Systems with Arbitrary Initial Conditions
107
Part Three Applications of Spectral Element Method 111
5 Dynamics of Beams and Plates
113
5.1 Beams
113
5.1.1 Spectral Element Equation
113
5.1.2 Two-Element Method
114
5.2 Levy-Type Plates
119
5.2.1 Equation of Motion
119
5.2.2 Spectral Element Modeling
120
5.2.3 Equivalent 1-D Structure Representation
125
5.2.4 Computation of Dynamic Responses
126
Appendix 5A: Finite Element Model of Bernoulli–Euler Beam
130
6 Flow-Induced Vibrations of Pipelines
133
6.1 Theory of Pipe Dynamics
133
6.1.1 Equations of Motion of the Pipeline
134
6.1.2 Fluid-Dynamics Equations
136
6.1.3 Governing Equations for Pipe Dynamics
137
6.2 Pipelines Conveying Internal Steady Fluid
138
6.2.1 Governing Equations
138
6.2.2 Spectral Element Modeling
139
6.2.3 Finite Element Model
144
6.3 Pipelines Conveying Internal Unsteady Fluid
146
6.3.1 Governing Equations
146
6.3.2 Spectral Element Modeling
147
6.3.3 Finite Element Model
153
Appendix 6.A: Finite Element Matrices: Steady Fluid
157
Appendix 6.B: Finite Element Matrices: Unsteady Fluid
159
7 Dynamics of Axially Moving Structures
163
7.1 Axially Moving String
163
7.1.1 Equation of Motion
163
7.1.2 Spectral Element Modeling
165
7.1.3 Finite Element Model
170
7.2 Axially Moving Bernoulli—Euler Beam
172
7.2.1 Equation of Motion
172
7.2.2 Spectral Element Modeling
174
7.2.3 Finite Element Model
178
7.2.4 Stability Analysis
178
7.3 Axially Moving Timoshenko Beam
181
7.3.1 Equations of Motion
181
7.3.2 Spectral Element Modeling
183
7.3.3 Finite Element Model
188
7.3.4 Stability Analysis
189
7.4 Axially Moving Thin Plates
192
7.4.1 Equation of Motion
192
7.4.2 Spectral Element Modeling
195
7.4.3 Finite Element Model
204
Appendix 7.A: Finite Element Matrices for Axially Moving String
209
Appendix 7.B: Finite Element Matrices for Axially Moving Bernoulli—Euler Beam
210
Appendix 7.C: Finite Element Matrices for Axially Moving Timoshenko Beam
210
Appendix 7.D: Finite Element Matrices for Axially Moving Plate
212
8 Dynamics of Rotor Systems
219
8.1 Governing Equations
219
8.1.1 Equations of Motion of the Spinning Shaft
220
8.1.2 Equations of Motion of Disks with Mass Unbalance
223
8.2 Spectral Element Modeling
228
8.2.1 Spectral Element for the Spinning Shaft
228
8.2.2 Spectral Element for the Disk
237
8.2.3 Assembly of Spectral Elements
239
8.3 Finite Element Model
242
8.3.1 Finite Element for the Spinning Shaft
243
8.3.2 Finite Element for the Disk
246
8.3.3 Assembly of Finite Elements
247
8.4 Numerical Examples
249
Appendix 8.A: Finite Element Matrices for the Transverse Bending Vibration
253
9 Dynamics of Multi-Layered Structures
255
9.1 Elastic–Elastic Two-Layer Beams
255
9.1.1 Equations of Motion
255
9.1.2 Spectral Element Modeling
258
9.1.3 Spectral Modal Analysis
263
9.1.4 Finite Element Model
266
9.2 Elastic–Viscoelastic–elastic–Three-Layer (PCLD) Beams
269
9.2.1 Equations of Motion
269
9.2.2 Spectral Element Modeling
272
9.2.3 Spectral Modal Analysis
279
9.2.4 Finite Element Model
283
Appendix 9.A: Finite Element Matrices for the Elastic–Elastic Two-Layer Beam
288
Appendix 9.B: Finite Element Matrices for the Elastic–VEM–Elastic Three-Layer Beam
289
10 Dynamics of Smart Structures
293
10.1 Elastic–Piezoelectric Two-Layer Beams
293
10.1.1 Equations of Motion
293
10.1.2 Spectral Element Modeling
297
10.1.3 Spectral Element with Active Control
300
10.1.4 Spectral Modal Analysis
301
10.1.5 Finite Element Model
303
10.2 Elastic–Viscoelastic–Piezoelctric Three-Layer (ACLD) Beams
305
