Christopher R. Bowen University of Bath, UK Andrew R. Plummer University of Bath, UK Series Editors Arthur Willoughby University of Southampton, Southampton, UK Peter Capper formerly of SELEX Galileo Infrared Ltd, Southampton, UK Safa Kasap University of Saskatchewan, Saskatoon, Canada

• Preface xiAcknowledgements xiii1 Introduction 11.1 Active and Sensory Materials for Smart Systems 11.2 Energy Harvesting Materials 31.3 Multifunctional Materials, Devices, Systems and Structures 31.4 Piezoelectric, Pyroelectric and Ferroelectric Materials 4References 52 Piezoelectric Fundamentals 72.1 Piezoelectric Materials 72.2 Ferroelectric Materials 102.2.1 Non-centrosymmetric Unit Cells 102.2.2 Lead Zirconate Titanate (Pb(ZrXTi1−x)O3 , Pzt) Ferroelectrics 132.2.3 Ferroelectric Domains 142.2.4 Poling of Ferroelectric Materials 162.3 Pyroelectric Materials 182.4 Piezoelectric Forms: Bulk, Thin Films and Fibre Composites 192.4.1 Piezoelectric Composites and Connectivity 192.4.2 Active Fibre Composites and Macro-Fibre Composites 202.5 Concluding Remarks 22References 233 Properties of Piezoelectric Materials 273.1 Introduction 273.2 Constitutive Equations 283.2.1 Alternative Single-Axis Formulations 283.2.2 Multi-Axis Linear Model 303.2.2.1 Example Piezoelectric Element 323.2.3 Coupling Coefficients 343.3 Polarisation–Electric Field Response of a Ferroelectric 363.4 Strain–Field Response of a Ferroelectric 393.5 Material Properties and Selection of Materials 413.5.1 Barium Titanate (BaTiO3) 413.5.2 Lead Zirconate Titanate (PZT, Pb(Zr,Ti)O3) 423.5.3 Ferroelectric Polymers 483.6 Mechanical Depolarisation of Ferroelectric Materials 483.7 Creep of Ferroelectric Materials 523.8 Strain Limits of Piezoelectric Actuators (Expansion) 543.9 Strain Limits of Piezoelectric Actuators (Contraction) 553.10 Resonance Behaviour of Piezoelectric Materials and Ceramic Structures 553.11 Ageing of Ferroelectrics 573.12 Temperature Limits and Self-Heating 583.13 Cyclic Operation – Frequency Effects 583.13.1 Self-Heating Due to Ferroelectric Hysteresis 593.13.2 Current Requirements During Frequency Cycling 603.14 Thermal Expansion Coefficient 613.15 Summary 62References 624 Piezoelectric Actuators 654.1 Introduction 654.2 Free Displacement and Blocking Force 654.3 Single-Layer Actuator 674.4 Stack Actuators 714.4.1 Actuator Preloading 724.4.2 Piezoelectric Stack Actuator Selection Example 734.4.3 Optimum Stack Dimensions 764.4.4 Piezoelectric Actuator Stack Sizing Guidelines 774.5 Rectangular Bending Actuators (Bimorphs) 794.5.1 Bimorph Characteristics 794.5.2 Other Rectangular Benders 834.6 Ring Benders 844.6.1 Ring Bender Deformation Analysis 844.6.2 Ring Bender Free Displacement and Blocking Force 924.6.3 Other Circular Benders 954.7 Mechanical Amplification 954.8 Complex Actuator Design 974.8.1 Motion Accumulation 974.8.2 Ultrasonic Motors 984.9 Concluding Remarks 99References 1005 Sensors 1015.1 Introduction 1015.2 Piezoelectric Accelerometers 1015.2.1 Accelerometer Modes of Operation (Compressive, Shear and Flexural d33 and d15) 1055.2.2 Material Selection for Accelerometers 1065.3 Force and Pressure Sensors 1105.3.1 High-Frequency Capability 1115.3.2 Sensor Sensitivity 1115.4 Temperature and Thermal Effects 1135.5 Hydrophones 1155.5.1 Background to Hydrostatic Coefficients 1155.5.2 Derivation of Performance Indicators for Hydrophone Materials 1165.5.3 Hydrophone Construction 1205.6 Piezocomposite Sensors 1235.6.1 Production of Piezoelectric Composites 1275.7 Conclusions 130References 