Contents -- Preface -- Chapter 1: Theory of Piezoelectricity -- 1.1 Basic Equations -- 1.2 Free Vibration Eigenvalue Problem -- 1.2.1. Abstract formulation -- 1.2.2. Self-adjointness -- 1.2.3. Reality -- 1.2.4. Orthogonality -- 1.2.5. Positivity -- 1.2.6. Variational formulation -- 1.2.7. Perturbation based on variational formulation -- 1.2.8. Perturbation based on differential equations -- 1.3 Inertial Effect of a Mass Layer: Perturbation Integral -- 1.3.1. Governing equations -- 1.3.2. Perturbation analysis -- 1.4 Effect of Mass Layer Stiffness: Perturbation Integral -- 1.4.1. Governing equations -- 1.4.2. Perturbation analysis -- 1.4.3. Example -- 1.5 Frequency Perturbation Due to Contact with a Fluid -- 1.5.1. Governing equations -- 1.5.2. Perturbation analysis -- 1.6 Quartz and Langasite -- 1.7 Lithium Niobate and Lithium Tantalate -- 1.8 Polarized Ceramics and Crystals in Class 6mm -- Chapter 2: Thickness Modes in Plates: Elastic Analysis -- 2.1 Equations of Anisotropic Elasticity -- 2.1.1. General anisotropic crystals -- 2.1.2. Rotated Y-cut Quartz -- 2.2 Thickness Modes in a Quartz Plate -- 2.2.1. TS1 modes -- 2.2.2. Coupled TS3 and TT modes -- 2.3 Inertial Effect of a Mass Layer: Sauerbrey Equation -- 2.4 Inertial Effect of a Mass Layer: Perturbation -- 2.5 Inertial Effect of a Mass Layer: Differential Equation -- 2.6 Plate with Asymmetric Mass Layers -- 2.6.1. General anisotropic crystals -- 2.6.2. Monoclinic crystals -- 2.7 Plate in Contact with a Fluid: Differential Equation -- 2.7.1. Fields in the crystal plate -- 2.7.2. Fields in the fluid -- 2.7.3. Continuity conditions and frequency equation -- 2.7.4. Perturbation solution of the frequency equation -- 2.8 Plate in Contact with a Fluid: Perturbation -- 2.9 Plate with Particles -- 2.9.1. Frequency equation -- 2.9.2. Approximate frequency solution.

2.9.3. Discussion and numerical results -- 2.10 Plate with an Array of Rods in Extension -- 2.10.1. Crystal plate -- 2.10.2. Rod array -- 2.10.3. Plate-rod interaction -- 2.10.4. Equivalent mass layer -- 2.10.5. Approximate frequency solution -- 2.10.6. Special cases -- 2.11 Plate with an Array of Beams in Bending -- 2.11.1. Crystal plate -- 2.11.2. Beam array -- 2.11.3. Plate-beam interaction -- 2.11.4. Equivalent mass layer -- 2.11.5. Approximate frequency solution -- 2.11.6. Special case -- 2.12 Plate with Beams: Effect of Couple Stress -- 2.12.1. Equations and fields of the plate -- 2.12.2. Equations of the beams -- 2.12.3. Continuity conditions and frequency equation -- 2.12.4. Case of h = 0 and N = 0 -- 2.12.5. Case of h = 0 and N 0 -- 2.12.6. Case of h 0 and N = 0 -- 2.13 Plate with an Inhomogeneous Layer of Finite Thickness -- Chapter 3: Thickness Modes in Plates: Piezoelectric Analysis -- 3.1 Unelectroded Plate -- 3.2 Thickness Field Excitation -- 3.2.1. Free vibration -- 3.2.2. Forced vibration -- 3.3 Lateral Field Excitation -- 3.4 Plate with Separated Electrodes -- 3.5 Effect of Electrode Inertia -- 3.5.1. General analysis -- 3.5.2. Identical electrodes -- 3.6 Imperfectly Bonded Electrodes -- 3.6.1. General analysis -- 3.6.2. Identical electrodes -- 3.6.2.1. Identical electrodes in general -- 3.6.2.2. Large k' limit -- 3.6.2.3. Small k' limit -- 3.7 Effect of Electrode Shear Stiffness -- 3.7.1. General analysis -- 3.7.2. Special cases -- 3.7.2.1. Very thin electrodes without mechanical effects -- 3.7.2.2. Identical electrodes -- 3.7.2.3. Electrode inertia -- 3.7.2.4. Nonpiezoelectric plates -- 3.7.3. Numerical results -- 3.8 Plate in Contact with a Fluid under a Separated Electrode -- 3.8.1. Governing equations and fields -- 3.8.2. Free vibration -- 3.8.3. Forced vibration -- 3.8.4. Numerical results.