10.2.1 Equations of Motion
305
10.2.2 Spectral Element Modeling
308
10.2.3 Spectral Element with Active Control
312
10.2.4 Spectral Modal Analysis
313
10.2.5 Finite Element Model
315
11 Dynamics of Composite Laminated Structures
319
11.1 Theory of Composite Mechanics
319
11.1.1 Three-Dimensional Stress–Strain Relationships
319
11.1.2 Stress–Strain Relationships for an Orthotropic Lamina
320
11.1.3 Strain–Displacement Relationships
322
11.1.4 Resultant Forces and Moments
323
11.2 Equations of Motion for Composite Laminated Beams
324
11.2.1 Axial–Bending–Shear Coupled Vibration
325
11.2.2 Bending–Torsion–Shear Coupled Vibration
327
11.3 Dynamics of Axial–Bending–Shear Coupled Composite Beams
330
11.3.1 Equations of Motion
330
11.3.2 Spectral Element Modeling
330
11.3.3 Finite Element Model
336
11.4 Dynamics of Bending–Torsion–Shear Coupled Composite Beams
339
11.4.1 Equations of Motion
339
11.4.2 Spectral Element Modeling
339
11.4.3 Finite Element Model
346
Appendix 11.A: Finite Element Matrices for Axial–Bending–Shear Coupled Composite Beams
349
Appendix 11.B: Finite Element Matrices for Bending–Torsion–Shear Coupled Composite Beams
351
12 Dynamics of Periodic Lattice Structures
355
12.1 Continuum Modeling Method
355
12.1.1 Transfer Matrix for the Representative Lattice Cell (RLC)
356
12.1.2 Transfer Matrix for an ET-Beam Element
361
12.1.3 Determination of Equivalent Continuum Structural Properties
362
12.2 Spectral Transfer Matrix Method
365
12.2.1 Transfer Matrix for a Lattice Cell
366
12.2.2 Transfer Matrix for a 1-D Lattice Substructure
367
12.2.3 Spectral Element Model for a 1-D Lattice Substructure
368
12.2.4 Spectral Element Model for the Whole Lattice Structure
369
13 Biomechanics: Blood Flow Analysis
373
13.1 Governing Equations
373
13.1.1 One-Dimensional Blood Flow Theory
373
13.1.2 Simplified Governing Equations
375
13.2 Spectral Element Modeling: I. Finite Element
376
13.2.1 Governing Equations in the Frequency Domain
377
13.2.2 Weak Form of Governing Equations
378
13.2.3 Spectral Nodal DOFs
379
13.2.4 Dynamic Shape Functions
380
13.2.5 Spectral Element Equation
381
13.3 Spectral Element Modeling: II. Semi-Infinite Element
384
13.4 Assembly of Spectral Elements
385
13.5 Finite Element Model
386
13.6 Numerical Examples
388
Appendix 13.A: Finite Element Model for the 1-D Blood Flow
391
14 Identification of Structural Boundaries and Joints
393
14.1 Identification of Non-Ideal Boundary Conditions
393
14.1.1 One-End Supported Beam
394
14.1.2 Two-Ends Supported Beam
397
14.2 Identification of Joints
404
14.2.1 Spectral T-Beam Element Model for Uniform Beam Parts
404
14.2.2 Equivalent Spectral Element Model of the Joint Part
405
14.2.3 Determination of Joint Parameters
407
15 Identification of Structural Damage
413
15.1 Spectral Element Modeling of a Damaged Structure
413
15.1.1 Assembly of Spectral Elements
413
15.1.2 Imposition of Boundary Conditions
414
15.1.3 Reordering of Spectral Nodal DOFs
415
15.2 Theory of Damage Identification
416
15.2.1 Uniform Damage Representation
416
15.2.2 Damage Identification Algorithms
417
15.3 Domain-Reduction Method
425
15.3.1 Domain-Reduction Method
425
15.3.2 Three-Step Process
427
16 Other Applications
429
16.1 SEM–FEM Hybrid Method
429
16.2 Identification of Impact Forces
434
16.2.1 Force-History Identification
435
16.2.2 Force-Location Identification
436
16.3 Other Applications
439
References 441
Index 449
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.
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