This book introduces acoustic wave theories using a reader-friendly matrix-based linear algebra approach. It will enable the reader to take advantage of software tools such as MATLAB (commercial codes) and OCTAVE (open-source codes) to gain better and deeper understanding of the underlying physics quickly. In this aspect, this text can be regarded as a practical introduction of the acoustic wave theories in an easy-to-follow linear algebra format using matrix manipulations instead of an abstract approach relying on tensor manipulations. The book also uses case studies to demonstrate how the fundamentals on acoustic waves discussed throughout the book are applied in device designs and analyses such that the connections and interdependences between the underlying sciences and the observed behavior and performances can be better appreciated by the reader. To achieve this, all problems for illustrations, examples, case studies, and device analyses are developed and solved based on the mathematical foundations laid out in the book.
Author(s): Guigen Zhang
Publisher: Jenny Stanford Publishing
Year: 2022
Language: English
Pages: 360
City: Singapore
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Chapter 1: Introduction
1.1: Sound Waves and Acoustics
1.2: Main Types of Acoustic Waves
1.3: A Brief History of Wave Theory Development
1.4: Uniqueness of Acoustic Wave Devices
1.5: An Overview of the Book
1.6: Study Problems
Chapter 2: Elasticity and Piezoelectricity
2.1: Elastic and Piezoelectric Behavior of Materials
2.2: Free Body Diagram and Equations of Motion
2.2.1: Free Body Diagram
2.2.2: Equations of Motion
2.2.3: The State of Stresses and Strains
2.3: Elastic Constitutive Relations
2.3.1: Generalized Hooke’s Law
2.3.2: Isotropic Materials
2.3.3: Anisotropic Materials
2.4: Simplification of 3D Problems
2.4.1: 2D Plane‐Stress Situation
2.4.2: 2D Plane‐Strain Situation
2.4.3: 1D Situation
2.5: Governing Equation for Acoustic Waves in Elastic Solids
2.6: Coupled Elastic and Piezoelectric Constitutive Relations
2.6.1: Direct Piezoelectric Effect
2.6.2: Reverse Piezoelectric Effect
2.6.3: Piezoelectric Coupling Equations
2.7: Governing Equation Piezoelectric Solids
2.8: Unit Analysis
2.9: Study Problems
Chapter 3: Coordinate Rotation and Matrix Transformation
3.1: Coordinate Rotation and Transformation Matrix
3.2: Transformation of Stress and Strain Matrices
3.2.1: Transformation of Matrices of Primary and Secondary Variables
3.2.2: Transformation of the Stress Matrix
3.2.3: Transformation of the Strain Matrix
3.3: Transformation of Piezoelectric Properties
3.3.1: Transformation of [c] and [s] Matrices
3.3.2: Transformation of [e], [d] and [ϵ] Matrices
3.4: Transformation by Euler‐Angles
3.4.1: Transformation by the First Euler Angle Alone
3.4.2: Transformation by the Second Euler Angle Alone
3.4.3: Transformation by the Third Euler Angle Alone
3.4.4: Transformation by a Set of Euler Angles Sequentially
3.5: Study Problems
Chapter 4: Classes of Crystal Symmetry
4.1: The Concept of Crystal Symmetry
4.2: Triclinic Crystals
4.2.1: Class 1: Triclinic 1
4.2.2: Class 2: Triclinic 1
4.3: Monoclinic Crystals
4.3.1: Class 3: Monoclinic 2
4.3.2: Class 4: Monoclinic m
4.3.3: Class 5: Monoclinic 2/m
4.4: Orthorhombic Crystals
4.4.1: Class 6: Orthorhombic 2mm
4.4.2: Class 7: Orthorhombic 222
4.4.3: Class 8: Orthorhombic mmm
4.5: Tetragonal Crystals
4.5.1: Class 9: Tetragonal 4
4.5.2: Class 10: Tetragonal 4
4.5.3: Class 11: Tetragonal 4/m
4.5.4: Class 12: Tetragonal 422
4.5.5: Class 13: Tetragonal 4mm
4.5.6: Class 14: Tetragonal 42m
4.5.7: Class 15: Tetragonal 4/mmm
4.6: Trigonal Crystals
4.6.1: Class 16: Trigonal 3
4.6.2: Class 17: Trigonal 3
4.6.3: Class 18: Trigonal 32
4.6.4: Class 19: Trigonal 3m
4.6.5: Class 20: Trigonal 3m
4.7: Hexagonal Crystals
4.7.1: Class 21: Hexagonal 6
4.7.2: Class 22: Hexagonal 6
4.7.3: Class 23: Hexagonal 6/m
4.7.4: Class 24: Hexagonal 622
4.7.5: Class 25: Hexagonal 6mm
4.7.6: Class 26: Hexagonal 6m2
4.7.7: Class 27: Hexagonal 6/mmm
4.8: Cubic Crystals