1306 Energy Harvesting 1336.1 Introduction 1336.2 Concept of Piezoelectric-Based Energy Harvesting 1346.3 Piezoelectric Properties and Performance Figures of Merit (FoMs) 1416.3.1 Derivation of Harvesting Figures of Merit (FoMs) 1426.3.2 Mechanical Energy Input 1426.3.3 Converting the Mechanical (Input) into Electrical Energy (Stored) 1456.3.4 Producing an Output from the Stored Electrical Energy 1476.4 Case Study: Piezoelectric Hydraulic Ripple Energy Harvesting 1516.5 Pyroelectric Materials and Thermal Energy Harvesting 1576.5.1 Performance Figures of Merit for Pyroelectric Harvesting and Sensing 1596.6 Summary 163References 1637 Drive Electronics and Control 1677.1 Introduction 1677.2 Op-Amp Circuits 1677.3 Voltage Amplifiers for Driving Actuators 1697.4 Charge Amplifiers for Driving Actuators 1717.5 Regenerative Amplifiers 1747.6 Position Sensors for Feedback Control 1767.6.1 Linear Variable Differential Transformer (LVDT) 1767.6.2 Eddy Current Sensor 1777.6.3 Capacitive Sensor 1787.6.4 Laser Triangulation Sensor 1787.6.5 Strain Gauge Sensor 1787.7 Closed-Loop Controllers: Case Study 1807.8 Signal Conditioning for Piezoelectric Sensors 1827.8.1 Op-Amp Filtering Circuits 1827.8.2 Signal Conditioning in Detail 1867.9 Concluding Remarks 188References 1888 Case Studies 1918.1 Introduction 1918.2 Piezoelectric Valve Actuation 1918.2.1 Internal Combustion Engine Fuel Injectors 1918.2.2 Hydraulic Servo Valves 1918.3 Piezoelectric Pumps 1978.3.1 Introduction 1978.3.2 Piezo Pump Example 1988.4 Vibration Control of Flexible Structures 2018.4.1 Smart Structure 2018.4.2 Dynamic Modelling 2038.4.3 Derivative Feedback Control 2038.5 A Case Study of Actuator Self-Heating 2058.5.1 Model for Temperature Increase Due to Hysteresis 2058.5.2 Testing Actuator Self-Heating 2078.5.3 Comparing Actuator Test Data with Expected Behaviour from Model 2098.6 Piezoelectric Actuation of Bistable Morphing Structures 2118.6.1 Composite Structure Manufacture 2138.6.2 Actuator Materials and Attachment 2148.6.3 Change in Laminate Shape in Response to Piezoelectric Actuation 2148.7 Force Sensors, Shear Sensors and Hydrophones 2178.7.1 Freeze Casting to Produce Porous Ceramics 2178.7.2 Fabrication of Strain Sensor (d31 -Mode) 2228.7.3 d 33 -Mode and d 15 -Mode Piezocomposite Sensors 2238.8 Concluding Remarks 225References 225Index 229

Christopher R. Bowen University of Bath, UK Andrew R. Plummer University of Bath, UK Series Editors Arthur Willoughby University of Southampton, Southampton, UK Peter Capper formerly of SELEX Galileo Infrared Ltd, Southampton, UK Safa Kasap University of Saskatchewan, Saskatoon, Canada

• Preface xiAcknowledgements xiii1 Introduction 11.1 Active and Sensory Materials for Smart Systems 11.2 Energy Harvesting Materials 31.3 Multifunctional Materials, Devices, Systems and Structures 31.4 Piezoelectric, Pyroelectric and Ferroelectric Materials 4References 52 Piezoelectric Fundamentals 72.1 Piezoelectric Materials 72.2 Ferroelectric Materials 102.2.1 Non-centrosymmetric Unit Cells 102.2.2 Lead Zirconate Titanate (Pb(ZrXTi1−x)O3 , Pzt) Ferroelectrics 132.2.3 Ferroelectric Domains 142.2.4 Poling of Ferroelectric Materials 162.3 Pyroelectric Materials 182.4 Piezoelectric Forms: Bulk, Thin Films and Fibre Composites 192.4.1 Piezoelectric Composites and Connectivity 192.4.2 Active Fibre Composites and Macro-Fibre Composites 202.5 Concluding Remarks 22References 233 Properties of Piezoelectric Materials 273.1 Introduction 273.2 Constitutive Equations 283.2.1 