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Abstract

Nonlinear differential equations and boundary conditions in small-field variables, for small fields superposed on large static biasing stages, are obtained from general invariant nonlinear electroelastic equations. The influence of a prestress (six independent tensor coefficients) on Surface Acoustic Waves (SAW) velocity is analyzed. The biasing stress tensor is involved directly into equations of motion, and the linearization about the static state is done. Change of the mass density as well as the effective elastic constants of the piezoelectric substrate as a consequence of a prestress is taken into account. Numerical results, given SAW velocity on the prestressed substrate for different direction of stress and wave propagation are obtained for lithium niobate.

Developed theory and numerical program may be useful in analyzing and designing SAW sensors of temperature, pressure, acceleration or force.

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References

Prager

, Introduction to Mechanics of Continua (New York, 1961).

Eringen

A.C.

, Nonlinear Theory of Continuous Media (New York, 1962).

Baumhauer

J.C.

and Tiersten

H.F.

, Nonlinear elec-troelastic equation for small fields superposed on a bias, J. Ac. Soc. Am. 54 (1973) 1017–1034.

Nakagawa

, Yamanouchi

and Shibayama

, Third-order elastic constants of Lithium Niobate J. Appl. Phys. 44 (1975) 3969–3974.

Cullen

D.E.

and Reeder

T.M.

, Measurement of SAW velocity versus strain for YX and ST quartz, 1975 Ultrasonic Symposium Proceedings, p. 519.

Nalamwar

A.L.

and Epstein

, SAW in strained media, J. Appl. Phys. 47 (1976) 43–48.

Tiersten

H.F.

, Perturbation theory for linear electroelastic equations for small fields superposed on a bias, J. Ac. Soc. Am. 64 (1978) 832–837.

Oliner

A.A.

, Acoustic surface waves, in: Topics in Appl. Phys. ser., Vol. 24 (Springer Verlag, New York, 1978).

Sinha

B.K.

and Tiersten

H.F.

, On the influence of flexural biasing state on the velocity of piezoelectric surface waves, Wave Motion 1 (1979) 37–51.

10.

Nelson

D.F.

, Theory of nonlinear electroacoustics of dielectric, piezoelectric, and pyroelectric crystals, J. Ac. Soc. Am. 63 (1978) 1738–1748.

11.

Tiersten

H.F.

and Sinha

B.K.

, A perturbation analysis of the attenuation and dispersion of surface waves, J. Appl. Phys. 49 (1978) 87–95.

12.

Hauden

, Plant

and Gagnepain

J.J.

, Nonlinear properties of SAW: applications to oscillators and sensors, IEEE Trans. SU 28 (1981) 342–348.

13.

Maugin

G.A.

, Nonlinear Electromechanical Effects and Applications (World Scientific, Singapore 1985).

14.

Morgan

D.P.

, Surface-Wave Devices for Signal Processing (Elsevier, New York, 1985).

15.

Bigler

, Coquerel

and Hauden

, Temperature and stress sensitivities of SAW quartz cuts, 1987 Ultras. Symp. Proc, pp. 285–288.

16.

Filler

R.L.

, The acceleration sensitivity of quartz crystal oscillators: a review, IEEE Trans UFFC 35 (1988) 297–305.

17.

Tiersten

H.F.

and Shick

D.V.

, An analysis of the normal acceleration sensitivity of contoured quartz resonators rigidly supported along the edges, 1988 Ultras. Symp. Proc, pp. 357–363.

18.

Maugin

G.A.

, Continuum Mechanics of Electromagnetic Solids (North-Holland, 1988).

19.

Danicki

and Czerwinska

, SAW parameters in piezoelectric crystals, Inst. Fund. Techn. Res. Reports 18/1988 (in Polish).

20.

Bigler

, Theobald

and Hauden

, Stress-sensitivity mapping for SAW on quartz, IEEE Trans. UFFC 36 (1989) 57–62.

21.

Gafka

and Tani

, Parametric constitutive equations for electroelastic crystals upon electrical or mechanical bias, in print, J. Appl. Phys. (to appear).

Surface Acoustic Waves Propagation in Stressed Media-Force Sensor *

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