This is a review article on a few special topics in piezoelectricity: gradient and nonlocal theories, fully dynamic theory with Maxwell equations, piezoelectric semiconductors, and motions of rotating piezoelectric bodies. They all require some extension of the classical theory of piezoelectricity. They are relatively new, more advanced, and growing subjects with applications or potential applications in various electromechanical devices. The article contains 209 references. (In memory of Raymond D. Mindlin (1906–1987)).
Issue Section:
Review Articles
1.
Dokmeci
, M. C.
, 1988, “Recent Progress in the Dynamic Applications of Piezoelectric Crystals
,” Shock Vib. Dig.
0583-1024, 20
, pp. 3
–20
.2.
Wang
, J.
, and Yang
, J. S.
, 2000, “Higher-Order Theories of Piezoelectric Plates and Applications
,” Appl. Mech. Rev.
0003-6900, 53
, pp. 87
–99
.3.
Yang
, J. S.
, and Hu
, Y. T.
, 2004, “Mechanics of Electroelastic Bodies Under Biasing Fields
,” Appl. Mech. Rev.
0003-6900, 57
, pp. 173
–189
.4.
Rao
, S. S.
, and Sunar
, M.
, 1994, “Piezoelectricity and its Use in Disturbance Sensing and Control of Flexible Structures: A Survey
,” Appl. Mech. Rev.
0003-6900, 47
, pp. 113
–123
.5.
Sunar
, M.
, and Rao
, S. S.
, 1999, “Recent Advances in Sensing and Control of Flexible Structures via Piezoelectric Materials Technology
,” Appl. Mech. Rev.
0003-6900, 52
, pp. 1
–15
.6.
Chee
, C. Y. K.
, Tong
, L.
, and Steven
, G. P.
, 1998, “A Review on the Modeling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures
,” J. Intell. Mater. Syst. Struct.
1045-389X, 9
, pp. 3
–19
.7.
Tani
, J.
, Takagi
, T.
, and Qiu
, J.
, 1998, “Intelligent Material Systems: Application of Functional Materials
,” Appl. Mech. Rev.
0003-6900, 51
, pp. 505
–521
.8.
Toupin
, R. A.
, 1956, “The Elastic Dielectric
,” Arch. Ration. Mech. Anal.
0003-9527, 5
, pp. 849
–915
.9.
Tiersten
, H. F.
, 1981, “Electroelastic Interactions and the Piezoelectric Equations
,” J. Acoust. Soc. Am.
0001-4966, 70
, pp. 1567
–1576
.10.
Mindlin
, R. D.
, 1968, “Polarization Gradient in Elastic Dielectrics
,” Int. J. Solids Struct.
0020-7683, 4
, pp. 637
–642
.11.
Mindlin
, R. D.
, 1969, “Continuum and Lattice Theories of Influence of Electromechanical Coupling on Capacitance of Thin Dielectric Films
,” Int. J. Solids Struct.
0020-7683, 5
, pp. 1197
–1208
.12.
Mindlin
, R. D.
, 1972, “Elasticity, Piezoelectricity and Crystal Lattice Dynamics
,” J. Elast.
0374-3535, 2
, pp. 217
–282
.13.
Askar
, A.
, Lee
, P. C. Y.
, and Cakmak
, A. S.
, 1970, “A Lattice Dynamics Approach to the Theory of Elastic Dielectrics With Polarization Gradient
,” Phys. Rev. B
0556-2805, 1
, pp. 3525
–3537
.14.
Mindlin
, R. D.
, 1973, “On the Electrostatic Potential of a Point Charge in a Dielectric Solid
,” Int. J. Solids Struct.
0020-7683, 9
, pp. 233
–235
.15.
Mindlin
, R. D.
, 1971, “Electromechanical Vibrations of Centrosymmetric Cubic Crystal Plates
,” Q. J. Mech. Appl. Math.
0033-5614, 35
, pp. 404
–408
.16.
Mindlin
, R. D.
, 1972, “Coupled Elastic and Electromagnetic Fields in a Diatomic, Electric Continuum
,” Int. J. Solids Struct.
0020-7683, 8
, pp. 401
–408
.17.
Mindlin
, R. D.
, 1974, “Electromagnetic Radiation From a Vibrating, Elastic Sphere
,” Int. J. Solids Struct.
0020-7683, 10
, pp. 1307
–1314
.18.
Askar
, A.
, Lee
, P. C. Y.
, and Cakmak
, A. S.
, 1971, “The Effect of Surface Curvature and Discontinuity on the Surface Energy Density and Other Induced Fields in Electric Dielectrics With Polarization Gradient
,” Int. J. Solids Struct.
0020-7683, 7
, pp. 523
–537
.19.
Schwartz
, J.
, 1969, “Solutions of the Equations of Equilibrium of Elastic Dielectrics: Stress Functions, Concentrated Force, Surface Energy
,” Int. J. Solids Struct.
0020-7683, 5
, pp. 1209
–1220
.20.
Chowdhury
, K. L.
, and Glockner
, P. G.
, 1977, “Point Charge in the Interior of an Elastic Dielectric Half Space
,” Int. J. Eng. Sci.
0020-7225, 15
, pp. 481
–493
.21.
Chowdhury
, K. L.
, and Glockner
, P. G.
, 1981, “On a Similarity Solution of the Boussinesq Problem of Elastic Dielectrics
,” Arch. Mech.
0373-2029, 32
, pp. 429
–442
.22.
Collet
, B.
, 1981, “One-Dimensional Acceleration Waves in Deformable Dielectrics With Polarization Gradients
,” Int. J. Eng. Sci.
0020-7225, 19
, pp. 389
–407
.23.
Dost
, S.
, 1983, “Acceleration Waves in Elastic Dielectrics With Polarization Gradient Effects
,” Int. J. Eng. Sci.
0020-7225, 21
, pp. 1305
–1311
.24.
Collet
, B.
, 1982, “Shock Waves in Deformable Dielectrics With Polarization Gradients
,” Int. J. Eng. Sci.
0020-7225, 20
, pp. 1145
–1160
.25.
Yang
, J. S.
, and Batra
, R. C.
, 1995, “Conservation Laws in Linear Piezoelectricity
,” Eng. Fract. Mech.
0013-7944, 51
, pp. 1041
–1047
.26.
Suhubi
, E. S.
, 1969, “Elastic Dielectrics With Polarization Gradients
,” Int. J. Eng. Sci.
