Nonlinearity in Energy Harvesting Systems (eBook)

Since 2007, Elena Blokhina has been with the School of Electrical, Electronic and Communications Engineering, University College Dublin, Ireland and is currently a lecturer and the research manager of the Circuits and Systems Research Group. Abdelaili El Aroudi is a professor at the University of Rovira, Finland, in the Department of Electronic, Electrical and Automatic Engineering. Eduard Alarcon is a tenured Associate Professor at the Technical University of Catalonia, Spain.

Preface 5
Contents 7
1 Introduction to Vibration Energy Harvesting 8
1.1 Historical Background 8
1.2 Ambient Energy Sources for Harvesting 9
1.3 Vibration Energy Harvesters 11
1.4 Components of Vibration Energy Harvesters 15
1.5 Nonlinearity in Vibration Energy Harvesters 18
1.5.1 Role of Nonlinearities 18
1.5.2 Examples of Useful Nonlinearities 19
1.6 Scope and Structure of the Book 24
References 25
2 MEMS Technologies for Energy Harvesting 29
2.1 Introduction 29
2.2 MEMS Fabrication Processes 30
2.2.1 IC Versus MEMS Fabrication 30
2.2.2 Addition Processes for MEMS 32
2.2.3 Etching Processes for MEMS 35
2.2.4 MEMS Fabrication Strategies 37
2.3 Nonlinear Mechanisms Used in Energy Harvesting with MEMS 44
2.3.1 Bistable Potentials 45
2.3.2 Nonlinear Springs 48
2.3.3 Nonlinear Energy Transfer by Impact 51
2.4 Transduction Principles 53
2.4.1 Electrostatic Transduction 53
2.4.2 Electromagnetic Transduction 55
2.5 MEMS Devices Based on the Piezoelectric Transduction Mechanism 56
2.5.1 Piezoelectricity 57
2.5.2 Properties of Piezoelectric Materials 58
2.5.3 Piezoelectric Materials 61
2.5.4 Piezoelectric Energy Harversters 62
References 65
3 Oscillators for Energy Harvesting 70
3.1 Linear Oscillator 70
3.1.1 Free Linear Oscillator 70
3.1.2 Forced Oscillator and Linear Resonance 75
3.1.3 Equilibrium Points and Stability. An Oscillator as a Dynamical System 79
3.2 Nonlinear Oscillators 82
3.2.1 Free Nonlinear Oscillator 82
3.2.2 Forced Nonlinear Oscillator 93
3.3 Resonators and Kinetic Energy Harvesting 97
3.3.1 Architecture of a Kinetic Energy Harvester (KEH) 97
3.3.2 Design and Optimization of KEH 100
3.3.3 Study of a General Case 101
3.3.4 Case of a Narrow Band Resonator 105
3.3.5 Conclusion 107
References 110
4 Transducers for Energy Harvesting 112
4.1 Capacitive Transducers 112
4.1.1 Presentation of a Capacitive Transducer 113
4.1.2 Electrical Operation of a Variable Capacitor 117
4.1.3 Forces in a Capacitive Transducer 118
4.1.4 Energy Conversion with a Capacitive Transducer 119
4.1.5 Optimization of the Operation of a Capacitive Transducer 121
4.1.6 Electromechanical Coupling 122
4.2 Piezoelectric Transducers 123
4.2.1 Piezoelectric Mechanism 123
4.2.2 Energy Harvesting Using Piezoelectric Transducers 124
References 129
5 Nonlinear Structural Mechanics of Micro-and Nanosystems 131
5.1 Literature Review 132
5.2 Background 136
5.2.1 Beams 136
5.2.2 Electric Actuation 143
5.2.3 Perturbation Series and the Method of Multiple Scales 145
5.2.4 Carbon Nanotubes 152
5.3 Structural Behavior of Straight Carbon Nanotube Resonators 154
5.3.1 Problem Formulation 154
5.4 Dynamics of Slacked Carbon Nanotube Resonators 171
5.4.1 Problem Formulation 172
5.4.2 The Reduced-Order Model 174
5.4.3 The Dynamic Response for Small DC and AC Loads 180
5.4.4 The String Model 190
References 194
6 Nonlinear Dynamics of Ambient Noise-Driven Graphene Nanostructured Devices for Energy Harvesting 200
6.1 Introduction 200
6.2 Graphene-Based Nanomaterials for Energy Harvesting 201
6.3 Chapter Outline 202
6.4 Mathematical Model of the Graphene Vibrating Membrane for Energy Harvesting Applications 202
6.4.1 Nonlinear Mathematical Model 202
6.4.2 Dynamics of the Unforced System 204
