Analysis Of The Effects Of Electrode On Vibration Of Piezoelectric Plate With Dissipation

It is well known that piezoelectric materials are widely used in resonators, sensors and transducers. Almost all the modeling and analysis of vibration and wave propagation are based on the linear theory of piezoelectricity with quasi-electrostatic approximation, where the medium is assumed to be perfectly elastic and perfectly insulating to electric current. As operating frequencies get higher and sizes of acoustic wave devices become smaller, the dissipation of energies becomes more significant and should be considered in more realistic theories or modeling. In resonator manufacturing, one electrode is deposited first with a pre-determined thickness. Then the electrode on the other side of the piezoelectric plate has a thickness that is determined by the desired frequency of the electroded plate. If the electrodes on the crystal plate are very thin, their mechanical effects can be neglected. When the electrodes are not very thin, their mechanical effects, e.g. inertia and stiffness, need to be considered.(1) We analyze the thickness-shear vibration of a simple resonator model by means of complex material constants with consideration of the electrode inertia. The effects of viscosity on frequency behavior of piezoelectric plate are presented and discussed. The results can be useful for design of the relevant resonators;(2) And we mainly investigate the mechanical effect of metal electrodes, such as mass effect and shear stiffness effect, and effects of viscosity and conductivity on the resonance frequency, capacitance ratio, and quality factor. Some results are presented and discussed in detail.(3) We investigate the way of vibrations of a Y-cut quartz plate with consideration of dissipation which has a pair of identical electrode. Based on the Mindlin's first-order theory of piezoelectric plates, we can analysis the coupled vibration motions like thickness-shear (TSh),flexure (F) and face-shear (FS) separately and clearly. The point, therefore, is that the plate is driven by a uniform and time-harmonic voltage across top and bottom electrodes, and we here improve the electrical boundary conditions. An analytical solution is obtained. Numerical results including the admittance and motional capacitance of the structure as a resonator are presented.(4) Furthermore, we study thickness-shear and thickness-twist vibrations of a rotated Y-cut quartz plate with two pairs of electrodes based on the Mindlin's first-order plat theory. One pair of electrodes is applied to a known driving voltage. The other is connected to an output circuit. The structure can operate as a filter. Both free and electrically forced vibrations are studied. Resonant frequencies, mode shapes and the related energy trapping, output voltage, input admittance, input and output powers are calculated and examined.