Alternative Single-Axis Formulations 283.2.2 Multi-Axis Linear Model 303.2.2.1 Example Piezoelectric Element 323.2.3 Coupling Coefficients 343.3 Polarisation–Electric Field Response of a Ferroelectric 363.4 Strain–Field Response of a Ferroelectric 393.5 Material Properties and Selection of Materials 413.5.1 Barium Titanate (BaTiO3) 413.5.2 Lead Zirconate Titanate (PZT, Pb(Zr,Ti)O3) 423.5.3 Ferroelectric Polymers 483.6 Mechanical Depolarisation of Ferroelectric Materials 483.7 Creep of Ferroelectric Materials 523.8 Strain Limits of Piezoelectric Actuators (Expansion) 543.9 Strain Limits of Piezoelectric Actuators (Contraction) 553.10 Resonance Behaviour of Piezoelectric Materials and Ceramic Structures 553.11 Ageing of Ferroelectrics 573.12 Temperature Limits and Self-Heating 583.13 Cyclic Operation – Frequency Effects 583.13.1 Self-Heating Due to Ferroelectric Hysteresis 593.13.2 Current Requirements During Frequency Cycling 603.14 Thermal Expansion Coefficient 613.15 Summary 62References 624 Piezoelectric Actuators 654.1 Introduction 654.2 Free Displacement and Blocking Force 654.3 Single-Layer Actuator 674.4 Stack Actuators 714.4.1 Actuator Preloading 724.4.2 Piezoelectric Stack Actuator Selection Example 734.4.3 Optimum Stack Dimensions 764.4.4 Piezoelectric Actuator Stack Sizing Guidelines 774.5 Rectangular Bending Actuators (Bimorphs) 794.5.1 Bimorph Characteristics 794.5.2 Other Rectangular Benders 834.6 Ring Benders 844.6.1 Ring Bender Deformation Analysis 844.6.2 Ring Bender Free Displacement and Blocking Force 924.6.3 Other Circular Benders 954.7 Mechanical Amplification 954.8 Complex Actuator Design 974.8.1 Motion Accumulation 974.8.2 Ultrasonic Motors 984.9 Concluding Remarks 99References 1005 Sensors 1015.1 Introduction 1015.2 Piezoelectric Accelerometers 1015.2.1 Accelerometer Modes of Operation (Compressive, Shear and Flexural d33 and d15) 1055.2.2 Material Selection for Accelerometers 1065.3 Force and Pressure Sensors 1105.3.1 High-Frequency Capability 1115.3.2 Sensor Sensitivity 1115.4 Temperature and Thermal Effects 1135.5 Hydrophones 1155.5.1 Background to Hydrostatic Coefficients 1155.5.2 Derivation of Performance Indicators for Hydrophone Materials 1165.5.3 Hydrophone Construction 1205.6 Piezocomposite Sensors 1235.6.1 Production of Piezoelectric Composites 1275.7 Conclusions 130References 1306 Energy Harvesting 1336.1 Introduction 1336.2 Concept of Piezoelectric-Based Energy Harvesting 1346.3 Piezoelectric Properties and Performance Figures of Merit (FoMs) 1416.3.1 Derivation of Harvesting Figures of Merit (FoMs) 1426.3.2 Mechanical Energy Input 1426.3.3 Converting the Mechanical (Input) into Electrical Energy (Stored) 1456.3.4 Producing an Output from the Stored Electrical Energy 1476.4 Case Study: Piezoelectric Hydraulic Ripple Energy Harvesting 1516.5 Pyroelectric Materials and Thermal Energy Harvesting 1576.5.1 Performance Figures of Merit for Pyroelectric Harvesting and Sensing 1596.6 Summary 163References 1637 Drive Electronics and Control 1677.1 Introduction 1677.2 Op-Amp Circuits 1677.3 Voltage Amplifiers for Driving Actuators 1697.4 Charge Amplifiers for Driving Actuators 1717.5 Regenerative Amplifiers 1747.6 Position Sensors for Feedback Control 1767.6.1 Linear Variable Differential Transformer (LVDT) 1767.6.2 Eddy Current Sensor 1777.6.3 Capacitive Sensor 1787.6.4 Laser Triangulation Sensor 1787.6.5 Strain Gauge Sensor 1787.7 Closed-Loop Controllers: Case Study 1807.8 Signal Conditioning for Piezoelectric Sensors 1827.8.1 Op-Amp