Spectral Element Method in Structural Dynamics

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