0020-7225, 7
, pp. 993
–997
.27.
Chowdhury
, K. L.
, Epstein
, M.
, and Glockner
, P. G.
, 1979, “On the Thermodynamics of Non-Linear Elastic Dielectrics
,” Int. J. Non-Linear Mech.
0020-7462, 13
, pp. 311
–322
.28.
Chowdhury
, K. L.
, and Glockner
, P. G.
, 1976, “Constitutive Equations for Elastic Dielectrics
,” Int. J. Non-Linear Mech.
0020-7462, 11
, pp. 315
–324
.29.
Chowdhury
, K. L.
, and Glockner
, P. G.
, 1977, “On Thermoelastic Dielectrics
,” Int. J. Solids Struct.
0020-7683, 13
, pp. 1173
–1182
.30.
Tiersten
, H. F.
, and Tsai
, C. F.
, 1972, “On the Interaction of the Electromagnetic Field With Heat Conducting Deformable Insulators
,” J. Math. Phys.
0022-2488, 13
, pp. 361
–378
.31.
Maugin
, G. A.
, 1977, “Deformable Dielectrics II. Voigt’s Intramolecular Force Balance in Elastic Dielectrics
,” Arch. Mech.
0373-2029, 29
, pp. 143
–151
.32.
Maugin
, G. A.
, 1977, “Deformable Dielectrics III. A Model of Interactions
,” Arch. Mech.
0373-2029, 29
, pp. 251
–258
.33.
Maugin
, G. A.
, and Pouget
, J.
, 1980, “Electroacoustic Equations for One-Domain Ferroelectric Bodies
,” J. Acoust. Soc. Am.
0001-4966, 68
, pp. 575
–587
.34.
Askar
, A.
, Pouget
, J.
, and Maugin
, G. A.
, 1984, “Lattice Model for Elastic Ferroelectrics and Related Continuum Theories
,” Mechanical Behavior of Electromagnetic Solid Continua
, G. A.
Maugin
, ed., Elsevier
, North-Holland, Amsterdam
, pp. 151
–156
.35.
Pouget
, J.
, Askar
, A.
, and Maugin
, G. A.
, 1986, “Lattice Model for Elastic Ferroelectric Crystals: Microscopic Approximation
,” Phys. Rev. B
0163-1829, 33
, pp. 6304
–6319
.36.
Pouget
, J.
, Askar
, A.
, and Maugin
, G. A.
, 1986, “Lattice Model for Elastic Ferroelectric Crystals: Continuum Approximation
,” Phys. Rev. B
0163-1829, 33
, pp. 6320
–6325
.37.
Pouget
, J.
, and Maugin
, G. A.
, 1980, “Coupled Acoustic-Optic Modes in Deformable Ferroelectrics
,” J. Acoust. Soc. Am.
0001-4966, 68
, pp. 588
–601
.38.
Pouget
, J.
, and Maugin
, G. A.
, 1981, “Bleustein-Gulyaev Surface Modes in Elastic Ferroelectrics
,” J. Acoust. Soc. Am.
0001-4966, 69
, pp. 1304
–1318
.39.
Pouget
, J.
, and Maugin
, G. A.
, 1981, “Piezoelectric Rayleigh Waves in Elastic Ferroelectrics
,” J. Acoust. Soc. Am.
0001-4966, 69
, pp. 1319
–1325
.40.
Collet
, B.
, 1984, “Shock Waves in Deformable Ferroelectric Materials
,” Mechanical Behavior of Electromagnetic Solid Continua
, G. A.
Maugin
, ed., Elsevier
, North-Holland, Amsterdam
, pp. 157
–163
.41.
Sahin
, E.
, and Dost
, S.
, 1988, “A Strain-Gradient Theory of Elastic Dielectrics With Spatial Dispersion
,” Int. J. Eng. Sci.
0020-7225, 26
, pp. 1231
–1245
.42.
Demiray
, H.
, and Dost
, S.
, 1989, “Diatomic Elastic Dielectrics With Polarization Gradient
,” Int. J. Eng. Sci.
0020-7225, 27
, pp. 1275
–1284
.43.
Askar
, A.
, and Lee
, P. C. Y.
, 1974, “Lattice Dynamics Approach to the Theory of Diatomic Elastic Dielectrics
,” Phys. Rev. B
0556-2805, 9
, pp. 5291
–5299
.44.
Maugin
, G. A.
, 1988, Continuum Mechanics of Electromagnetic
, Bodies
, North-Holland, Amsterdam
, Chap. 7.45.
Maugin
, G. A.
, Pouget
, J. P.
, Drouot
, R.
, and Collet
, B.
, 1992, Nonlinear Electromechanical Couplings
, Wiley
, Chichester
, p. 335
.46.
Li
, J. Y.
, 2003, “Exchange Coupling in P(VDF-TrFE) Copolymer Based All-Organic Composites With Giant Electrostriction
,” Phys. Rev. Lett.
0031-9007, 90
, p. 217601
.47.
Landau
, L. D.
, and Lifshitz
, E. M.
, 1984, Electrodynamics of Continuous Media
, 2nd ed., Butterworth-Heinemann
, Oxford
, pp. 358
–371
.48.
Kafadar
, C. B.
, 1971, “Theory of Multipoles in Classical Electromagnetism
,” Int. J. Eng. Sci.
0020-7225, 9
, pp. 831
–853
.49.
Demiray
, H.
, and Eringen
, C. A.
, 1973, “On the Constitutive Relations of Polar Elastic Dielectrics
,” Lett. Appl. Eng. Sci.
0090-6913, 1
, pp. 517
–527
.50.
Prechtl
, A.
, 1980, “Deformable Bodies With Electric and Magnetic Quadrupoles
,” Int. J. Eng. Sci.
0020-7225, 18
, pp. 665
–680
.51.
Nelson
, D. F.
, 1979, Electric, Optic and Acoustic Interactions in Crystals
, Wiley
, New York
, p. 74
.52.
Kalpakides
, V. K.
, Hadjigeorgiou
, E. P.
, and Massalas
, C. V.
, 1995, “A Variational Principle for Elastic Dielectrics With Quadruple Polarization
,” Int. J. Eng. Sci.
0020-7225, 33
, pp. 793
–801
.53.
Kalpakides
, V. K.
, and Massalas
, C. V.
, 1993, “Tiersten’s Theory of Thermoelectroelasticity: An Extension
,” Int. J. Eng. Sci.