Filtering Circuits 1827.8.2 Signal Conditioning in Detail 1867.9 Concluding Remarks 188References 1888 Case Studies 1918.1 Introduction 1918.2 Piezoelectric Valve Actuation 1918.2.1 Internal Combustion Engine Fuel Injectors 1918.2.2 Hydraulic Servo Valves 1918.3 Piezoelectric Pumps 1978.3.1 Introduction 1978.3.2 Piezo Pump Example 1988.4 Vibration Control of Flexible Structures 2018.4.1 Smart Structure 2018.4.2 Dynamic Modelling 2038.4.3 Derivative Feedback Control 2038.5 A Case Study of Actuator Self-Heating 2058.5.1 Model for Temperature Increase Due to Hysteresis 2058.5.2 Testing Actuator Self-Heating 2078.5.3 Comparing Actuator Test Data with Expected Behaviour from Model 2098.6 Piezoelectric Actuation of Bistable Morphing Structures 2118.6.1 Composite Structure Manufacture 2138.6.2 Actuator Materials and Attachment 2148.6.3 Change in Laminate Shape in Response to Piezoelectric Actuation 2148.7 Force Sensors, Shear Sensors and Hydrophones 2178.7.1 Freeze Casting to Produce Porous Ceramics 2178.7.2 Fabrication of Strain Sensor (d31 -Mode) 2228.7.3 d 33 -Mode and d 15 -Mode Piezocomposite Sensors 2238.8 Concluding Remarks 225References 225Index 229

Christopher R. Bowen University of Bath, UK Andrew R. Plummer University of Bath, UK Series Editors Arthur Willoughby University of Southampton, Southampton, UK Peter Capper formerly of SELEX Galileo Infrared Ltd, Southampton, UK Safa Kasap University of Saskatchewan, Saskatoon, Canada

• Preface xiAcknowledgements xiii1 Introduction 11.1 Active and Sensory Materials for Smart Systems 11.2 Energy Harvesting Materials 31.3 Multifunctional Materials, Devices, Systems and Structures 31.4 Piezoelectric, Pyroelectric and Ferroelectric Materials 4References 52 Piezoelectric Fundamentals 72.1 Piezoelectric Materials 72.2 Ferroelectric Materials 102.2.1 Non-centrosymmetric Unit Cells 102.2.2 Lead Zirconate Titanate (Pb(ZrXTi1−x)O3 , Pzt) Ferroelectrics 132.2.3 Ferroelectric Domains 142.2.4 Poling of Ferroelectric Materials 162.3 Pyroelectric Materials 182.4 Piezoelectric Forms: Bulk, Thin Films and Fibre Composites 192.4.1 Piezoelectric Composites and Connectivity 192.4.2 Active Fibre Composites and Macro-Fibre Composites 202.5 Concluding Remarks 22References 233 Properties of Piezoelectric Materials 273.1 Introduction 273.2 Constitutive Equations 283.2.1 Alternative Single-Axis Formulations 283.2.2 Multi-Axis Linear Model 303.2.2.1 Example Piezoelectric Element 323.2.3 Coupling Coefficients 343.3 Polarisation–Electric Field Response of a Ferroelectric 363.4 Strain–Field Response of a Ferroelectric 393.5 Material Properties and Selection of Materials 413.5.1 Barium Titanate (BaTiO3) 413.5.2 Lead Zirconate Titanate (PZT, Pb(Zr,Ti)O3) 423.5.3 Ferroelectric Polymers 483.6 Mechanical Depolarisation of Ferroelectric Materials 483.7 Creep of Ferroelectric Materials 523.8 Strain Limits of Piezoelectric Actuators (Expansion) 543.9 Strain Limits of Piezoelectric Actuators (Contraction) 553.10 Resonance Behaviour of Piezoelectric Materials and Ceramic Structures 553.11 Ageing of Ferroelectrics 573.12 Temperature Limits and Self-Heating 583.13 Cyclic Operation – Frequency Effects 583.13.1 Self-Heating Due to Ferroelectric Hysteresis 593.13.2 Current Requirements During Frequency Cycling 603.14 Thermal Expansion Coefficient 613.15 Summary 62References 624 Piezoelectric Actuators 654.1 Introduction 654.2 Free Displacement and Blocking Force 654.3 Single-Layer Actuator 674.4 Stack Actuators 714.4.1 Actuator Preloading 724.4.2 