Jianke Du

Thickness vibration of piezoelectric plates of 6 mm crystals with tilted six-fold axis and two-layered thick electrodes

We perform a theoretical analysis of thickness vibrations in piezoelectric plates of crystals with 6mm symmetry. The six-fold axis is tilted with respect to the plate surfaces. The major surfaces of the plate are covered with two layers of electrodes of different metals. The equations of linear piezoelectricity are used for the crystal plate. The electrodes are modeled by the equations of elasticity. Thickness vibrations frequencies and modes as well as impedance are calculated and examined.

Love wave propagation in piezoelectric layered structure with dissipation.

We investigate analytically the effect of the viscous dissipation of piezoelectric material on the dispersive and attenuated characteristics of Love wave propagation in a layered structure, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of the viscous coefficient on the phase velocity of Love waves and attenuation are presented and discussed in detail. The analytical method and the results can be useful for the design of the resonators and sensors.

The analysis of the third-order thickness-shear overtone vibrations of quartz crystal plates with Mindlin plate theory

The design and analysis of quartz crystal resonators in the fundamental thickness-shear mode have been extensively studied with many methods including the simple model based on finite plates for the vibration frequency and Mindlin plate theory for couplings of the fundamental thickness-shear and spurious modes. These methods are widely used in the design process for the optimal determination of crystal blanks and electrode configuration. In order to study the overtone vibrations of quartz crystal resonators, Mindlin plate theory is used in the form of the third-order equations with selected modes to obtain the dispersion and frequency spectra in the vicinity of the third-order thickness-shear mode. In our earlier studies, a set of correction factors have been suggested for the Mindlin plate equations to be accurate at the cut-off frequency at the third-order thickness-shear mode. By checking the accuracy at the cutoff frequencies and of the dispersion relations, the third-order plate equations of selected modes are chosen for the calculation. The coupling of modes and effect of electrodes for the third-order overtone vibrations at the thickness-shear mode will be used for the design of quartz crystal resonators of overtone types.

The calculation of electrical parameters of AT-cut quartz crystal resonators with the consideration of material viscosity.

Electrical parameters like resistance and quality factor of a quartz crystal resonator cannot be determined through vibration analysis without considering the presence of material dissipation. In this study, we use the first-order Mindlin plate equations of piezoelectric plates for thickness-shear vibrations of a simple resonator model with partial electrodes. We derive the expressions of electrical parameters with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity, of quartz crystal. Since all electrical parameters are frequency dependent, this procedure provides the chance to study the frequency behavior of crystal resonators with a direct formulation. We understand that the electrical parameters are strongly affected by the manufacturing process, with the plating techniques in particular, but the theoretical approach we presented here will be the first step for the precise estimation of such parameters and their further applications in the analysis of nonlinear behavior of resonators. We calculated the parameters from our simple resonator model of AT-cut quartz crystal with the first-order Mindlin plate theory to demonstrate the procedure and show that the numerical results are consistent with earlier measurements.

The effect of inhomogeneous initial stress on Love wave propagation in layered magneto-electro-elastic structures

The effect of inhomogeneous initial stress on Love wave propagation in layered magneto-electro-elastic structures is investigated in this paper. The coupled magneto-electro-elastic field equations are solved by adopting the Wentzel–Kramers–Brillouin (WKB) approximate approach. Then the phase velocity can be calculated by applying boundary and continuity conditions. A specific example of a structure consisting of a CoFe2O4 layer and a BaTiO3 substrate is used to illustrate the influence of inhomogeneous initial stress on the phase velocity, corresponding coupled magneto-electric factor and stress fields. The different influence between constant initial stress and inhomogeneous initial stress is discussed and the results are expected to be helpful for the preparation and application of Love wave sensors.

The analysis of high frequency vibrations of layered anisotropic plates for FBAR applications

In this paper, the thickness-extension vibration of a layered piezoelectric plate is investigated. The vibration deformation consists of symmetric and asymmetric deformation. Thicknesses of the adhered layers will influence the frequency of the plate and the amplitude ratio between the layers significantly.

