Dynamics of Smart Systems and Structures (eBook)

Prof Dr. Vicente Lopes Junior has more than 25 years of experience in teaching vibration and control in Mechanical Engineering courses. He has been working with smart structures for the last 15 years and has published over 200 technical articles, book chapters, journal and conference papers. He has given numerous short courses in smart structures, control design, and wave motion in elastic structures. He is full professor in the Department of Mechanical Engineering at the São Paulo State University (UNESP), Brazil. Valder Steffen, Jr is Mechanical Engineer (UNICAMP, Brazil, 1976) and PhD in Mechanical Engineering (University of Franche-Comté, France, 1979). He did his Habilitation at the University of Franche-Comté in 1991. He worked as a visiting scientist at the INSA de Lyon, France, in 1986-87 and was a Fulbright Scholar at Virginia Tech, USA, in 1999-2000. He is the author of over 300 scientific papers published in international journals and proceedings. He has supervised 24 MSc students and 18 PhD students.  He is now Professor at the School of Mechanical Engineering at the Federal University of Uberlândia, Brazil. He is also member of the National Academy of Engineering. His research interest is focused on dynamics of mechanical systems, optimization and inverse problems, rotordynamics, and smart structures.  Marcelo A. Savi is Ph.D. in Mechanical Engineering and Professor at the Federal University of Rio de Janeiro (Department of Mechanical Engineering, COPPE/Poli) where he develops research and teaching activities. He is the author of several scientific papers published in international journals, proceedings and books summing over 350 publications. He is involved with several research projects sponsored by Brazilian and international agencies, and also industrial partners. He has supervised graduate and undergraduate students, summing more than 100 works. He has administrative experience as head of department, graduate school coordinator, and university committee member. He is member of academic societies including ABCM, where he participates of the Committee of Dynamics; Smart Materials and Structures; and Nonlinear Phenomena and Chaos. His research interests are related to nonlinear mechanics and dynamics, chaos and control; biomechanics and environmental systems.

Preface 6
Contents 8
Introduction 10
References 12
Part I: Fundamentals 13
Continuum Mechanics 14
1 Introduction 14
2 Tensor Analysis 15
2.1 Kronecker Delta Tensor 17
2.2 Permutation Tensor 18
2.3 Coordinate Transformations 18
3 Motion 20
3.1 Deformation Tensors 22
3.2 Strain Tensors 23
3.3 Infinitesimal Strain Tensors 24
3.4 Principal Strains 25
3.5 Material Derivative and Reynolds Transport Theorem 26
4 Stress 27
4.1 Coordinate Transformations 28
4.2 Principal Stress 29
4.3 Piola-Kirchhoff Tensors 29
5 Conservation Principles 31
5.1 Conservation of Linear Momentum 31
5.2 Conservation of Angular Momentum 32
5.3 Conservation of Mass 33
5.4 Conservation of Energy 34
5.5 Principle of Entropy 37
5.6 Summary of the Fundamental Equations 39
6 Constitutive Equations 39
6.1 Elasticity 42
6.2 Elastoplasticity 43
6.3 Piezoelectricity 44
6.4 Pseudoelasticity and Shape Memory Effect 45
References 47
Wave Motion in Elastic Structures 48
1 Introduction 48
2 Some Features of Harmonic Wave Motion 49
2.1 Interference of Waves 51
2.1.1 Waves Propagating in the Same Direction 51
2.1.2 Waves Propagating in Opposite Directions 53
3 Basic Wave-Types in One-Dimensional Structures 54
3.1 Transverse Waves in a String 54
3.2 Longitudinal Waves in a Rod 57
3.3 Flexural (Bending) Waves 58
3.3.1 Beam 58
3.3.2 Plate 61
4 Dispersion 62
5 Flexural Beam Vibration at High Frequencies 63
5.1 Wavenumbers 63
5.2 Wave Mode-Shapes 68
References 69
Passive and Active Structural Vibration Control 71
1 Fundamentals of Structural Vibrations 71
1.1 Basic Concepts on Structural Vibration and Potential Mitigation Solutions 72
1.2 Natural Frequencies, Vibration Modes and Damping Factors 72
1.3 Principle of Modal Superposition 73
1.4 Frequency Response Functions and Transfer Functions 73
1.5 Analysis of Poles and Zeros for a Simple Spring-Mass Example 75
2 Passive Vibration Control 79
2.1 Passive Vibration Dampers 80
2.2 Passive Dynamic Vibration Absorbers 83
3 Active Vibration Control 85
3.1 Feedback Control Strategies 87
3.2 Positioning of Sensors and Actuators 91
3.3 Simple Control Laws Using Output Feedback 93
References 97
Nonlinear Dynamics and Chaos 99
1 Introduction 99
2 Dynamical Systems: Background 100
2.1 Equilibrium Points and Linearization 101
2.2 Stability 103