0020-7225, 31
, pp. 157
–164
.54.
Hadjigeorgiou
, E. P.
, Kalpakides
, V. K.
, and Massalas
, C. V.
, 1999, “A General Theory for Elastic Dielectrics. II. The Variational Approach
,” Int. J. Non-Linear Mech.
0020-7462, 34
, pp. 967
–980
.55.
Kalpakides
, V. K.
, and Agiasofitou
, E. K.
, 2002, “On Material Equations in Second Order Gradient Electroelasticity
,” J. Elast.
0374-3535, 67
, pp. 205
–227
.56.
Maugin
, G. A.
, 1980, “The Principle of Virtual Power: Application to Coupled Fields
,” Acta Mech.
0001-5970, 35
, pp. 1
–70
.57.
Yang
, X. M.
, Hu
, Y. T.
, and Yang
, J. S.
, 2004, “Electric Field Gradient Effects in Anti-Plane Problems of Polarized Ceramics
,” Int. J. Solids Struct.
0020-7683, 41
, pp. 6801
–6811
.58.
Yang
, J. S.
, and Yang
, X. M.
, 2004, “Electric Field Gradient Effect and Thin Film Capacitance
,” World J. Eng.
, 2
, pp. 41
–45
.59.
Yang
, J. S.
, 2004, “Effects of Electric Field Gradient on an Anti-Plane Crack in Piezoelectric Ceramics
,” Int. J. Fract.
0376-9429, 127
, pp. L111
–L116
.60.
Zeng
, Y.
, Hu
, Y. T.
, and Yang
, J. S.
, 2005, “Electric Field Gradient Effects in Piezoelectric Anti-Plane Crack Problems
,” J. Huazhong Univ. Sci. Technol.
0253-4274, 22
, pp. 31
–35
.61.
Zeng
, Y.
, 2005, “Electric Field Gradient Effects in Anti-Plane Crack Problems of Piezoelectric Ceramics
,” Master’s degree thesis, Huazhong University of Science and Technology.62.
Yang
, X. M.
, Hu
, Y. T.
, and Yang
, J. S.
, 2005, “Electric Field Gradient Effects in Anti-Plane Problems of a Circular Cylindrical Hole in Piezoelectric Materials of 6mm Symmetry
,” Acta Mech.
0001-5970, 18
, pp. 29
–36
.63.
Huang
, Y.-N.
, and Batra
, R. C.
, 1996, “Energy-Momentum Tensors in Nonsimple Elastic Dielectrics
,” J. Elast.
0374-3535, 42
, pp. 275
–281
.64.
Ma
, W. H.
, and Cross
, L. E.
, 2001, “Observation of the Flexoelectric Effect in Relaxor Pb(Mg1∕3Nb2∕3)O3 Ceramics
,” Appl. Phys. Lett.
0003-6951, 78
, pp. 2920
–2921
.65.
Maugin
, G. A.
, 1999, Nonlinear Waves in Elastic Crystals
, Oxford University Press
, Oxford
, p. 49
.66.
Maugin
, G. A.
, 1979, “Nonlocal Theories or Gradient-Type Theories: A Matter of Convenience
?,” Arch. Mech.
0373-2029, 31
, pp. 15
–26
.67.
Eringen
, A. C.
, and Kim
, B. S.
, 1977, “Relation Between Non-Local Elasticity and Lattice Dynamics
,” Cryst. Lattice Defects
0011-2305, 7
, pp. 51
–57
.68.
Eringen
, A. C.
, 1984, “Theory of Nonlocal Piezoelectricity
,” J. Math. Phys.
0022-2488, 25
, pp. 717
–727
.69.
Eringen
, A. C.
, and Maugin
, G. A.
, 1990, Electrodynamics of Continua
, Vol. 2
, Springer
, New York
, Chap. 14.70.
Yang
, J. S.
, 1997, “Thin Film Capacitance in Case of a Nonlocal Polarization Law
,” Int. J. Appl. Electromagn. Mech.
1383-5416, 8
, pp. 307
–314
.71.
Mindlin
, R. D.
, 1978, “A Variational Principle for the Equations of Piezoelectromagnetism in a Compound Medium
,” Complex Variable Analysis and Its Applications
(I. N. Vekua 70th Birthday Volume), Academy of Sciences USSR
, Nauka, Moscow
, pp. 397
–400
.72.
Lee
, P. C. Y.
, 1991, “A Variational Principle for the Equations of Piezoelectromagnetism in Elastic Dielectric Crystals
,” J. Appl. Phys.
0021-8979, 69
, pp. 7470
–7473
.73.
Yang
, J. S.
, 1991, “A Generalized Variational Principle for Piezoelectromagnetism in an Elastic Medium
,” Arch. Mech.
0373-2029, 43
, pp. 795
–798
.74.
Yang
, J. S.
, 1993, “Variational Principles for the Vibration of an Elastic Dielectric
,” Arch. Mech.
0373-2029, 45
, pp. 279
–284
.75.
Yang
, J. S.
, and Wu
, X. Y.
, 1995, “The Vibration of an Elastic Dielectric With Piezoelectromagnetism
,” Q. Appl. Math.
0033-569X, 53
, pp. 753
–760
.76.
Kyame
, J. J.
, 1949, “Wave Propagation in Piezoelectric Crystals
,” J. Acoust. Soc. Am.
0001-4966, 21
, pp. 159
–167
.77.
Kyame
, J. J.
, 1953, “Conductivity and Viscosity Effects on Wave Propagation in Piezoelectric Crystals
,” J. Acoust. Soc. Am.
0001-4966, 26
, pp. 990
–993
.78.
Pailloux
, P. M. H.
, 1958, “Piezoelectricite Calcul des Vitesses de Popagation
,” J. Phys. Radium
0368-3842, 19
, pp. 523
–526
.79.
Hruska
, H.
, 1966, “The Rate of Propagation of Ultrasonic Waves in ADP and in Voigt’s Theory
,” Czech. J. Phys., Sect. B
0011-4626, B16
, pp. 446
–453
.80.
Hruska
, H.
, 1966, “Relation Between the General and the Simplified Condition for the Velocity of Propagation of Ultrasonic Waves in a Piezoelectric Medium
,” Czech. J. Phys., Sect. B
0011-4626, B18
, pp. 214
–221
.81.
Tseng
, C.-C.
, and White
, P. M.
