Engineering Analysis of Smart Material Systems

Donald J. Leo is a professor in the mechanical engineering department of Virginia Polytechnic Institute and State University. Professor Leo has worked in the field of smart materials as a graduate student, a practicing engineer, and, most recently, a faculty member at Virginia Tech. He is the Associate Director for one of the leading centers of study in this area, the Center for Intelligent Material Systems and Structures.

• Preface xiii1 Introduction to Smart Material Systems 11.1 Types of Smart Materials, 21.2 Historical Overview of Piezoelectric Materials, Shape Memory Alloys, and Electroactive Polymers, 51.3 Recent Applications of Smart Materials and Smart Material Systems, 61.4 Additional Types of Smart Materials, 111.5 Smart Material Properties, 121.6 Organization of the Book, 161.7 Suggested Course Outlines, 191.8 Units, Examples, and Nomenclature, 20Problems, 22Notes, 222 Modeling Mechanical and Electrical Systems 242.1 Fundamental Relationships in Mechanics and Electrostatics, 242.1.1 Mechanics of Materials, 252.1.2 Linear Mechanical Constitutive Relationships, 322.1.3 Electrostatics, 352.1.4 Electronic Constitutive Properties of Conducting and Insulating Materials, 432.2 Work and Energy Methods, 482.2.1 Mechanical Work, 482.2.2 Electrical Work, 542.3 Basic Mechanical and Electrical Elements, 562.3.1 Axially Loaded Bars, 562.3.2 Bending Beams, 582.3.3 Capacitors, 642.3.4 Summary, 662.4 Energy-Based Modeling Methods, 672.4.1 Variational Motion, 682.5 Variational Principle of Systems in Static Equilibrium, 702.5.1 Generalized State Variables, 722.6 Variational Principle of Dynamic Systems, 782.7 Chapter Summary, 84Problems, 85Notes, 893 Mathematical Representations of Smart Material Systems 913.1 Algebraic Equations for Systems in Static Equilibrium, 913.2 Second-Order Models of Dynamic Systems, 923.3 First-Order Models of Dynamic Systems, 973.3.1 Transformation of Second-Order Models to First-Order Form, 983.3.2 Output Equations for State Variable Models, 993.4 Input–Output Models and Frequency Response, 1013.4.1 Frequency Response, 1033.5 Impedance and Admittance Models, 1093.5.1 System Impedance Models and Terminal Constraints, 1133.6 Chapter Summary, 118Problems, 118Notes, 1214 Piezoelectric Materials 1224.1 Electromechanical Coupling in Piezoelectric Devices: One-Dimensional Model, 1224.1.1 Direct Piezoelectric Effect, 1224.1.2 Converse Effect, 1244.2 Physical Basis for Electromechanical Coupling in Piezoelectric Materials, 1264.2.1 Manufacturing of Piezoelectric Materials, 1274.2.2 Effect of Mechanical and Electrical Boundary Conditions, 1314.2.3 Interpretation of the Piezoelectric Coupling Coefficient, 1334.3 Constitutive Equations for Linear Piezoelectric Material, 1354.3.1 Compact Notation for Piezoelectric Constitutive Equations, 1374.4 Common Operating Modes of a Piezoelectric Transducer, 1414.4.1 33 Operating Mode, 1424.4.2 Transducer Equations for a 33 Piezoelectric Device, 1474.4.3 Piezoelectric Stack Actuator, 1504.4.4 Piezoelectric Stack Actuating a Linear Elastic Load, 1524.5 Dynamic Force and Motion Sensing, 1574.6 31 Operating Mode of a Piezoelectric Device, 1604.6.1 Extensional 31 Piezoelectric Devices, 1624.6.2 Bending 31 Piezoelectric Devices, 1664.6.3 Transducer Equations for a Piezoelectric Bimorph, 1724.6.4 Piezoelectric Bimorphs Including Substrate Effects, 1754.7 Transducer Comparison, 1784.7.1 Energy Comparisons, 1824.8 Electrostrictive Materials, 1844.8.1 One-Dimensional Analysis, 1864.8.2 Polarization-Based Models of Electrostriction, 1884.8.3 Constitutive Modeling, 1924.8.4 Harmonic Response of Electrostrictive Materials, 1964.9 Chapter Summary, 199Problems, 200Notes, 2035 Piezoelectric Material Systems 2055.1 Derivation of the Piezoelectric Constitutive Relationships, 2055.1.1 Alternative Energy Forms and Transformation of the Energy Functions, 2085.1.2 Development of the Energy Functions, 2105.1.3 Transformation of the Linear Constitutive Relationships, 