Title :
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.
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;
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
Print_ISBN :
0-7803-5400-1
DOI :
10.1109/FREQ.1999.840815
