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Preface; Contents; List of symbols; 1 Piezoelectricity and Piezoelectric Properties; 1.1 Pyroelectricity; 1.2 Piezoelectricity Discovery; 1.3 Ferroelectricity Discovery; 1.4 Piezoelectric Properties; References; 2 Piezoelectric Ceramic Materials; 2.1 PZT Ceramics; 2.2 Other Ceramic Compositions; 2.3 Example of Crystallographic Symmetry for Mechanically Textured Ceramics; References; 3 Piezoelectric Ceramic Resonators (Resonance Frequency and Equivalent Electrical Circuit); 3.1 Introduction; 3.1.1 Basic Assumptions and Approximations; 3.1.2 Solution of Free Vibrations
3.1.3 Electromechanical Coupling Factor3.1.4 Electrical Equivalent Circuit; 3.2 Length Extensional Mode (Side Electrodes); 3.2.1 Solution of Free Vibrations; 3.2.2 Parameters of Electrical Equivalent Circuit; 3.3 Length Extensional Mode (End Electrodes); 3.3.1 Solution of Free Vibrations; 3.3.2 Parameters of Electrical Equivalent Circuit; 3.4 Thickness Shear Mode (Side Electrodes); 3.4.1 Solution of Free Vibrations; 3.4.2 Parameters of Electrical Equivalent Circuit; 3.5 Thickness Shear Mode (End Electrodes); 3.5.1 Solution of Free Vibrations; 3.5.2 Parameters of Electrical Equivalent Circuit
3.6 Thickness Extensional Mode3.6.1 Solution of Free Vibrations; 3.6.2 Parameters of Electrical Equivalent Circuit; 3.7 Radial Mode of Circular Plate; 3.7.1 Solution of Free Vibrations; 3.7.2 Parameters of Electrical Equivalent Circuit; 3.7.3 Solution Using Planar Material Constants; 3.8 Radial Mode of Circular Rod; 3.8.1 Solution of Free Vibrations; 3.8.2 Parameters of Electrical Equivalent Circuit; 3.9 Contour Extensional Mode of Square Plate; 3.9.1 Solution of Free Vibrations; 3.9.2 Parameters of Electrical Equivalent Circuit; 3.10 Width Extensional Mode; 3.10.1 Solution of Free Vibrations
3.10.2 Parameters of Electrical Equivalent Circuit3.11 Width Extensional Mode (Side Electrodes); 3.11.1 Solution of Free Vibrations; 3.11.2 Parameters of Electrical Equivalent Circuit; 3.12 Thickness Extensional Mode (Side Electrodes); 3.12.1 Solution of Free Vibrations; 3.12.2 Parameters of Electrical Equivalent Circuit; 3.13 Width Extensional Mode (End Electrodes); 3.13.1 Solution of Free Vibrations; 3.13.2 Parameters of Electrical Equivalent Circuit; 3.14 Radial Axisymmetric Vibrations of Rings and Tubes; 3.14.1 Radial Mode of Thin Rings; 3.14.2 Radial Mode of Axially Polarized Ring
3.14.3 Radial Mode of Radially Polarized Ring3.15 Miscellaneous Vibration Modes; 3.16 Approximative Theories for the Solution of Piezoelectric Resonator Vibrations; References; 4 Applications of Piezoelectric Resonators; 4.1 Introduction; 4.2 Impedance Spectrum Characteristics; 4.3 Electromechanical Coupling Factor; 4.4 Material Property Measurement for Piezoelectric Ceramics; 4.4.1 Thickness Poled Bar with Electrodes on Major Faces (\varvec {k}_{31}-mode); 4.4.2 Longitudinally Poled Bar with Electrodes at the Ends ({\varvec k}_{\bf 33}-mode)
3.1.3 Electromechanical Coupling Factor3.1.4 Electrical Equivalent Circuit; 3.2 Length Extensional Mode (Side Electrodes); 3.2.1 Solution of Free Vibrations; 3.2.2 Parameters of Electrical Equivalent Circuit; 3.3 Length Extensional Mode (End Electrodes); 3.3.1 Solution of Free Vibrations; 3.3.2 Parameters of Electrical Equivalent Circuit; 3.4 Thickness Shear Mode (Side Electrodes); 3.4.1 Solution of Free Vibrations; 3.4.2 Parameters of Electrical Equivalent Circuit; 3.5 Thickness Shear Mode (End Electrodes); 3.5.1 Solution of Free Vibrations; 3.5.2 Parameters of Electrical Equivalent Circuit
3.6 Thickness Extensional Mode3.6.1 Solution of Free Vibrations; 3.6.2 Parameters of Electrical Equivalent Circuit; 3.7 Radial Mode of Circular Plate; 3.7.1 Solution of Free Vibrations; 3.7.2 Parameters of Electrical Equivalent Circuit; 3.7.3 Solution Using Planar Material Constants; 3.8 Radial Mode of Circular Rod; 3.8.1 Solution of Free Vibrations; 3.8.2 Parameters of Electrical Equivalent Circuit; 3.9 Contour Extensional Mode of Square Plate; 3.9.1 Solution of Free Vibrations; 3.9.2 Parameters of Electrical Equivalent Circuit; 3.10 Width Extensional Mode; 3.10.1 Solution of Free Vibrations
3.10.2 Parameters of Electrical Equivalent Circuit3.11 Width Extensional Mode (Side Electrodes); 3.11.1 Solution of Free Vibrations; 3.11.2 Parameters of Electrical Equivalent Circuit; 3.12 Thickness Extensional Mode (Side Electrodes); 3.12.1 Solution of Free Vibrations; 3.12.2 Parameters of Electrical Equivalent Circuit; 3.13 Width Extensional Mode (End Electrodes); 3.13.1 Solution of Free Vibrations; 3.13.2 Parameters of Electrical Equivalent Circuit; 3.14 Radial Axisymmetric Vibrations of Rings and Tubes; 3.14.1 Radial Mode of Thin Rings; 3.14.2 Radial Mode of Axially Polarized Ring
3.14.3 Radial Mode of Radially Polarized Ring3.15 Miscellaneous Vibration Modes; 3.16 Approximative Theories for the Solution of Piezoelectric Resonator Vibrations; References; 4 Applications of Piezoelectric Resonators; 4.1 Introduction; 4.2 Impedance Spectrum Characteristics; 4.3 Electromechanical Coupling Factor; 4.4 Material Property Measurement for Piezoelectric Ceramics; 4.4.1 Thickness Poled Bar with Electrodes on Major Faces (\varvec {k}_{31}-mode); 4.4.2 Longitudinally Poled Bar with Electrodes at the Ends ({\varvec k}_{\bf 33}-mode)