, 1967, “Propagation of Piezoelectric and Elastic Surface Waves on the Basal Plane of Hexagonal Piezoelectric Crystals
,” J. Appl. Phys.
0021-8979, 38
, pp. 4274
–4280
.82.
Tseng
, C.-C.
, 1967, “Elastic Surface Waves on Free Surface and Metallized Surface of CdS, ZnO, and PZT-4
,” J. Appl. Phys.
0021-8979, 38
, pp. 4281
–4284
.83.
Spaight
, R. N.
, and Koerber
, G. G.
, 1971, “Piezoelectric Surface Waves on LiNbO3
,” IEEE Trans. Sonics Ultrason.
0018-9537, 18
, pp. 237
–238
.84.
Mindlin
, R. D.
, 1972, “Electromagnetic Radiation From a Vibrating Quartz Plate
,” Int. J. Solids Struct.
0020-7683, 9
, pp. 697
–702
.85.
Lee
, P. C. Y.
, 1989, “Electromagnetic Radiation From an AT-Cut Quartz Plate Under Lateral-field Excitation
,” J. Appl. Phys.
0021-8979, 65
, pp. 1395
–1399
.86.
Lee
, P. C. Y.
, Kim
, Y.-G.
, and Prevost
, J. H.
, 1990, “Electromagnetic Radiation From Doubly Rotated Piezoelectric Crystal Plates Vibrating at Thickness Frequencies
,” J. Appl. Phys.
0021-8979, 67
, pp. 6633
–6642
.87.
Campbell
, C. F.
, and Weber
, R. J.
, 1993, “Calculation of Radiated Electromagnetic Power From Bulk Acoustic Wave Resonators
,” Proc. IEEE International Frequency Control Symposium
, pp. 472
–475
, June 2–4, Salt Lake City.88.
Sedov
, A.
, and Schmerr
, L. W.
, Jr., 1986, “Some Exact Solutions for the Propagation of Transient Electroacoustic I: Piezoelectric Half-Space
,” Int. J. Eng. Sci.
0020-7225, 24
, pp. 557
–568
.89.
Schmerr
, L. W.
, Jr., and Sedov
, A.
, 1986, “Some Exact Solutions for the Propagation of Transient Electroacoustic Waves II: Plane Interface Between Two Piezoelectric Media
,” Int. J. Eng. Sci.
0020-7225, 24
, pp. 921
–932
.90.
Li
, S.
, 1996, “The Electromagneto-Acoustic Surface Wave in a Piezoelectric Medium: The Bleustein-Gulyaev Mode
,” J. Appl. Phys.
0021-8979, 80
, pp. 5264
–5269
.91.
To
, A. C.
, and Glaser
, S. D.
, 2005, “On the Quasi-Static Assumption in Modeling Shear Horizontal, (SH) Waves in a Transversely Isotropic, (6mm) Medium
,” http://www.ce.berkeley.edu/~albertto/piezo.pdfhttp://www.ce.berkeley.edu/~albertto/piezo.pdf.92.
Yang
, J. S.
, 2000, “Bleustein-Gulyaev Waves in Piezoelectromagnetic Materials
,” Int. J. Appl. Electromagn. Mech.
1383-5416, 12
, pp. 235
–240
.93.
Yang
, J. S.
, 2004, “Love Waves in Piezoelectromagnetic Materials
,” Acta Mech.
0001-5970, 168
, pp. 111
–117
.94.
Yang
, J. S.
, 2004, “Piezoelectromagnetic Waves in a Ceramic Plate
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 51
, pp. 1035
–1039
.95.
Yang
, J. S.
, “Acoustic Gap Waves in Piezoelectromagnetic Materials
,” Math. Mech Solids
(accepted).96.
Yang
, J. S.
, 2004, “Effects of Electromagnetic Coupling on a Moving Crack in Polarized Ceramics
,” Int. J. Fract.
0376-9429, 126
, pp. L83
–L88
.97.
Yang
, J. S.
, 2004, “A Moving Dislocation in Piezoelectromagnetic Ceramics
,” Acta Mech.
0001-5970, 172
, pp. 123
–129
.98.
Li
, X. F.
, and Yang
, J. S.
, 2005, “Electromagnetoelastic Behavior Induced by a Crack Under Antiplane Mechanical and Inplane Electric Impacts
,” Int. J. Fract.
0376-9429, 132
, pp. 49
–65
.99.
Yang
, J. S.
, 2005, An Introduction to the Theory of Piezoelectricity, Springer
, New York, Sec. 6.5.100.
Huston
, A. R.
, and White
, D. L.
, 1962, “Elastic Wave Propagation in Piezoelectric Semiconductors
,” J. Appl. Phys.
0021-8979, 33
, pp. 40
–47
.101.
Weinreich
, G.
, Sanders
, T. M.
, Jr., and White
, H. G.
, 1959, “Acoustoelectric Effect in n-type Germanium
,” Phys. Rev.
0031-899X, 114
, pp. 33
–44
.102.
White
, D. L.
, 1962, “Amplification of Ultrasonic Waves in Piezoelectric Semiconductors
,” J. Appl. Phys.
0021-8979, 33
, pp. 2547
–2554
.103.
Fischler
, C.
, 1970, “Acoustoelectric Amplification in a Many-Carrier System
,” J. Appl. Phys.
0021-8979, 41
, pp. 1439
–1443
.104.
Lakin
, K. M.
, and Shaw
, H. J.
, 1969, “Surface Wave Delay Line Amplifiers
,” IEEE Trans. Sonics Ultrason.
0018-9537, 17
, pp. 912
–920
.105.
Ramakrishna
, P. S.
, 1971, “Amplification of Acoustic Surface and Layer Waves
,” MS thesis, McGill University, Montreal, Canada.106.
Ingebrigtsen
, K. A.
, 1970, “Linear and Nonlinear Attenuation of Acoustic Surface Waves in a Piezoelectric Coated With a Semiconducting Film
,” J. Appl. Phys.
0021-8979, 41
, pp. 454
–459
.107.
Kino
, G. S.
, and Reeder
, T. M.
, 1971, “A Normal Mode Theory for the Rayleigh Wave Amplifier
,” IEEE Trans. Electron Devices
0018-9383, 18
, pp. 909
–920
.108.
Kino
, G. S.
, 1976, “Acoustoelectric Interactions in Acoustic-Surface-Wave Devices
,” Proc. IEEE
0018-9219, 64
, pp. 724
–748
.109.