6.5 Dynamical Behavior of the Noise-Driven System from Numerical Simulations 206
6.6 Performance of the System in Terms of Design Parameters 208
6.7 Coupled Graphene Vibrating Membrane for Energy Harvesting 209
6.7.1 Nonlinear Mathematical Model 209
6.8 Dynamics of the Coupled Membranes from Numerical Simulations 210
6.9 Conclusions 213
References 214
7 End-Stop Nonlinearities in Vibration Energy Harvesters 216
7.1 Introduction 216
7.2 Modeling of the End-Stops 219
7.2.1 Mathematical Analysis 219
7.2.2 Analysis of the Numerical Results 223
7.2.3 Transducing End-Stops 234
7.3 Conclusions 239
References 240
8 Conditioning Circuits for Capacitive Energy Harvesters 242
8.1 Introduction 242
8.1.1 Generalities 242
8.1.2 Classification of Conditioning Circuits for Capacitive Harvesters 243
8.1.3 Frame of the Analysis of Conditioning Circuit 244
8.2 Continuous Conditioning Circuit 244
8.2.1 Qualitative Discussion on Operation of the Circuit 245
8.2.2 Analytical Model in the Electrical Domain 246
8.3 Conditioning Circuits Implementing Triangular QV Cycles 251
8.3.1 Constant Voltage Conditioning Circuit 252
8.3.2 Constant Charge Conditioning Circuits 253
8.4 Circuits Implementing Rectangular QV Cycles 255
8.4.1 Study of the Rectangular QV Cycle 255
8.4.2 Practical Implementation of the Charge Pump 258
8.4.3 Evolution of the Harvested Energy 260
8.4.4 Shortcomings of the Single Charge Pump 262
8.5 Circuits Derived from the Primitive Charge Pump 264
8.5.1 Resistive Flyback 264
8.5.2 Inductive Flyback 265
8.6 Conditioning Circuits Based on the Bennet's Doubler 266
8.6.1 Introduction of the Principle 266
8.6.2 Operation of a Bennet's Doubler in the Electrical Domain 269
8.6.3 QV Cycle of the Bennet's Doubler and Approximated Analysis in Steady State 272
8.7 Dynamic behavior and Electromechanical Coupling of Rectangular QV Cycle Conditioning Circuits 273
8.8 Practical Use of Conditioning Circuits with Rectangular QV Cycle 276
8.9 Conclusion on Conditioning Circuits for eVEHs 278
References 278
9 Analysis and Modelling of Nonlinearties in Vibration Energy Harvesters 281
9.1 Introduction 281
9.2 Mathematical Model of an eVEH 281
9.2.1 Basis of Mathematical Model 281
9.2.2 The Transducer Force 283
9.2.3 The Constant Charge Energy Conversion Cycle 285
9.2.4 The Complete Normalised Mathematical Model 288
9.3 Semi-analytical Methods 289
9.3.1 Harmonic Balance Method 292
9.3.2 The Multiple Scales Method (MSM) 297
9.3.3 Mechanical Impedance Method 302
9.3.4 Comparison of the Semi-analytical Methods 305
9.4 Visualisation of Results 306
9.4.1 Bifurcation Diagrams 306
9.4.2 Results of the MSM 311
9.5 Stability Analysis 315
References 322
10 Nonlinear Conditioning Circuits for Piezoelectric Energy Harvesters 323
10.1 Introduction 323
10.2 A First Very Simple Model for Kinetic Energy Harvesters 324
10.2.1 Consideration on the Harvested Power 324
10.2.2 Consideration on the Frequency Bandwidth 326
10.2.3 Figure of Merit 328
10.3 Modeling and Parameter Identification for Piezoelectric VEH 330
10.3.1 Model for Piezoelectric Vibration Energy Harvester 330
10.3.2 Electrical Model for SPICE-Type Simulations 332
10.3.3 Model Identification Procedure 333
10.4 Optimal Impedance Matching 334
10.4.1 Theory 335
10.4.2 Practical Implementation 340
10.5 The Classical Rectifier Followed by a Resistive Load 341
10.5.1 Power and Bandwidth 341
10.5.2 Practical Implementation 344
10.6 Nonlinear Energy Harvesting Circuits 345
10.6.1 Principle 345
10.6.2 Comparison of Various Nonlinear Circuits 347
10.6.3 The OSECE Approach 350
10.7 Electrical Frequency tuning 354
10.7.1 The Need for Wideband PEH 354
10.7.2 Frequency Tuning SECE (FTSECE) 355
10.8 Conclusion 359
References 359