4.8.1: Class 28: Cubic 23
4.8.2: Class 29: Cubic m3
4.8.3: Class 30: Cubic 432
4.8.4: Class 31: Cubic m3m
4.8.5: Class 32: Cubic 43m
4.9: Properties of Some Common Crystal Materials
4.10: Study Problems
Chapter 5: Bulk Acoustic Waves
5.1: Different Types of Bulk Acoustic Waves
5.1.1: Longitudinal and Transverse Acoustic Waves
5.1.2: Polarization and Propagation of BAWs
5.2: Bulk Acoustic Waves in Elastic Solids
5.2.1: Christoffel Equation in a Matrix Form
5.2.2: Slowness Curves in Anisotropic Solids
5.3: Slowness Curves Interpreted
5.3.1: Information Contained in Slowness Curves
5.3.2: Slowness Shells or Surfaces
5.3.3: More Examples of Slowness Curves
5.3.4: Poynting Vector, Energy Velocity, Wave and Velocity Surfaces
5.4: Bulk Acoustic Waves in Piezoelectric Solids
5.4.1: Governing Equation for BAWs with Piezoelectric Coupling
5.4.2: Slowness Curves Affected by Piezoelectric Coupling
5.4.3: Electromechanical Coupling Coefficient K for BAWs
5.4.4: A Few Other Crystals with Strong Piezoelectric Coupling Effect
5.4.5: Energy Velocity, Wave Velocity and Poynting Angle
5.5: Study Problems
Chapter 6: Surface Acoustic Waves
6.1: Fixed and Rotated Coordinates Systems
6.2: Propagation of SAWs in Isotropic Solids
6.2.1: Governing Eqs. for SAWs in Isotropic Solids
6.2.2: Rayleigh Waves
6.2.3: Displacements and Stresses Caused by Rayleigh Waves
6.2.4: Transverse Wave
6.3: Propagation of SAWs in Piezoelectric Solids
6.3.1: Governing Equations for SAWs in Piezoelectric Solids
6.3.2: Displacement and Potential Fields
6.3.3: Mechanical and Electrical Conditions at the Surface
6.4: Common Crystal Cuts for SAW Applications
6.4.1: Z‐Cut Crystals
6.4.2: Y‐Cut Crystals
6.4.3: X‐Cut Crystals
6.4.4: Rotated Y‐Cut Crystals with X(‖) Wave Propagation
6.4.5: Rotated Y‐Cut Crystals with X(┴) Wave Propagation
6.4.6: 45° Rotated Y‐Cut Crystals
6.4.7: Rotated X‐Cut Crystals with Y(┴) Wave Propagation
6.5: Decoupling SAWs with Specific Cut Orientations
6.5.1: Cuts with xz‐Plane Perpendicular to Axes of Rotation of Even‐Fold
6.5.2: Cuts with xz‐Plane Parallel with Mirror Planes
6.6: Characterization of SAWs in Piezoelectric Solids
6.6.1: Non‐Piezoelectric Rayleigh Waves
6.6.2: Influence of Anisotropy on Rayleigh Waves
6.6.3: Piezoelectric Stiffened Bleustein–Gulyaev Waves
6.6.4: Piezoelectric Stiffened Rayleigh Waves
6.7: Fully Coupled SAWs in Piezoelectric Solids
6.7.1: Phase Velocity of SAWs in LiTaO3
6.7.2: Phase Velocity of SAWs in LiNbO3
6.7.3: Phase Velocity of SAWs in Langasite
6.7.4: Phase Velocity of SAWs in SiO2
6.7.5: Electromechanical Coupling Coefficient K for SAWs
6.7.6: Poynting Angle for SAWs
6.8: Study Proble
Chapter 7: Temperature Effect
7.1: Temperature‐Dependent Behavior
7.1.1: Temperature Coefficient of Delay
7.1.2: Temperature Coefficient of Velocity
7.1.3: Approximate Values of TCD and TCV
7.2: Temperature‐Dependent Material Properties
7.2.1: Temperature‐Dependent [c], [e] and [ϵ] Constants
7.2.2: Temperature‐Dependent Thermal Coefficient of Expansion
7.2.3: Temperature‐Dependent Density
7.3: Case Studies of Temperature Effect on SAWs
7.3.1: TCD for Langasite
7.3.2: TCD for Quartz
7.3.3: TCD for Lithium Niobate
7.3.4: TCD for Lithium Tantalate
7.4: Study Problems
Chapter 8: Acoustic Waves in Thin Layers
8.1: Love Waves
8.2: Effect of Layer Thickness on Love Waves
8.3: Lamb Waves
8.4: Lamb Waves of the Zeroth Order
8.4.1: Lamb Waves with Asymmetric Flexure‐Mode Displacements
8.4.2: Lamb Waves with Symmetric Dilation‐Mode Displacements
8.5: Lamb Waves of Higher Orders
8.6: Effect of Plate Thickness on Lamb Waves
8.7: Rayleigh Waves in Thin Layers
8.8: Study Problems
Chapter 9: Applications and Devices
9.1: BAW Devices
9.1.1: Disc Resonators
9.1.2: Temperature Influence on Quartz Disc Resonators
9.1.3: Disc Resonator as Sensors
9.1.4: Tuning‐Fork Resonators
9.1.5: Temperature Influence on Quartz Tuning‐Fork Resonators
9.2: SAW Devices
9.2.1: SAW Transversal Filters
9.2.2: Leaky SAWs
9.2.3: SAW Sensors
9.2.4: SAW Resonators
Appendix
References and Further Reading
Index