Wang
, W.-C.
, Schachter
, H.
, Elasir
, B.
, Wu
, Z. S.
, and Onishi
, S.
, 1985, “Acoustoelectric Interactions in Thin-Film Semiconductors Induced by Two Contra-Directed Surface Acoustic Waves
,” IEEE Trans. Sonics Ultrason.
0018-9537, 32
, pp. 645
–662
.110.
Ganguly
, M.
, and Pal
, A. K.
, 1988, “Amplification of B-G Waves in a Pre-Stressed Piezoelectric Half Space of Hexagonal Symmetry
,” Acta Phys. Hung.
0231-4428, 63
, pp. 321
–329
.111.
Wauer
, J.
, and Suherman
, S.
, 1997, “Thickness Vibrations of a Piezo-Semiconducting Plate Layer
,” Int. J. Eng. Sci.
0020-7225, 35
, pp. 1387
–1404
.112.
Fischler
, C.
, 1971, “Propagation and Amplification of Shear-Horizontal Waves in Piezoelectric Plates
,” J. Appl. Phys.
0021-8979, 42
, pp. 919
–924
.113.
Fischler
, C.
, 1971, “Acoustoelectric Amplification in Composite Piezoelectric and Semiconducting Structures
,” IEEE Trans. Electron Devices
0018-9383, 17
, pp. 214
–218
.114.
Dietz
, D. R.
, Busse
, L. J.
, and Fife
, M. J.
, 1988, “Acoustoelectric Detection of Ultrasound Power With Composite Piezoelectric and Semiconductor Devices
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 35
, pp. 146
–151
.115.
Josse
, F.
, 1986, “Acoustoelectric Interactions in RNWS in a Piezoelectric-Semiconductor Structure
,” Proc. IEEE Ultrasonics Symp.
, pp. 469
–474
, Nov. 17–19, Williamsburg.116.
Palma
, F.
, and Das
, P. K.
, 1986, “Acoustoelectric Interaction and Transverse Acoustoelectric Voltage in Multilayered Semiconductor
,” Proc. IEEE Ultrasonics Symp.
, pp. 457
–461
, Nov. 17–19, Williamsburg.117.
Palma
, F.
, and Das
, P. K.
, 1987, “Acoustoelectric Interaction in Layered Semiconductor
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 34
, pp. 376
–382
.118.
Palanichamy
, P.
, and Singh
, S. P.
, 1983, “Acoustic Second Harmonic Generation in Piezoelectric Semiconductors: Effect of Nonuniform Electric Field Intensity
,” J. Appl. Phys.
0021-8979, 54
, pp. 3958
–3964
.119.
Yang
, J. S.
, and Zhou
, H. G.
, 2005, “Amplification of Acoustic Waves in Piezoelectric Semiconductor Plates
,” Int. J. Solids Struct.
0020-7683, 42
, pp. 3171
–3183
.120.
Yang
, J. S.
, and Zhou
, H. G.
, 2004, “Acoustoelectric Amplification of Piezoelectric Surface Waves
,” Acta Mech.
0001-5970, 172
, pp. 113
–122
.121.
Yang
, J. S.
, and Zhou
, H. G.
, 2005, “Propagation and Amplification of Gap Waves Between a Piezoelectric Half-Space and a Semiconductor Film
,” Acta Mech.
0001-5970, 176
, pp. 83
–93
.122.
Yang
, J. S.
, and Zhou
, H. G.
, 2005, “Interface Waves Between Two Piezoelectric Half-Spaces With a Semiconductor Film
,” J. Zhejiang Univ., Sci.
1009-3095, 6A
, pp. 90
–96
.123.
Yang
, J. S.
, Yang
, X. M.
, and Turner
, J. A.
, 2004, “Amplification of Acoustic Waves in Laminated Piezoelectric Semiconductor Plates
,” Arch. Appl. Mech.
0939-1533 74
, pp. 288
–298
.124.
Yang
, J. S.
, Yang
, X. M.
, and Turner
, J. A.
, 2004, “Amplification of Acoustic Waves in Piezoelectric Semiconductor Shells
,” Proc. International Conference on Heterogeneous Material Mechanics
, Chongqing, China, June 21
–26
, pp. 258
–261
.125.
Yang
, J. S.
, 2004, “A Semi-Infinite Anti-Plane Crack in a Piezoelectric Semiconductor
,” Int. J. Fract.
0376-9429, 130
, pp. L169
–L174
.126.
de Lorenzi
, H. G.
, and Tiersten
, H. F.
, 1975, “On the Interaction of the Electromagnetic Field With Heat Conducting Deformable Semiconductors
,” J. Math. Phys.
0022-2488, 16
, pp. 938
–957
.127.
Tiersten
, H. F.
, 1984, “Electric Fields, Deformable Semiconductors and Piezoelectric Devices
,” The Mechanical Behavior of Electromagnetic Solid Continua
, G. A.
Maugin
, ed., North-Holland
, Amsterdam
, pp. 99
–113
.128.
Ancona
, M. G.
, and Tiersten
, H. F.
, 1980, “Fully Macroscopic Description of Bounded Semiconductors With an Application to the Si-SiO2 Interface
,” Phys. Rev. B
0163-1829, 22
, pp. 6014
–6119
.129.
Ancona
, M. G.
, and Tiersten
, H. F.
, 1983, “Fully Macroscopic Description of Electrical Conduction in Metal-Insulator-Semiconductor Structures
,” Phys. Rev. B
0163-1829, 27
, pp. 7018
–7045
.130.
McCarthy
, M. F.
, and Tiersten
, H. F.
, 1976, “One-Dimensional Acceleration Waves and Acoustoelectric Domains in Piezoelectric Semiconductors
,” J. Appl. Phys.
0021-8979, 47
, pp. 3389
–3396
.131.
McCarthy
, M. F.
, and Tiersten
, H. F.
, 1977, “Shock Waves and Acoustoelectric Domains in Piezoelectric Semiconductors
,” J. Appl. Phys.
0021-8979, 48
, pp. 159
–166
.132.
McCarthy
, M. F.
, 1984, “Nonlinear Wave Propagation in Electroelastic Semiconductors
,” The Mechanical Behavior of Electromagnetic Solid Continua
, G. A.
Maugin
, ed., North-Holland
, Amsterdam
, pp. 121
–127
.133.
Maugin
, G. A.
, and Daher
, N.