Solutions of nonlinear thickness-shear vibrations of an infinite isotropic plate with the homotopy analysis method

As a preliminary attempt for the study on nonlinear vibrations of a finite crystal plate, the thickness-shear mode of an infinite and isotropic plate is investigated. By including nonlinear constitutive relations and strain components, we have established nonlinear equations of thickness-shear vibrations. Through further assuming the mode shape of linear vibrations, we utilized the standard Galerkin approximation to obtain a nonlinear ordinary differential equation depending only on time. We solved this nonlinear equation and obtained its amplitude–frequency relation by the homotopy analysis method (HAM). The accuracy of the present results is shown by comparison between our results and the perturbation method. Numerical results show that the homotopy analysis solutions can be adjusted to improve the accuracy. These equations and results are useful in verifying the available methods and improving our further solution strategy for the coupled nonlinear vibrations of finite piezoelectric plates.

Shear-horizontal waves in a rotated Y-cut quartz plate with an imperfectly bonded mass layer

We study shear-horizontal (SH) waves in an unbounded plate of rotated Y-cut quartz carrying a thin mass layer imperfectly or nonrigidly bonded to the surface of the quartz plate. The imperfect interface is described by the so-called shear-lag model that allows the displacement to be discontinuous across the interface. A transcendental frequency equation that determines the dispersion relations of the waves is obtained. Exact and approximate solutions to the frequency equation are presented. The effects of the mass layer and the imperfect interface on the dispersion relations are examined. A quantitative criterion is given which distinguishes whether the combined effect of the mass layer and the imperfect interface raises or lowers the wave frequencies.

An analysis of vibrations of quartz crystal plates with nonlinear Mindlin plate equations

The nonlinear effects of material constants and initial stresses and strains in quartz crystal resonators is well known f on the frequency-temperature curves, drive-level dependency, acceleration sensitivity, and stress compensation. Consequently, accurate predictions on resonator behavior and their electrical circuit parameters require the use of nonlinear vibration equations and their solutions. The effectiveness of nonlinear analyses has been shown by a few researchers with the finite element and perturbation methods. The Mindlin plate theory, which has been used extensively for understanding plate modes and their coupling effects in plate vibrations analysis, is not enough in the study of the nonlinear behavior of quartz resonators. We have followed the Mindlin plate theory to derive the nonlinear equations with the inclusion of large displacements and higher order elastic constants. The coupling of vibration modes due to nonlinearity is clearly observed and it is quite different from linear cases that we are familiar with. We start from the equations of vibration for the thickness-shear mode to validate the solution techniques, which could be the perturbation method and the latest Homotopy Analytical Method (HAM). Then the methods are applied to the coupled equations of thickness-shear and flexural vibrations which are the two dominant modes of quartz crystal resonators of the thickness-shear type. These solutions, in the absence of the strong electrical field, can be used to study the frequency, deformation, and mode conversion in nonlinear vibrations. We hope the frequency spectra and spatial variations of the thickness-shear and flexural displacements from the accurate solutions of nonlinear equations will provide insights on the changes in each mode when compared with their linear vibrations. The further extension of nonlinear plate equations with the inclusion of piezoelectric effects will also provide useful examination of nonlinear behavior of quartz crystal resonators.

Effects of viscous liquid on SH-SAW in layered magnetoelectric structures

We investigate analytically shear horizontal surface acoustic wave (SH-SAW) propagation in layered magnetoelectric structures loaded with viscous liquid, which involves a thin piezomagnetic layer bonded perfectly to an unbounded piezoelectric substrate. The dispersive relations are obtained and the effects of liquid viscosity on the phase velocity and attenuation of the waves are analyzed and discussed. From the results we can find that the effects of the liquid viscosity on the properties of SH-SAW are remarkable. The phase velocity decreases with increase of the viscous coefficient, or with increase of the frequency, and the attenuation increases with the frequency of the waves and the liquid viscosity, respectively. The relationship between attenuation and frequency or viscosity is nonlinear, but the former is a concave curve, whereas the latter is a convex curve. The attenuation decreases with the piezomagnetic coefficient, and increases obviously with the thickness of the layer. The analytical method and the results are useful for the design of acoustic wave devices based on magnetoelectric materials for liquid phase application, which could be resonated by either magnetic or electric fields.