Journal ArticleDOI
Analysis of trapped‐energy resonators operating in overtones of coupled thickness‐shear and thickness‐twist
Reads0
Chats0
TLDR
In this article, the equations of three-dimensional linear piezoelectricity were applied in the analysis of trapped energy resonators with rectangular electrodes vibrating in coupled thickness shear and thickness twist in the vicinity of the fundmantal and odd overtone thickness-shear frequencies.Abstract:
The equations of three‐dimensional linear piezoelectricity are applied in the analysis of trapped‐energy resonators with rectangular electrodes vibrating in coupled thickness shear and thickness twist in the vicinity of the fundmantal and odd overtone thickness‐shear frequencies. Closed form asymptotic expressions for the frequency wave‐number dispersion relations for the fundamental and odd overtone coupled thickness‐shear and thickness‐twist waves near cutoff are obtained for both the electroded and unelectroded regions of the trapped‐energy resonator. The influence of piezoelectric stiffening, electrode mass loading, and electrical shorting is included in the analysis. Simple approximate boundary conditions at a junction between an electroded and unelectroded region of the plate are obtained in a manner exhibiting the natural limitations inherent in the approximation. In order that these boundary conditions can be satisfied at each such junction, in the adjacent regions the wave numbers in the direction of the junction line are assumed to be the same. The boundary conditions to be satisfied at the junctions between the unelectroded corner region and the unelectroded regions adjacent to the electroded region are obtained from an extended version of the variational principle of linear piezoelectricity. These latter conditions result in the form of the solution in the corner region. One result of the foregoing analysis is the determination of a two‐dimensional condition which is a generalization of Bechmann’s number in one dimension. The above‐mentioned dispersion relations and edge conditions are applied in the analysis of the steady‐state vibrations of a trapped‐energy resonator and a lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained.Subject Classification: [43]40.24; [43]85.52, [43]85.32.read more
Citations
More filters
Journal ArticleDOI
Higher-Order Theories of Piezoelectric Plates and Applications
Ji Wang,Jiashi Yang +1 more
TL;DR: A review article summarizes the development of higher order theories for the dynamic analysis of piezoelectric plates, and describes their applications, especially for crystal resonators as mentioned in this paper, where the displacement components and electric potential are assumed to vary through the plate thickness.
Journal ArticleDOI
An analysis of thickness‐extensional trapped energy resonant device structures with rectangular electrodes in the piezoelectric thin film on silicon configuration
H. F. Tiersten,D.S. Stevens +1 more
TL;DR: In this article, an analysis of essentially thickness-extensional trapped energy modes in the thin piezoelectric film on silicon composite structure is performed, and the dispersion equation is isotropic in the plane of the plate even though the silicon is severely anisotropic in that plane.
Journal ArticleDOI
Quartz crystal resonators as sensors in liquids using the acoustoelectric effect
Zack A. Shana,Fabien Josse +1 more
TL;DR: In this paper, a transition region is created in which the lateral decaying acoustic field is enhanced by modifying the geometry of the electrode at the QCR surface in contact with the solution, which contributes to the total change in frequency.
Journal ArticleDOI
Vibrations of piezoelectric crystals
TL;DR: In this article, the fundamental differential equations of the linear theory of apolar and nonrelativistic, thermopiezoelectricity and also its variational description are presented.