, 1986, “Phenomenological Theory of Elastic Semiconductors
,” Int. J. Eng. Sci.
0020-7225, 24
, pp. 703
–731
.134.
Daher
, N.
, and Maugin
, G. A.
, 1988, “Nonlinear Electroacoustic Equations in Semiconductors With Interfaces (Relation Between the Macroscopic and the Quasi-Microscopic Descriptions)
,” Int. J. Eng. Sci.
0020-7225, 26
, pp. 37
–58
.135.
Daher
, N.
, 1984, “Waves in Elastic Semiconductors in a Bias Electric Field
,” The Mechanical Behavior of Electromagnetic Solid Continua
, G. A.
Maugin
, ed., North-Holland
, Amsterdam
, pp. 115
–120
.136.
Daher
, N.
, and Maugin
, G. A.
, 1986, “Waves in Elastic Semiconductors in a Bias Electric Field
,” Int. J. Eng. Sci.
0020-7225, 24
, pp. 733
–754
.137.
Daher
, N.
, and Maugin
, G. A.
, 1988, “Bulk Waves in Elastic Semiconductors in the Presence of an Initial State
,” Int. J. Eng. Sci.
0020-7225, 26
, pp. 993
–1012
.138.
Verma
, P. D. S.
, Rana
, O. H.
, and Verma
, M.
, 1988, “Radial Oscillations of an Elastic Semiconductor
,” Int. J. Eng. Sci.
0020-7225, 26
, pp. 27
–36
.139.
Burdess
, J. S.
, Harris
, A. J.
, Cruickshank
, J.
, Wood
, D.
, and Cooper
, G.
, 1994, “A Review of Vibratory Gyroscopes
,” Eng. Sci. Educ. J.
0963-7346, 3
, pp. 249
–254
.140.
Soderkvist
, J.
, 1994, “Micromachined Gyroscopes
,” Sens. Actuators, A
0924-4247, 43
, pp. 65
–71
.141.
Loveday
, P. W.
, 1999, “Analysis and Compensation of Imperfection Effects in Piezoelectric Vibratory Gyroscopes
,” Ph.D. dissertation, Virginia Polytechnic Institute and State University.142.
Fang
, H. Y.
, 2000, “Vibrations of a Rotating Piezoelectric Body and Applications in Gyroscopes
,” Ph.D. dissertation, University of Nebraska-Lincoln.143.
Baumhauer
, J. C.
, and Tiersten
, H. F.
, 1973, “Nonlinear Electroelastic Equations for Small Fields Superposed on a Bias
,” J. Acoust. Soc. Am.
0001-4966, 54
, pp. 1017
–1034
.144.
Tiersten
, H. F.
, 1971, “On the Nonlinear Equations of Thermo-Electroelasticity
,” Int. J. Eng. Sci.
0020-7225, 9
, pp. 587
–604
.145.
Gates
, W. D.
, 1968, “Vibrating Angular Rate Sensor May Threaten the Gyroscope
,” Electronics
0013-5070, 41
, pp. 130
–134
.146.
Chou
, C. S.
, Yang
, J. W.
, Hwang
, Y. C.
, and Yang
, H. J.
, 1991, “Analysis on Vibrating Piezoelectric Beam Gyroscope
,” Int. J. Appl. Electromagn. Mater.
0925-2096, 2
, pp. 227
–241
.147.
Fang
, H. Y.
, and Yang
, J. S.
, 2001, “Analysis of a Beam Piezoelectric Gyroscope
,” Applied Electromagnetics and Mechanics
, T.
Takagi
and M.
Uesaka
, eds., Tokyo
, pp. 445
–446
.148.
Fang
, H. Y.
, and Yang
, J. S.
, 2001, “Vibration Analysis of a Rotating Elastic Beam With Piezoelectric Films as an Angular Rate Sensor
,” Proc., IEEE International Frequency Control Symp.
, pp. 507
–513
, June 6–8, Seattle.149.
Soderkvist
, J.
, 1990, “Piezoelectric Beams and Angular Rate Sensors
,” Proc. IEEE Forty-Fourth Annual Symp. on Frequency Control
, pp. 406
–415
, May 23–25, Baltimore.150.
Soderkvist
, J.
, 1991, “Piezoelectric Beams and Vibrating Angular Rate Sensors
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 38
, pp. 271
–280
, May 29–31, Los Angeles.151.
Yang
, J. S.
, 1998, “Some Analytical Results on Piezoelectric Gyroscopes
,” Proc. IEEE Int. Frequency Symp.
, pp. 733
–741
, May 27–29, Pasadena.152.
Yang
, J. S.
, and Fang
, H. Y.
, 2002, “Analysis of a Rotating Elastic Beam With Piezoelectric Films as an Angular Rate Sensor
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 49
, pp. 798
–804
.153.
Yang
, J. S.
, Fang
, H. Y.
, and Jiang
, Q.
, 1999, “Analysis of a Ceramic Bimorph Piezoelectric Gyroscope
,” Int. J. Appl. Electromagn. Mech.
1383-5416, 10
, pp. 459
–473
.154.
Yang
, J. S.
, Fang
, H. Y.
, and Jiang
, Q.
, 2000, “Analysis of a Few Piezoelectric Gyroscopes
,” Proc. IEEE/EIA Int. Frequency Control Symp. and Exhibition
, pp. 79
–86
, June 7–9, Kansas City.155.
Abe
, H.
, Yoshida
, T.
, and Turuga
, K.
, 1992, “Piezoelectric-Ceramic Cylinder Vibratory Gyroscope
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 31
, pp. 3061
–3063
.156.
Fujishima
, S.
, Nakamura
, T.
, and Fujimoto
, K.
, 1991, “Piezoelectric Vibratory Gyroscope Using Flexural Vibration of a Triangular Bar
,” Proc. IEEE 45th Annual Symp on Frequency Control
, pp. 261
–265
, May 29–31, Los Angeles.157.
Yang
, J. S.
, and Fang
, H. Y.
, 2003, “A New Ceramic Tube Piezoelectric Gyroscope
,” Sens. Actuators, A
0924-4247, 107
, pp. 42
–49
.158.
Bel
, O.
, and Bourquin
, R.
, 2001, “Effect of Geometrical Electrodes Defects on the Bias and Sensitivity of Tuning Fork Angular Rate Sensor
,” Proc. IEEE Int. Frequency Control Symp.
, pp. 502
–506
, June 6–8, Seattle.159.
