Summary
A set of two-dimensional equations for electroelastic plates in nonlinear face-shear motion are derived from the three-dimensional equations of nonlinear electroelasticity. The equations can describe the nonlinearity due to moderately large in-plane shear deformation associated with face-shear modes. The equations are used to study nonlinear face-shear vibration of a plate of 6mm crystals.
Similar content being viewed by others
References
Tiersten H. F. and Mindlin R. D. (1962). Forced vibrations of piezoelectric crystal plates. Qu. J. App. Math. XX: 107–119
Mindlin R. D. (1972). High frequency vibrations of piezoelectric crystal plates. Int. J. Solids Struct. 8: 895–906
Lee P. C. Y., Syngellakis S. and Hou J. P. (1987). A two-dimensional theory for high-frequency vibrations of piezoelectric plates with or without electrodes. J. Appl. Phys. 61: 1249–1262
Mindlin R. D. (1984). Frequencies of piezoelectrically forced vibrations of electroded, doubly rotated, quartz plates. Int. J. Solids Struct. 20: 141–157
Yu Y.-Y. (1996). Vibrations of elastic plates. Springer, New York
Yang J. S. (1999). Equations for the extension and flexure of electroelastic plates under strong electric fields. Int. J. Solids Struct. 36: 3171–3192
Yang J. S., Yang X. M., Turner J. A. and Kosinski J. A. (2003). Two-dimensional equations for electroelastic plates with relatively large shear deformations. IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 50: 765–772
Yang, J. S.: Coupling to extension in a thickness-shear resonator due to relatively large thickness-shear deformation. IEEE Trans. Ultrason., Ferroelect., Freq. Contr. (Accepted)
Adler E. L. (1989). Electromechanical coupling to Lamb and shear-horizontal modes in piezoelectric plates. IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 36: 223–230
Wang Z., Jen C. K. and Cheek J. D. N. (1994). Mass sensitivity of shear horizontal waves in three-layer plate sensors. IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 41: 397–401
Zaitsev B., Joshi S. G. and Kuznetsova I. E. (1999). Propagation of QSH (quasi shear horizontal) acoustic waves in piezoelectric plates. IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 46: 1298–1302
Tiersten H. F. (1971). On the nonlinear equations of thermo-electroelasticity. Int. J. Engng. Sci. 9: 587–604
Tiersten H. F. (1995). On the accurate description of piezoelectric resonators subject to biasing deformations. Int. J. Engng. Sci. 33: 2239–2259
Tiersten H. F. (1975). Analysis of intermodulation in thickness-shear and trapped energy resonators. J. Acoust. Soc. Am. 57: 667–681
Yang J. S. and Batra R. C. (1995). Mixed variational principles in nonlinear electroelasticity. Int. J. Nonlinear Mech. 30: 719–725
Tiersten H. F. (1969). Linear piezoelectric plate vibrations. Plenum, New York
Nelson D. F. (1979). Electric, Optic and acoustic interactions in crystals, Wiley, New York, 511
Eringen A. C. (1980). Mechanics of continua. Huntington. Krieger, New York
Nayfeh A. H. (1981). Introduction to perturbation techniques. John Wiley & Sons, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, J. Two-dimensional equations for electroelastic plates with relatively large in-plane shear deformation and nonlinear mode coupling in resonant piezoelectric devices. Acta Mech 196, 103–111 (2008). https://doi.org/10.1007/s00707-007-0494-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-007-0494-0