2125.2 Approximation Methods for Static Analysis of Piezolectric Material Systems, 2175.2.1 General Solution for Free Deflection and Blocked Force, 2215.3 Piezoelectric Beams, 2235.3.1 Cantilevered Bimorphs, 2235.3.2 Pinned–Pinned Bimorphs, 2275.4 Piezoelectric Material Systems: Dynamic Analysis, 2325.4.1 General Solution, 2335.5 Spatial Filtering and Modal Filters in Piezoelectric Material Systems, 2355.5.1 Modal Filters, 2395.6 Dynamic Response of Piezoelectric Beams, 2415.6.1 Cantilevered Piezoelectric Beam, 2495.6.2 Generalized Coupling Coefficients, 2635.6.3 Structural Damping, 2645.7 Piezoelectric Plates, 2685.7.1 Static Analysis of Piezoelectric Plates, 2695.7.2 Dynamic Analysis of Piezoelectric Plates, 2815.8 Chapter Summary, 289Problems, 290Notes, 2976 Shape Memory Alloys 2986.1 Properties of Thermally Activated Shape Memory Materials, 2986.2 Physical Basis for Shape Memory Properties, 3006.3 Constitutive Modeling, 3026.3.1 One-Dimensional Constitutive Model, 3026.3.2 Modeling the Shape Memory Effect, 3076.3.3 Modeling the Pseudoelastic Effect, 3116.4 Multivariant Constitutive Model, 3206.5 Actuation Models of Shape Memory Alloys, 3266.5.1 Free Strain Recovery, 3276.5.2 Restrained Recovery, 3276.5.3 Controlled Recovery, 3296.6 Electrical Activation of Shape Memory Alloys, 3306.7 Dynamic Modeling of Shape Memory Alloys forElectrical Actuation, 3356.8 Chapter Summary, 341Problems, 342Notes, 3457 Electroactive Polymer Materials 3467.1 Fundamental Properties of Polymers, 3477.1.1 Classification of Electroactive Polymers, 3497.2 Dielectric Elastomers, 3557.3 Conducting Polymer Actuators, 3627.3.1 Properties of Conducting Polymer Actuators, 3637.3.2 Transducer Models of Conducting Polymers, 3677.4 Ionomeric Polymer Transducers, 3697.4.1 Input–Output Transducer Models, 3697.4.2 Actuator and Sensor Equations, 3757.4.3 Material Properties of Ionomeric Polymer Transducers, 3777.5 Chapter Summary, 382Problems, 383Notes, 3848 Motion Control Applications 3858.1 Mechanically Leveraged Piezoelectric Actuators, 3868.2 Position Control of Piezoelectric Materials, 3918.2.1 Proportional–Derivative Control, 3928.2.2 Proportional–Integral–Derivative Control, 3968.3 Frequency-Leveraged Piezoelectric Actuators, 4028.4 Electroactive Polymers, 4098.4.1 Motion Control Using Ionomers, 4098.5 Chapter Summary, 412Problems, 413Notes, 4149 Passive and Semiactive Damping 4169.1 Passive Damping, 4169.2 Piezoelectric Shunts, 4199.2.1 Inductive–Resistive Shunts, 4259.2.2 Comparison of Shunt Techniques, 4319.3 Multimode Shunt Techniques, 4329.4 Semiactive Damping Methods, 4409.4.1 System Norms for Performance Definition, 4419.4.2 Adaptive Shunt Networks, 4439.4.3 Practical Considerations for Adaptive Shunt Networks, 4479.5 Switched-State Absorbers and Dampers, 4489.6 Passive Damping Using Shape Memory Alloy Wires, 4539.6.1 Passive Damping via the Pseudoelastic Effect, 4549.6.2 Parametric Study of Shape Memory Alloy Passive Damping, 4609.7 Chapter Summary, 464Problems, 465Notes, 46610 Active Vibration Control 46710.1 Second-Order Models for Vibration Control, 46710.1.1 Output Feedback, 46810.2 Active Vibration Control Example, 47110.3 Dynamic Output Feedback, 47510.3.1 Piezoelectric Material Systems with Dynamic Output Feedback, 48010.3.2 Self-Sensing Actuation, 48310.4 Distributed Sensing, 48610.5 State-Space Control Methodologies, 48810.5.1 Transformation to First-Order Form, 48810.5.2 Full-State Feedback, 49110.5.3 Optimal Full-State Feedback: Linear Quadratic Regulator Problem, 49610.5.4 State Estimation, 50510.5.5 Estimator Design, 50710.6 Chapter Summary, 508Problems, 509Notes, 51011 Power Analysis for Smart Material Systems 51111.1 Electrical Power for Resistive and Capacitive Elements, 51111.2 Power Amplifier Analysis, 52011.2.1 Linear Power Amplifiers, 52011.2.2 Design of Linear Power Amplifiers, 52411.2.3 Switching and Regenerative Power Amplifiers, 53011.3 Energy Harvesting, 53311.4 Chapter Summary, 542Problems, 543Notes, 544References 545Index 553