The propagation of surface acoustic waves in a rotating anisotropic crystal is studied. The crystal is monoclinic and cut along a plane containing the normal to the symmetry plane; this normal is also the axis of rotation. The secular equation is obtained explicitly using the “method of the polarization vector,” and it shows that the wave is dispersive and decelerates with increasing rotation rate. The case of orthorhombic symmetry is also treated. The surface wave speed is computed for 12 monoclinic and 8 rhombic crystals, and for a large range of the rotation rate/wave frequency ratio.

1.
Reindl
,
L.
,
Scholl
,
G.
,
Ostertag
,
T.
,
Scherr
,
H.
,
Wolff
,
U.
, and
Schmidt
,
F.
,
1998
, “
Theory and Application of Passive SWA Radio Transponders as Sensors
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
,
45
, pp.
1281
1292
.
2.
Pohl
,
A.
,
Ostermayer
,
G.
,
Reindl
,
L.
, and
Seifert
,
F.
,
1997
, “
Monitoring the Tire Pressure at Cars Using Passive SWA Sensors
,”
IEEE Ultrasonics Symposium
,
1
, pp.
471
474
.
3.
Pohl
,
A.
,
Steindl
,
R.
, and
Reindl
,
L.
,
1999
, “
The ‘Intelligent Tire’ Utilizing Passive SWA Sensors—Measurement of Tire Friction
,”
IEEE Trans. Instrum. Meas.
,
48
, pp.
1041
1046
.
4.
Clarke
,
N. S.
, and
Burdess
,
J. S.
,
1994
, “
A Rotation Rate Sensor Based Upon a Rayleigh Resonator
,”
ASME J. Appl. Mech.
,
61
, pp.
139
143
.
5.
Clarke
,
N. S.
, and
Burdess
,
J. S.
,
1994
, “
Rayleigh Waves on a Rotating Surface
,”
ASME J. Appl. Mech.
,
61
, pp.
724
726
.
6.
Fang
,
H.
,
Yang
,
J.
, and
Jiang
,
Q.
,
2000
, “
Rotation Perturbed Surface Acoustic Waves Propagating in Piezoelectric Crystals
,”
Int. J. Solids Struct.
,
37
, pp.
4933
4947
.
7.
Grigor’evskii˘
,
V. I.
,
Gulyaev
,
Yu. V.
, and
Kozlov
,
A. I.
,
2000
, “
Acoustic Waves in a Rotating Elastic Medium
,”
Acoust. Phys.
,
46
, pp.
236
238
.
8.
Collet, B., 2003, “Gyroscopic Effect on Surface Acoustic Waves in Anisotropic Solid Media,” Proceedings of the 5th World Congress on Ultrasonics, pp. 991–995.
9.
Jose
,
K. A.
,
Suh
,
W. D.
,
Xavier
,
P. B.
,
Varadan
,
V. K.
, and
Varadan
,
V. V.
,
2002
, “
Surface Acoustic Wave MEMS Gyroscope
,”
Wave Motion
,
36
, pp.
367
381
.
10.
Jahangir
,
E.
, and
Howe
,
R. M.
,
1993
, “
Time-Optimal Attitude Control Scheme for a Spinning Missile
,”
J. Guid. Control Dyn.
,
16
, pp.
346
353
.
11.
Schoenberg
,
M.
, and
Censor
,
D.
,
1973
, “
Elastic Waves in Rotating Media
,”
Q. Appl. Math.
,
31
, pp.
115
125
.
12.
Ting, T. C. T., 1996, Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York.
13.
Chadwick
,
P.
, and
Wilson
,
N. J.
,
1992
, “
The Behavior of Elastic Surface Waves Polarized in a Plane of Material Symmetry, II. Monoclinic Media
,”
Proc. R. Soc. London, Ser. A
,
438
, pp.
207
223
.
14.
Destrade
,
M.
,
2001
, “
The Explicit Secular Equation for Surface Acoustic Waves in Monoclinic Elastic Crystals
,”
J. Acoust. Soc. Am.
,
109
, pp.
1398
1402
.
15.
Stroh
,
A. N.
,
1962
, “
Steady State Problems in Anisotropic Elasticity
,”
J. Math. Phys.
,
41
, pp.
77
103
.
16.
Ingebrigsten
,
K. A.
, and
Tonning
,
A.
,
1969
, “
Elastic Surface Waves in Crystal
,”
Phys. Rev.
,
184
, pp.
942
951
.
17.
Ting
,
T. C. T.
,
2002
, “
Explicit Secular Equations for Surface Waves in Monoclinic Materials With the Symmetry Plane at x1=0, x2=0 or x3=0,
Proc. R. Soc. London, Ser. A
,
A458
, pp.
1017
1031
.
18.
Currie
,
P. K.
,
1979
, “
The Secular Equation for Rayleigh Waves on Elastic Crystals
,”
Q. J. Mech. Appl. Math.
,
32
, pp.
163
173
.
19.
Taziev
,
R. M.
,
1989
, “
Dispersion Relation for Acoustic Waves in an Anisotropic Elastic Half-Space
,”
Sov. Phys. Acoust.
,
35
, pp.
535
538
.
20.
Ting
,
T. C. T.
,
2004
, “
The Polarization Vector and Secular Equation for Surface Waves in an Anisotropic Elastic Half-Space
,”
Int. J. Solids Struct.
,
41
, pp.
2065
2083
.
21.
Destrade
,
M.
,
2004
, “
Surface Waves in Rotating Rhombic Crystals
,”
Proc. R. Soc. London, Ser. A
,
460
, pp.
653
665
.
22.
Destrade
,
M.
,
2004
, “
Explicit Secular Equation for Scholte Waves Over a Monoclinic Crystal
,” J. Sound Vib., to appear.
23.
Barnett
,
D. M.
, and
Lothe
,
J.
,
1973
, “
Synthesis of the Sextic and the Integral Formalism for Dislocations, Green’s Function, and Surface Wave (Rayleigh Wave) Solutions in Anisotropic Elastic Solids
,”
Phys. Norv.
,
7
, pp.
13
19
.
24.
Shutilov, V., 1988, Fundamental Physics of Ultrasound, Gordon and Breach, New York.
25.
Destrade
,
M.
,
2003
, “
Rayleigh Waves in Symmetry Planes of Crystals: Explicit Secular Equations and Some Explicit Wave Speeds
,”
Mech. Mater.
,
35
,
931
939
.
26.
Mozhaev, V. G., 1995, “Some New Ideas in the Theory of Surface Acoustic Waves in Anisotropic Media,” IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solids, D. F. Parker and A. H. England, eds., Kluwer, Dordrecht, The Netherlands, pp. 455–462.
27.
Furs
,
A. N.
,
1997
, “
Covariant Form of the Dispersion Equation for Surface Acoustic Waves in Symmetry Planes of Crystals
,”
Crystallogr. Rep.
,
4
, pp.
196
201
.
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