From Waves in Complex Systems to Dynamics of Generalized Continua: Tributes to Professor Yih-Hsing Pao on His 80th Birthday

CONTENTS......Page 8
PREFACE......Page 6
CONTRIBUTORS......Page 10
LAUDATIO FOR PROFESSOR YIH-HSING PAO ON THE OCCASION OF THE INTERNATIONAL SYMPOSIUM ON ENGINEERING MECHANICS 2010, ON THE OCCASION OF HIS 80TH BIRTHDAY (21/22 May 2010)......Page 14
List of Publications – Professor Y.-H. Pao......Page 26
CHAPTER 1 LAMB WAVES IN PHONONIC BAND GAP STRUCTURES......Page 34
1. Introduction......Page 35
2. Formulation and Numerical Methods......Page 39
2.1. Plane Wave Expansion Method21,75,76......Page 40
2.2. Finite-Difference Time-Domain Method......Page 45
2.3. Finite Element Analysis......Page 49
3.1. Phononic Band Gaps of Lamb Waves......Page 50
3.2. Phononic Waveguides......Page 60
3.3. Cavity......Page 66
4. Demonstrations of Band Gaps and Potential Applications......Page 67
4.1. Measurements of Band Gaps in a Stubbed PC Plate77......Page 68
4.2. Micro Phononic Cavity for Lamb Wave Resonator......Page 72
5. Conclusions......Page 75
References......Page 76
CHAPTER 2 ON GENERALIZATION OF THE PHASE RELATIONS IN THE METHOD OF REVERBERATION-RAY MATRIX......Page 82
1. Introduction......Page 83
2. System of First-Order Differential Equations and the Solution......Page 86
3. Dual Coordinate System and Coordinate Transform......Page 88
4. Generalized Phase Relations......Page 91
5. Wave Propagation in Anisotropic Laminates......Page 94
6. Summary......Page 103
Acknowledgments......Page 104
References......Page 105
1. Introduction......Page 108
3.1. Spectroscopy Measurement......Page 110
3.3. Background Nonlinearity by Magnetostrictive Effect......Page 112
4.1. Measurements......Page 115
4.2. Results......Page 116
5. Discussions......Page 118
5.1. First Nonlinearity Peak......Page 119
6. Conclusion......Page 120
References......Page 121
1. Introduction......Page 124
2. Background......Page 126
3.1. Acoustoelastic Bulk Waves......Page 127
3.2. Acoustoelastic Lamb Waves......Page 131
4. Numerical Results......Page 136
4.1. Stress Dependence at a Fixed Propagation Angle......Page 137
4.2. Angle Dependence at a Fixed Stress......Page 138
5.1. Description of Measurements......Page 140
5.2. Signal Analysis and Results......Page 141
6. Simulations and Discussion......Page 144
References......Page 148
5.1. Introduction......Page 152
5.2. Theory......Page 154
5.3. Numerical Example......Page 159
Acknowledgments......Page 167
References......Page 168
CHAPTER 6 AN INTRODUCTION TO AN ADAPTIVE DATA ANALYSIS METHOD......Page 170
1. Introduction......Page 171
2. The Hilbert-Huang Transform......Page 172
3. A Significant Product of HHT: The Determination of Trend......Page 180
4. Some Applications......Page 184
a. The Chirp Data......Page 185
b. Speech Signal Analysis......Page 186
Acknowledgements......Page 188
References......Page 189
CHAPTER 7 COMPUTATIONAL FLUID DYNAMICS BASED ON THE UNIFIED COORDINATES — AN EXPOSE......Page 192
1. CFD as Numerical Solution to Nonlinear Hyperbolic PDEs – An Overview of Major Developments......Page 193
2.1. Theoretical Issues......Page 194
2.2. Computational Issues......Page 195
3. The Unified Coordinate System......Page 196
4. One-Dimensional Flow......Page 198
5. Multi-Dimensional Flow......Page 201
6. Lagrangian Case......Page 202
7. Automatic Mesh-Generation......Page 203
8. Aerodynamics of Falling Leaves......Page 210
9. Conclusions......Page 211
References......Page 212
1. Introduction......Page 216
2. Imperfectly Diffuse Fields......Page 219
3. Retrieval of Attenuation......Page 222
References......Page 225
1. Introduction......Page 228
2. Two Scale Design Optimization for Global Structural Performance......Page 231
2.1. Minimum Compliance Design of Structure Subject to Mechanical Loads......Page 235
2.2. Minimum Compliance Design of Structure Subject to Mechanical and Thermal Loads......Page 239
2.3. Maximum Fundamental Frequency Design......Page 243
3. Two-Scale Optimization for Local Performance......Page 245
4. Concluding Remarks......Page 248
References......Page 249
10.1.1. Extended Summary......Page 252
10.1.2. Description of the Physical Problem......Page 253