Kudo
, S.
, 1998, “Consideration on Temperature Characteristics of Sensitivity in Quartz Tuning Fork Gyroscope
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 37
, pp. 2872
–2873
.160.
Kudo
, S.
, 2001, “Consideration of Figure of Merit of Piezoelectric Vibratory Gyroscope Using Charge Sensitivity
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 40
, pp. 3688
–3692
.161.
Kudo
, S.
, Sugawara
, S.
, and Wakatuki
, N.
, 1996, “Finite Element Analysis of Single Crystal Tuning Forks for Gyroscopes
,” Proc. IEEE Frequency Control Symp.
, pp. 640
–647
, June 5–7, Honolulu.162.
Kudo
, S.
, Konno
, M.
, Sugawara
, S.
, and Yoshida
, T.
, 1993, “Vibrational Analysis of Tuning Fork Gyroscope With Orthogonal Arms
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 32
, pp. 2310
–2313
.163.
Kudo
, S.
, 1997, “Finite Element Analysis of Mechanical Couplings in a Tuning Fork Gyroscope
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 36
, pp. 3028
–3029
.164.
Ulitiko
, I. A.
, 1995, “Mathematical Theory of the Fork-Type Wave Gyroscope
,” Proc. IEEE Frequency Control Symp.
, pp. 786
–793
, May 31–June 2, San Francisco.165.
Wakatsuki
, N.
, and Tanaka
, H.
, 1997, “Finite Element Method Analysis of Single Crystal Tuning Fork Gyroscope for Suppression of its Inner Leakage Coupling
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 36
, pp. 3037
–3040
.166.
Yachi
, M.
, Ishikawa
, H.
, and Satoh
, Y.
, 1998, “Design Methodology of Single Crystal Tuning Fork Gyroscope for Automotive Applications
,” Proc. IEEE Int Ultrasonics Symp.
, pp. 463
–466
, Oct. 5–8, Sendai, Japan.167.
Ishida
, N.
, and Tomikawa
, Y.
, 1999, “Basic Considerations of Trident Type Tuning Fork Accelerometers Using Corioils Force Phenomenon
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 38
, pp. 3228
–3232
.168.
Satoh
, A.
, Ohnishi
, K.
, Sakurai
, K.
, and Tomikawa
, Y.
, 1995, “Finite-Element Analysis of Trident-Type Tuning Fork Resonator for Vibratory Gyroscope
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 34
, pp. 2604
–2609
.169.
Ono
, K.
, Yachi
, M.
, and Wakatsuki
, N.
, 2001, “H-Type Single Crystal Piezoelectric Gyroscope of an Oppositely Polarized LiNbO3 Plate
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 40
, pp. 3699
–3703
.170.
Rodamaker
, M.
, and Newell
, C. R.
, 1989, “Finite Element Analysis of a Quartz Angular Rate Sensor
,” ANSYS Conference Proceedings
, No. 3.35–48, May 1–5, Pittsburgh.171.
Tanaka
, H.
, and Wakatsuki
, N.
, 1998, “Electromechanical Coupling Coefficients for a New H-Type LiTaO3 Piezoelectric Gyroscope
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 37
, pp. 2868
–2871
.172.
Yang
, J. S.
, and Fang
, H. Y.
, 2003, “A Piezoelectric Gyroscope Based on Extensional Vibrations of Rods
,” Int. J. Appl. Electromagn. Mech.
1383-5416, 17
, pp. 289
–300
.173.
Kagawa
, Y.
, Tsuchiya
, T.
, and Kawashima
, T.
, 1996, “Finite Element Simulation of Piezoelectric Vibrator Gyroscopes
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 43
, pp. 509
–518
.174.
Yang
, J. S.
, Fang
, H. Y.
, and Jiang
, Q.
, 2001, “One-Dimensional Equations for a Piezoelectric Ring and Applications in a Gyroscope
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 48
, pp. 1275
–1282
.175.
Burdess
, J. S.
, and Wren
, T.
, 1986, “The Theory of a Piezoelectric Disk Gyroscope
,” IEEE Trans. Aerosp. Electron. Syst.
0018-9251, 22
, pp. 410
–418
.176.
Reese
, G. M.
, Marek
, E. L.
, and Lobitz
, D. W.
, 1989, “Three-Dimensional Finite Element Calculations of an Experimental Quartz Resonator Sensor
,” Proc. IEEE Ultrasonics Symp.
, pp. 419
–422
, Oct. 3–6, Montréal.177.
Abe
, H.
, Yoshida
, T.
, Ishikawa
, T.
, Miyazaki
, N.
, and Watanabe
, H.
, 1998, “Trapped Energy Gyroscopes Using Thickness Shear Vibrations in Partially Polarized Piezoelectric Ceramic Plate
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 37
, pp. 5345
–5348
.178.
Ryoo
, H.
, Lee
, Y.
, and Roh
, Y.
, 1997, “Design and Fabrication of a Dual Axial Gyroscope With Piezoelectric Ceramics
,” Proc. IEEE Frequency Control Symp.
, pp. 189
–195
, May 28–30, Orlando.179.
Burdess
, J. S.
, 1986, “The Dynamics of a Thin Piezoelectric Cylinder Gyroscope
,” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci.
0263-7154, 200
, pp. 271
–280
.180.
Langdon
, R. M.
, 1982, “The Vibrating Cylinder Gyro
,” The Maconi Review, pp. 231
–249
.181.
Fox
, C. H. J.
, 1988, “Vibrating Cylinder Rate Gyro: Theory of Operation and Error Analysis
,” Proc Symp Gyro Technology
, Stuttgart, Germany
, pp. 5.0
–5.23
.182.
Loveday
, P. W.
1996, “A Coupled Electromechanical Model of an Imperfect Piezoelectric Vibrating Cylinder Gyroscope
,” J. Intell. Mater. Syst. Struct.
1045-389X, 7
, pp. 44
–53
.183.
Loveday
, P. W.
, and Rogers
, C. A.
, 1998, “Modification of Piezoelectric Vibratory Gyroscope Resonator Parameters by Feedback Control
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 45
, pp. 1211
–1215
.184.
Yang
, J. S.
, 1997, “A Circular Cylindrical Shell Piezoelectric Gyroscope
,” Int. J. Appl. Electromagn. Mech.
1383-5416, 8
, pp. 259
–271
.185.
Yang
, J. S.