2.3 Poincaré Maps 105
3 Chaos 105
3.1 Routes to Chaos 109
3.2 Lyapunov Exponents 110
4 Shape Memory Alloy System 112
4.1 Polynomial Constitutive Model 113
4.2 Single Degree of Freedom System 113
4.3 Two Degree of Freedom System 115
References 122
Part II: Smart Materials 124
Introduction to Smart Materials and Structures 125
1 Introduction 125
2 Piezoelectric Materials 127
2.1 Active Vibration, Aeroelastic and Noise Control 129
2.2 Passive Noise and Vibration Control Based on Shunted Piezoelectric Transducers 130
2.3 Piezoelectric Energy Harvesting 130
2.4 Structural Health Monitoring 131
3 Shape Memory Alloys 132
4 Magneto-Rheological and Electro-Rheological Fluids 134
5 Electroactive Polymers 136
6 Final Remarks 136
References 136
Piezoelectric Materials 139
1 Introduction 139
2 Finite Element Formulation of Electromechanical Systems 141
3 Eigenvalue Problem for the Short Circuit Case 148
4 Application: Clamped-Free Beam with Bonded PZT 149
References 158
Shape Memory Alloys 159
1 Introduction 159
2 Applications 162
3 Thermomechanical Characterization 169
3.1 Stress-Free Thermal Analysis 169
3.1.1 DSC Analysis 170
3.1.2 ERT Analysis 172
3.2 Isothermal Stress-Strain Tests 174
3.3 Isobaric Strain-Temperature Tests 176
3.4 Final Remarks 179
4 Constitutive Modeling 179
4.1 Numerical Simulations 182
4.1.1 Model Calibration 183
4.1.2 Qualitative Results 183
4.2 Final Remarks 190
References 190
Electro- and Magneto-Rheological Materials 193
1 Introduction 194
1.1 Variable Rheology Fluids 195
1.2 Sandwich Beams of ER/MR Fluids 198
2 Mathematical Model 200
2.1 Finite Element Discretization 201
2.2 The GHM Model of Material Properties 204
2.3 GHM Viscoelastic Finite Element Matrices 205
3 GHM Fe Model of a Sandwich Beam 206
4 Variable Magnetorheological Elastomers: Application and Characterization 209
4.1 Morphological Magnetic and Mechanical Characterizations of Magnetic Particles and MRE 211
4.2 Measuring the Dynamic Properties of MREs 214
References 217
Composite Structures Design and Analysis 220
1 Introduction 221
1.1 Composite Materials: Definition and Classification 222
1.2 Motivation: Advantages and Challenges 223
1.3 Methodology to Design Composite Structures 224
2 Micromechanical Analysis and Testing 226
2.1 Matrix, Reinforcements, and Interfaces 226
2.1.1 Polymeric Matrix 226
2.1.2 Reinforcements 227
2.2 Rule of Mixture 228
2.2.1 Longitudinal Young´s Modulus 232
2.2.2 Transversal Young's Modulus 233
2.2.3 Shear Modulus 234
2.2.4 Poisson´s Coefficient 236
2.3 Mechanical Testing 237
3 Macromechanical Analysis 238
3.1 Classical Laminate Theory 239
3.2 Strain and Stress Analyses in the Ply 250
4 Failure Analysis 254
4.1 Laminate Failure Modes 255
4.1.1 Intralaminar Damage 255
4.1.2 Interlaminar Failure (Delaminations) 258
4.2 Procedure to Analyze Failure in Laminates 260
4.2.1 Maximum Stress Criterion 261
4.2.2 Maximum Strain Criterion 262
4.2.3 TSAI-HILL Criterion 263
References 265
Part III: Applications 267
Piezoelectric Energy Harvesting 268
1 Introduction 268
2 Approximate Distributed Parameter Model of a Piezoelectric Energy Harvester 270
2.1 Generalized Hamilton´s Principle for a Piezoelectric Energy Harvester 270
2.2 Mathematical Model of a Piezoelectric Energy Harvester 273
3 Theoretical Case Study 277
4 Numerical and Experimental Results for a Tapered Bimorph with Tip Mass 283
5 Summary 287
References 287
Piezoelectric Structural Vibration Control 290
1 Introduction 290
2 Passive Vibration Control Using Piezoelectric Materials 291
2.1 Coupled Formulation for Structure, Piezoelectric Patches, and Shunt Circuits 291
2.1.1 Electric Potential Formulation 292
2.1.2 Electric Charge Formulation 293
2.2 Connection to Electric Circuits 294
2.3 Design of Passive Resistive Shunt Circuits 296
2.4 Design of Passive Resonant Shunt Circuits 299
2.5 Piezoelectric Shunted Damping Example 301
3 Active Vibration Control Using Piezoelectric Materials 303
References 309
Impedance-Based Structural Health Monitoring 311
1 Introduction 311
2 Impedance-Based Structural Health Monitoring: A Review 312
2.1 Damage Metrics 316
2.2 Environmental Influence on Impedance-Based SHM 319
3 Case Studies 320
3.1 Impedance-Based SHM Applied to a Beam-Like Structure 320
3.2 Fatigue Test 324
4 Conclusion 326
References 327
Damage Detection Systems for Commercial Aviation 329
1 Introduction 329
2 Maintenance of Commercial Aircraft 330
2.1 Economics in Aircraft Maintenance 331
2.2 Changes in MSG-3 and SHM 331
3 Commercial Aviation Efforts 332
3.1 Comparative Vacuum Monitoring 333
3.2 Electro-Mechanical Impedance 335
3.3 Lamb Waves 336
3.4 Acoustic Emission 339
3.5 Guidelines for SHM 339
References 341