Piezoelectric Stack Actuator Selection Example 734.4.3 Optimum Stack Dimensions 764.4.4 Piezoelectric Actuator Stack Sizing Guidelines 774.5 Rectangular Bending Actuators (Bimorphs) 794.5.1 Bimorph Characteristics 794.5.2 Other Rectangular Benders 834.6 Ring Benders 844.6.1 Ring Bender Deformation Analysis 844.6.2 Ring Bender Free Displacement and Blocking Force 924.6.3 Other Circular Benders 954.7 Mechanical Amplification 954.8 Complex Actuator Design 974.8.1 Motion Accumulation 974.8.2 Ultrasonic Motors 984.9 Concluding Remarks 99References 1005 Sensors 1015.1 Introduction 1015.2 Piezoelectric Accelerometers 1015.2.1 Accelerometer Modes of Operation (Compressive, Shear and Flexural d33 and d15) 1055.2.2 Material Selection for Accelerometers 1065.3 Force and Pressure Sensors 1105.3.1 High-Frequency Capability 1115.3.2 Sensor Sensitivity 1115.4 Temperature and Thermal Effects 1135.5 Hydrophones 1155.5.1 Background to Hydrostatic Coefficients 1155.5.2 Derivation of Performance Indicators for Hydrophone Materials 1165.5.3 Hydrophone Construction 1205.6 Piezocomposite Sensors 1235.6.1 Production of Piezoelectric Composites 1275.7 Conclusions 130References 1306 Energy Harvesting 1336.1 Introduction 1336.2 Concept of Piezoelectric-Based Energy Harvesting 1346.3 Piezoelectric Properties and Performance Figures of Merit (FoMs) 1416.3.1 Derivation of Harvesting Figures of Merit (FoMs) 1426.3.2 Mechanical Energy Input 1426.3.3 Converting the Mechanical (Input) into Electrical Energy (Stored) 1456.3.4 Producing an Output from the Stored Electrical Energy 1476.4 Case Study: Piezoelectric Hydraulic Ripple Energy Harvesting 1516.5 Pyroelectric Materials and Thermal Energy Harvesting 1576.5.1 Performance Figures of Merit for Pyroelectric Harvesting and Sensing 1596.6 Summary 163References 1637 Drive Electronics and Control 1677.1 Introduction 1677.2 Op-Amp Circuits 1677.3 Voltage Amplifiers for Driving Actuators 1697.4 Charge Amplifiers for Driving Actuators 1717.5 Regenerative Amplifiers 1747.6 Position Sensors for Feedback Control 1767.6.1 Linear Variable Differential Transformer (LVDT) 1767.6.2 Eddy Current Sensor 1777.6.3 Capacitive Sensor 1787.6.4 Laser Triangulation Sensor 1787.6.5 Strain Gauge Sensor 1787.7 Closed-Loop Controllers: Case Study 1807.8 Signal Conditioning for Piezoelectric Sensors 1827.8.1 Op-Amp Filtering Circuits 1827.8.2 Signal Conditioning in Detail 1867.9 Concluding Remarks 188References 1888 Case Studies 1918.1 Introduction 1918.2 Piezoelectric Valve Actuation 1918.2.1 Internal Combustion Engine Fuel Injectors 1918.2.2 Hydraulic Servo Valves 1918.3 Piezoelectric Pumps 1978.3.1 Introduction 1978.3.2 Piezo Pump Example 1988.4 Vibration Control of Flexible Structures 2018.4.1 Smart Structure 2018.4.2 Dynamic Modelling 2038.4.3 Derivative Feedback Control 2038.5 A Case Study of Actuator Self-Heating 2058.5.1 Model for Temperature Increase Due to Hysteresis 2058.5.2 Testing Actuator Self-Heating 2078.5.3 Comparing Actuator Test Data with Expected Behaviour from Model 2098.6 Piezoelectric Actuation of Bistable Morphing Structures 2118.6.1 Composite Structure Manufacture 2138.6.2 Actuator Materials and Attachment 2148.6.3 Change in Laminate Shape in Response to Piezoelectric Actuation 2148.7 Force Sensors, Shear Sensors and Hydrophones 2178.7.1 Freeze Casting to Produce Porous Ceramics 2178.7.2 Fabrication of Strain Sensor (d31 -Mode) 2228.7.3 d 33 -Mode and d 15 -Mode Piezocomposite Sensors 2238.8 Concluding Remarks 225References 225Index 229