Vibration modes of piezoelectric plates with small spatial thickness variation

Author

Nowotny, Helga ; Finger, N. ; Groschl, M.

Author_Institution

Inst. fur Theor. Phys., Wien Univ. of Technol.

Volume

1

fYear

1999

fDate

1999

Firstpage

501

Abstract

A general perturbation treatment is used to obtain the frequency spectrum and the modes of vibration for an electrically driven piezoelectric plate with small thickness variation in lateral direction. For all piezoelectric materials the coefficients of the differential equation for the displacement function are determined by the eigenvectors of the zero order solution without any assumptions about specific material properties, Considering in detail a plano-convex resonator, we obtain solutions of well known structure (quasiharmonic overtone modes described by harmonic oscillator functions). Frequency spectra calculated with the above method are in good agreement with measured and calculated spectra from literature

Keywords

crystal resonators; eigenvalues and eigenfunctions; partial differential equations; perturbation theory; piezoelectric oscillations; vibrations; 3D equations; boundary conditions; differential equation; dispersion relations; displacement function; eigenvectors; electrically driven plate; first order corrections; frequency spectrum; harmonic oscillator functions; linear piezoelectricity; perturbation treatment; piezoelectric plates; plano-convex resonator; quasiharmonic overtone modes; shape function; small spatial thickness variation; vibration modes; zero order solution; Differential equations; Distribution functions; Electric potential; Electrodes; Fingers; Frequency measurement; Material properties; Oscillators; Piezoelectric materials; Vibrations;

fLanguage

English

Publisher

ieee

Conference_Titel

Frequency and Time Forum, 1999 and the IEEE International Frequency Control Symposium, 1999., Proceedings of the 1999 Joint Meeting of the European

Conference_Location

Besancon

ISSN

1075-6787

Print_ISBN

0-7803-5400-1

Type

conf

DOI

10.1109/FREQ.1999.840815

Filename

840815