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)).

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
.
You do not currently have access to this content.