Vibrations of Linear Piezostructures
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Оглавление
Andrew J. Kurdila. Vibrations of Linear Piezostructures
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Wiley‐ASME Press Series
Vibrations of Linear Piezostructures
Foreword
Preface
Acknowledgments
List of Symbols
1 Introduction. 1.1 The Piezoelectric Effect
1.1.1 Ferroelectric Piezoelectrics
1.1.2 One Dimensional Direct and Converse Piezoelectric Effect
1.2 Applications
1.2.1 Energy Applications
1.2.2 Sensors
1.2.3 Actuators or Motors
1.3 Outline of the Book
2 Mathematical Background
2.1 Vectors, Bases, and Frames
2.2 Tensors
2.3 Symmetry, Crystals, and Tensor Invariance
2.3.1 Geometry of Crystals
2.3.2 Symmetry of Tensors
2.4 Problems
3 Review of Continuum Mechanics
3.1 Stress
3.1.1 The Stress Tensor
3.1.2 Cauchy's Formula
3.1.3 The Equations of Equilibrium
3.2 Displacement and Strain
3.3 Strain Energy
3.4 Constitutive Laws for Linear Elastic Materials
3.4.1 Triclinic Materials
3.4.2 Monoclinic Materials
3.4.3 Orthotropic Materials
3.4.4 Transversely Isotropic Materials
3.5 The Initial‐Boundary Value Problem of Linear Elasticity
3.6 Problems
4 Review of Continuum Electrodynamics
4.1 Charge and Current
4.2 The Electric and Magnetic Fields
4.2.1 The Definition of the Static Electric Field
4.2.2 The Definition of the Static Magnetic Field
4.3 Maxwell's Equations
4.3.1 Polarization and Electric Displacement
4.3.2 Magnetization and Magnetic Field Intensity
4.3.3 Maxwell's Equations in Gaussian Units
4.3.4 Scalar and Vector Potentials
4.4 Problems
5 Linear Piezoelectricity
5.1 Constitutive Laws of Linear Piezoelectricity
5.2 The Initial‐Value Boundary Problem of Linear Piezoelectricity. 5.2.1 Piezoelectricity and Maxwell's Equations
5.2.2 The Initial‐Boundary Value Problem
5.3 Thermodynamics of Constitutive Laws
5.4 Symmetry of Constitutive Laws for Linear Piezoelectricity
5.4.1 Monoclinic Crystals
5.4.2 Monoclinic Crystals
5.4.3 Trigonal Crystals
5.4.4 Hexagonal Crystals
5.5 Problems
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
7 Variational Methods
7.1 A Review of Variational Calculus
7.2 Hamilton's Principle
7.2.1 Uniaxial Rod
7.2.2 Bernoulli–Euler Beam
7.3 Hamilton's Principle for Piezoelectricity
7.3.1 Uniaxial Rod
7.3.2 Bernoulli–Euler Beam
7.4 Bernoulli–Euler Beam with a Shunt Circuit
7.5 Relationship to other Variational Principles
7.6 Lagrangian Densities
7.7 Problems
8 Approximations
8.1 Classical, Strong, and Weak Formulations
8.1.1 Classical Solutions
8.1.2 Strong and Weak Solutions
8.2 Modeling Damping and Dissipation
8.3 Galerkin Approximations
8.3.1 Modal or Eigenfunction Approximations
8.3.2 Finite Element Approximations
8.4 Problems
Supplementary Material. S.1 A Review of Vibrations
S.1.1 SDOF Systems
Homogeneous Solutions
Particular Solutions and FRFs
Total Solutions
Generalizations of SDOF Systems
S.1.2 Distributed Parameter Systems
Homogeneous Solutions: Separation of Variables
Eigenvalue Problems in Hilbert Spaces
Particular Solutions and FRFs
S.1.3 MDOF Equations of Motion. Generalized Algebraic Eigenvalue Problems
S.2 Tensor Analysis
S.3 Distributional and Weak Derivatives
Bibliography
Index
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