Thickness-shear vibration of a circular cylindrical ceramic cylinder with unattached electrodes and air gaps

Abstract

We analyze thickness-shear vibration of an axially poled circular cylindrical tube with unattached electrodes and air gaps. Both free and electrically forced vibrations are studied. Exact solutions are obtained from the equations of linear piezoelectricity. Resonant frequencies and the impedance of the transducer are calculated from the solution. Results show that the resonant frequencies are sensitive to the dimensions of the air gaps when the gaps are thin. The impedance depends strongly on the air gaps.vibration, cylindrical cylinder, piezoelectricity, air gap Circular cylindrical tubes of polarized ceramics are common structures for many piezoelectric devices. Examples include hydrophone [1] , transducer [2] , fluid sensor [3] , and power harvester [4] . The references are too numerous to enumerate. In most cases, the electrodes are directly deposited on the surface of the piezoelectric structure. Unattached electrodes at some distance from the surface have been occasionally used in piezoelectric devices [5][6][7] . There are limited theoretical results on devices with unattached electrodes. A formulation for waves in crystal plates was given in ref.[8] where materials of general anisotropy are considered and therefore the results are complicated. Numerical techniques had to be used to obtain quantitative results and only numerical results for the case of attached electrodes were presented. Ref.[9] is an approximate theoretical analysis on finite plates with unattached electrodes. In ref.[10] a theoretical analysis of thickness-shear vibration of a quartz plate was performed. Unattached electrodes offer certain advantages that are important for further improvement of device performance. Various undesirable effects of attached electrodes disappear when the electrodes are unattached. This includes, e.g., the residual stress in the electrodes, the frequency effect of electrode irregularity in manufacturing, and the field concentration at electrode edges. In this paper we analyze thickness-shear vibration of an axially poled circular cylindrical ceramic tube with unattached electrodes and air gaps. This problem includes the classical result in ref.[2] as a special case. Both free and electrically forced vibrations are studied.

Geometric eccentricity effect on thickness-shear vibration of an elliptical flexoelectric crystal plate

“…Thickness-shear vibration as one of the important working modes of quartz crystal resonators has always been the focus of attention [28][29][30][31][32]. The rapid development of communication industry has accelerated the development of miniaturization of device, making the device size an important factor affecting the thicknessshear vibration of resonators.…”