10.1.3. Gravity Flow Specifics......Page 255
10.1.4. Earlier Theoretical Approaches......Page 257
10.2. Kinematics, Balance Laws, Saturation and Constituent Density Constraints......Page 259
10.2.1. Kinematics of Multi-Phase Mixtures......Page 260
10.2.2. Balance Equations......Page 262
10.2.3. Saturation and Constituent Density Constraints......Page 265
10.3.1. Material Equations for Hot Lava......Page 266
10.3.2. Material Equations for Cold Lava......Page 270
10.4.1. Preliminaries......Page 279
10.4.2. Entropy Principle......Page 282
10.4.3. Inferences Implied by the Liu-Identities......Page 283
10.4.4. Implications of the Residual Entropy Inequality......Page 288
10.4.5. Simplifying Assumptions for Lava Flows......Page 291
10.4.6. Parameterization of the Constituent Equilibrium Stresses and Interaction Forces......Page 292
10.4.7. Parameterization for the Non-Equilibrium Stresses and Interaction Forces......Page 296
10.4.8. Parameterization of the Melting/Freezing Rate......Page 297
10.5.1. General Jump Conditions......Page 299
10.5.2. Kinematic and Dynamic Boundary Conditions at the Free Surface......Page 301
10.5.3. Kinematic and Dynamic Boundary Conditions at the HTS......Page 303
10.5.4. Kinematic and Dynamic Boundary Conditions at the Bottom......Page 306
10.6.1. Summary......Page 310
10.6.2. Outlook......Page 311
References......Page 312
CHAPTER 11 RIGOROUS MECHANICS AND ELEGANT MATHEMATICS ON
THE FORMULATION OF CONSTITUTIVE LAWS FOR
COMPLEX MATERIALS: AN EXAMPLE FROM
BIOMECHANICS......Page 318
1. Introduction......Page 319
2. Triphasic Mixture Theory: A Unified Model for Soft Tissue......Page 322
2.1. Continuity Equation and Electroneutrality Condition......Page 323
2.2. Momentum Equations......Page 324
2.3. Constitutive Equations......Page 325
3.1. A Generalized Correspondence Principle of Triphasic Theory......Page 326
3.2. Determination of Fixed Charge Density......Page 329
4. Curling Behavior of Articular Cartilage: Anisotropic Lamination Model and Triphasic Theory......Page 331
4.1. Mathematical Modeling for Cartilage Curling......Page 332
4.2. Modeling Results and Discussion......Page 334
5. Summary......Page 336
References......Page 337
CHAPTER 12 PROFESSOR PAO’S INFLUENCE ON RESEARCH IN COUPLED FIELD PROBLEMS, CHIRALITY AND ACOUSTIC AND ELECTROMAGNETIC METAMATERIALS AND THEIR APPLICATIONS......Page 340
Preamble......Page 341
1. Helmholtz Decomposition of Vector Fields and Implications on Acoustic, Electromagnetic and Elastodynamic Fields......Page 342
Acoustic Waves in Viscous and Inviscid Fluids......Page 343
Elastic Waves in Solids......Page 345
Electromagnetic Waves......Page 346
2. Chirality and Its Effect on the Propagation of Electromagnetic and Elastic Waves......Page 350
Electromagnetic Waves in Chiral Materials......Page 352
Elastic Waves in Non-Centro Symmetric Solids......Page 354
3. Coupled Elastic-Electric Field Problems......Page 358
4. Electromagnetic and Acoustic Metamaterials......Page 360
Acknowledgements......Page 362
References......Page 363
1. Introduction......Page 366
2. Governing Equations......Page 367
3. Formal Solution......Page 369
4. Inversion of Ī......Page 371
5. Displacements......Page 378
Acknowledgments......Page 383
References......Page 384
CHAPTER 14 MAGNETIC FORCE MODELS FOR MAGNETIZABLE ELASTIC BODIES IN THE MAGNETIC FIELD......Page 386
1. Introduction......Page 387
2.1. Typical Physics Models......Page 392
2.2. Brown’s Model and Eringen-Maugin’s Model......Page 396
2.4. Zhou-Zheng’s Model......Page 402
2.4. Discussions......Page 404
3. Applications to Special Cases......Page 405
4. Conclusions......Page 409
References......Page 410
Dedication......Page 418
1. Introduction......Page 419
3. Physics of Vibro-Wind Power Generation......Page 420
4. Literature Review......Page 422
Energy in an Array of Structural Oscillators......Page 424
Fluid Mechanics Research in Vibro-Wind Systems......Page 425
5. Preliminary Experimental Results......Page 427
Energy Converters for Vibro-Wind Systems......Page 429
Multi-Blunt Body Aerodynamic Induced Wave Motion......Page 430
6. Architectural Issues in Vibro-Wind Energy Harvesting......Page 431
References......Page 433