Vibrations of Linear Piezostructures. Andrew J. Kurdila

      

      Table of Contents

      1  Cover

      2  Title Page

      3  Copyright

      4  Foreword

      5  Preface

      6  Acknowledgments

      7  List of Symbols

      8  1 Introduction 1.1 The Piezoelectric Effect 1.2 Applications 1.3 Outline of the Book

      9  2 Mathematical Background 2.1 Vectors, Bases, and Frames 2.2 Tensors 2.3 Symmetry, Crystals, and Tensor Invariance 2.4 Problems

      10  3 Review of Continuum Mechanics 3.1 Stress 3.2 Displacement and Strain 3.3 Strain Energy 3.4 Constitutive Laws for Linear Elastic Materials 3.5 The Initial‐Boundary Value Problem of Linear Elasticity 3.6 Problems

      11  4 Review of Continuum Electrodynamics 4.1 Charge and Current 4.2 The Electric and Magnetic Fields 4.3 Maxwell's Equations 4.4 Problems

      12  5 Linear Piezoelectricity 5.1 Constitutive Laws of Linear Piezoelectricity 5.2 The Initial‐Value Boundary Problem of Linear Piezoelectricity 5.3 Thermodynamics of Constitutive Laws 5.4 Symmetry of Constitutive Laws for Linear Piezoelectricity 5.5 Problems

      13  6 Newton's Method for Piezoelectric Systems 6.1 An Axial Actuator Model 6.2 An Axial, Linear Potential, Actuator Model 6.3 A Linear Potential, Beam Actuator 6.4 Composite Plate Bending 6.5 Problems

      14  7 Variational Methods 7.1 A Review of Variational Calculus 7.2 Hamilton's Principle 7.3 Hamilton's Principle for Piezoelectricity 7.4 Bernoulli–Euler Beam with a Shunt Circuit 7.5 Relationship to other Variational Principles 7.6 Lagrangian Densities 7.7 Problems

      15  8 Approximations 8.1 Classical, Strong, and Weak Formulations 8.2 Modeling Damping and Dissipation 8.3 Galerkin Approximations 8.4 Problems

      16  Supplementary Material S.1 A Review of Vibrations S.2 Tensor Analysis S.3 Distributional and Weak Derivatives

      17  Bibliography

      18  Index

      19  End User License Agreement

      List of Tables

      1 Chapter 2Table 2.1 The crystal systems and their point groups. See [13] Table A.2 or [...

      2 Chapter 6Table 6.1 Boundary conditions for piezoelectric composite beam driven by two vol...

      3 Chapter 8Table 8.1 Axial composite piezoelectric actuator, system properties.Table 8.2 A piezoelectric composite beam material and system properties.Table 8.3 Material and system properties for the piezoelectric composite beam wi...

      List of Illustrations

      1 Chapter 1Figure 1.1 Barium titanate and lead zirconate titanate. (Left) Barium titana...Figure 1.2 Polarization versus applied electrical field for ferroelectric ab...Figure 1.3