, Fang
, H. Y.
, and Jiang
, Q.
, 2000, “A Vibrating Piezoelectric Ceramic Shell as a Rotation Sensor
,” Smart Mater. Struct.
0964-1726, 9
, pp. 445
–451
.186.
Yang
, J. S.
, 1996, “Analysis of Ceramic Thickness Shear Piezoelectric Gyroscopes
,” Proc. IEEE Ultrasonics Symp.
, pp. 909
–912
, Nov. 3–6, Antonio.187.
Yang
, J. S.
, 1997, “Analysis of Ceramic Thickness Shear Piezoelectric Gyroscopes
,” J. Acoust. Soc. Am.
0001-4966, 102
, pp. 3542
–3548
.188.
Cohen
, H.
, and Muncaster
, R. G.
, 1988, The Theory of Pseudo-Rigid Bodies
, Springer
, New York
, pp. 89
–120
.189.
Yang
, J. S.
, Fang
, H. Y.
, and Jiang
, Q.
, 1999, “Equations for a Piezoelectric Parallelepiped and Applications in a Gyroscope
,” Int. J. Appl. Electromagn. Mech.
1383-5416, 10
, pp. 337
–350
.190.
Yang
, J. S.
, Fang
, H. Y.
, and Jiang
, Q.
, 1999, “Analysis of a Plate Piezoelectric Gyroscope by Equations for a Piezoelectric Parallelepiped
,” Proc. Joint Meeting EFTF—IEEE IFCS
, pp. 433
–437
, April 13–16, Besancon, France.191.
Fang
, H. Y.
, Yang
, J. S.
, and Jiang
, Q.
, 2000, “Analysis of a Quartz Plate Thickness-Shear Piezoelectric Gyroscope
,” Mechanics of Electromagnetic Materials and Structures
, J. S.
Yang
and G. A.
Maugin
, eds., IOS Press
, pp. 159
–172
, Amsterdam.192.
Tiersten
, H. F.
, Stevens
, D. S.
, and Das
, P. K.
, 1980, “Acoustic Surface Wave Accelerometer and Rotation Rate Sensor
,” Proc IEEE Ultrasonics Symp.
, pp. 692
–695
, Nov. 5–7, Boston.193.
Lao
, B. Y.
, 1980, “Gyroscopic Effect in Surface Acoustic Waves
,” Proc. IEEE Ultrasonics Symp.
, pp. 687
–691
, Nov. 5–7, Boston.194.
Wren
, T.
, and Burdess
, J. S.
, 1987, “Surface Waves Perturbed by Rotation
,” J. Appl. Mech.
0021-8936, 54
, pp. 464
–466
.195.
Clarke
, N. S.
, and Burdess
, J. S.
, 1994, “A Rotation Rate Sensor Based Upon a Rayleigh Resonator
,” J. Appl. Mech.
0021-8936, 61
, pp. 139
–143
.196.
Clarke
, N. S.
, and Burdess
, J. S.
, 1994, “Rayleigh Waves on a Rotating Surface
,” J. Appl. Mech.
0021-8936 61
, pp. 724
–726
.197.
Destrade
, M.
, 2004, “Rayleigh Waves in Anisotropic Crystals Rotating About the Normal to a Symmetry Plane
,” J. Appl. Mech.
0021-8936, 77
, pp. 516
–520
.198.
Destrade
, M.
, 2004, “Surface Acoustic Waves in Rotating Orthorhombic Crystals
,” Proc. R. Soc. London, Ser. A
1364-5021, 460
, pp. 653
–665
.199.
Ting
, T. C. T.
, 2004, “Surface Waves in a Rotating Anisotropic Elastic Half-Space
,” Wave Motion
0165-2125, 40
, pp. 329
–346
.200.
Fang
, H. Y.
, Yang
, J. S.
, and Jiang
, Q.
, 1999, “Gyroscopic Effect in Surface Piezoelectric Waves
,” Proc IEEE Ultrasonics Symp.
, pp. 497
–500
.201.
Fang
, H. Y.
, Yang
, J. S.
, and Jiang
, Q.
, 2000, “Rotation Perturbed Surface Acoustic Waves Propagating in Piezoelectric Crystals
,” Int. J. Solids Struct.
0020-7683, 37
, pp. 4933
–4947
.202.
Fang
, H. Y.
, Yang
, J. S.
, and Jiang
, Q.
, 2001, “Surface Waves Propagating Over a Rotating Piezoelectric Half-Space
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, 48
, pp. 998
–1004
.203.
Zhou
, Y.-H.
, and Jiang
, Q.
, 2001, “Effects of Coriolis Force and Centrifugal Force on Acoustic Waves Propagating Along the Surface of a Piezoelectric Half-Space
,” ZAMP
0044-2275, 52
, pp. 950
–965
.204.
Tiersten
, H. F.
, Stevens
, D. S.
, and Das
, P. K.
, 1981, “Circulating Flexural Wave Rotation Rate Sensor
,” Proc IEEE Ultrasonics Symp.
, pp. 163
–166
, Oct. 14–16, Chicago.205.
Yang
, J. S.
, Fang
, H. Y.
, and Jiang
, Q.
, 1998, “Thickness Vibrations of Rotating Piezoelectric Plates
,” J. Acoust. Soc. Am.
0001-4966, 104
, pp. 1427
–1435
.206.
Kosinski
, J. A.
, Pastore
, R. A.
, Jr., Fang
, H. Y.
, and Yang
, J. S.
, 2001, “Thickness Vibrations of a Rotating AT-Cut Quartz Plate
,” Proc. IEEE Int. Ultrasonics Symp.
, pp. 795
–798
, Oct. 7–10, Atlanta.207.
Fang
, H. Y.
, Yang
, J. S.
, and Jiang
, Q.
, 2002, “Rotation Sensitivity of Waves Propagating in a Rotating Piezoelectric Plate
,” Int. J. Solids Struct.
0020-7683, 39
, pp. 5241
–5251
.208.
Wauer
, J.
, 1999, “Waves in Rotating Conducting Piezoelectric Media
,” J. Acoust. Soc. Am.
0001-4966, 106
, pp. 626
–636
.209.
Wauer
, J.
, 1997, “Wave Propagation in Rotating Thermo-Piezoelectric Solids
,” Modern Practice in Stress and Vibration Analysis
, M. D.
Gilchrist
, ed., Balkema
, Rotterdam
, pp. 127
–134
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