3.9 Plate in Contact with a Fluid: Lateral Field Excitation -- 3.9.1. Governing equations and fields -- 3.9.2. Free vibration -- 3.9.3. Forced vibration -- 3.9.4. Numerical results -- 3.10 Plate with Surface Load Described by Acoustic Impedance -- 3.10.1. Unelectroded plates -- 3.10.2. Electroded plates -- 3.11 Transient Thickness-shear Vibration -- 3.11.1. Governing equations -- 3.11.2. Free vibration solution -- 3.11.3. Forced vibration solution -- 3.11.4. Numerical results -- 3.11.4.1. Resonator startup -- 3.11.4.2. Driving voltage amplitude rise -- 3.11.4.3. Driving voltage amplitude pulse -- 3.11.4.4. Driving voltage frequency rise -- 3.11.4.5. Driving voltage frequency pulse -- Chapter 4: Shear-horizontal Waves in Unbounded Plates -- 4.1 Governing Equations -- 4.2 Face-shear Wave -- 4.3 Thickness-twist Wave -- 4.3.1. Antisymmetric waves -- 4.3.2. Symmetric waves -- 4.3.3. Dispersion curves -- 4.4 Symmetric Mass Layers -- 4.4.1. Antisymmetric waves -- 4.4.2. Symmetric waves -- 4.4.3. Dispersion curves -- 4.4.4. Approximate dispersion relation -- 4.5 Partial Mass Layers and Bechmann's Number -- 4.6 Asymmetric Mass Layers -- 4.6.1. Dispersion relation -- 4.6.2. Special case: one mass layer -- 4.7 Imperfectly Bonded Mass Layer -- 4.7.1. Dispersion relation -- 4.7.2. Approximate dispersion relation (small R) -- 4.7.3. Approximate dispersion relation (large k) -- 4.8 Mass Layer Stiffness -- 4.8.1. Dispersion relation -- 4.8.2. Numerical example -- 4.9 Thick Mass Layer -- 4.9.1. Dispersion relation -- 4.9.2. Long-wave approximation -- 4.9.3. Thin-film approximation -- 4.10 Plate on a Substrate -- 4.10.1. Dispersion relation -- 4.10.2. Numerical result -- 4.11 Plate in Contact with a Fluid -- 4.11.1. Dispersion relation -- 4.11.2. Special case: a plate without fluid -- 4.11.3. Low viscosity fluid -- 4.11.4. Long-wave approximation.

4.12 Effect of Piezoelectric Coupling -- 4.12.1. Governing equations -- 4.12.2. Propagating wave solution -- 4.12.3. Numerical results and discussion -- Chapter 5: Shear-horizontal Vibrations of Finite Plates -- 5.1 Plate with Tilted Edges -- 5.2 Unelectroded Plate -- 5.3 Fully Electroded Plate -- 5.4 Partially Electroded Plate -- 5.4.1. Fourier series solution -- 5.4.2. Numerical result -- 5.5 Plate with a Partial Mass Layer -- 5.6 Plate with Misaligned Electrodes -- 5.7 Plate with a Mass Layer Array -- 5.7.1. Governing equations and series solution -- 5.7.2. Effect of mass layer thickness -- 5.7.3. Effect of mass layer length -- 5.7.4. An array of four mass layers -- 5.8 Mesa Resonator -- 5.8.1. Governing equations -- 5.8.2. Fourier series solution -- 5.8.3. Boundary and continuity conditions -- 5.8.4. Numerical result -- 5.9 Filter -- 5.9.1. Governing equations -- 5.9.2. Fourier Series solution -- 5.9.3. Symmetric filter (L1 = L2, R1 = R2) -- 5.9.4. Asymmetric filter -- 5.10 Contoured Resonator -- 5.10.1. Governing equation -- 5.10.2. Solutions of the Helmholtz equation -- 5.10.2.1. Solutions of the angular Mathieu equation -- 5.10.2.2. Solutions of the radial Mathieu equation -- 5.10.3. Shear-horizontal modes -- 5.10.3.1. Antisymmetric modes -- 5.10.3.2. Symmetric modes -- 5.10.4. Numerical result and discussion -- 5.10.4.1. Thickness-shear modes -- 5.10.4.2. Thickness-twist modes -- 5.11 Plate with a Nonuniform Mass Layer -- 5.11.1. Fourier series solution -- 5.11.2. Numerical result -- 5.12 Plate with an Imperfectly Bonded Mass Layer -- 5.12.1. Fourier series solution -- 5.12.2. Numerical result -- 5.13 Frequency Spectra -- Chapter 6: Waves Propagating along Digonal Axis -- 6.1 Governing Equations -- 6.2 Wave Solution -- 6.3 Dispersion Curves -- 6.4 Long Wavelength Limit -- 6.5 Other Results -- 6.6 Approximate Equations for u1 and u2.

6.7 Straight-crested Waves of u1 and u2 -- Chapter 7: Vibration of Rectangular Plates -- 7.1 Approximate Equation for u1 -- 7.2 Unelectroded Plate -- 7.3 Fully Electroded Plate -- 7.4 Partially Electroded Plate -- 7.4.1. Series solution -- 7.4.2. Numerical result -- 7.5 Contoured Plate -- Chapter 8: Scalar Equation for Thickness Modes -- 8.1 Scalar Equation for AT-cut Quartz Plates -- 8.1.1. Unelectroded plate -- 8.1.2. Electroded plate -- 8.2 Rectangular Plate -- 8.3 Elliptical Plate -- 8.4 Circular Plate -- 8.4.1. Governing Equation -- 8.4.2. Solution -- 8.4.3. Numerical Result -- 8.5 Unbounded Plate with Parabolic Contour -- 8.5.1. Governing equation and solution -- 8.5.2. Numerical result -- 8.6 Unbounded Plate with Hyperbolic Contour -- 8.6.1. Governing equation -- 8.6.2. Analytical solution -- 8.6.3. Numerical result -- 8.7 Elliptical Plate with Parabolic Contour -- 8.7.1. Governing equation and solution -- 8.7.2. Numerical result -- 8.8 Scalar Equation for SC-cut Quartz Plates -- 8.8.1. Pure thickness waves -- 8.8.2. Unelectroded plate -- 8.8.3. Electroded plate -- 8.8.4. Canonical form -- 8.9 Optimal Electrode Shape and Size -- Appendix 1 Notation -- Appendix 2 Material Constants -- References -- Index.