Propagation of thickness-twist waves in a piezoelectric ceramic plate in contact with viscous fluids

We study theoretically the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with unattached electrodes and viscous fluids between the plate surfaces and the electrodes. Based on the theories of piezoelectricity and viscous fluids, an equation that determines the dispersion relations of the waves is obtained, showing the dependence of the phase velocity on material and geometric parameters. Due to the viscosity of the fluid, the dispersion relations are complex in general, representing damped waves with attenuation. The dispersion relations obtained can reduce to the results of a few special cases with known results. The results of the present paper are useful for developing and designing fluid sensors for measuring fluid viscosity or density.     

Antiplane piezoelectric surface waves over a ceramic half-space with an imperfectly bonded layer

We study surface wave propagation over a piezoelectric half-space with an imperfectly bonded mass layer. The imperfect interface between the half-space and the layer is described by the so-called shear-lag model with an elastic constant characterizing the interface physical property. An analytical solution is obtained. Discussion and numerical solutions are presented.     

Propagation of thickness-twist waves in a quartz plate with asymmetric mass layers

An exact solution is obtained for thickness-twist waves in a quartz plate with asymmetric mass layers. A simple, approximate expression for cutoff frequencies is given.     

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 socalled 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.     

Propagation of thickness-twist waves through a joint between two semi-infinite piezoelectric plates

We study the propagation of thickness-twist waves through a joint between two semi-infinite piezoelectric plates of crystals with 6-mm symmetry or polarized ceramics. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The solution shows the cutoff of certain waves and the presence of localized electromechanical fields near the joint. The results are of fundamental importance to the understanding and design of resonators and other devices made from plates of these materials, in particular thin film resonators of ZnO and AlN.     

非理想界面正交各向异性层/压电半空间结构中Love波的传播特性

研究了正交各向异性层与压电半空间非理想连接时Love波的传播特性。其中,界面条件由剪切滞后模型表征,正交各向异性层表面机械自由。首先,对压电材料和正交各向异性材料的波动方程进行求解,然后利用界面条件和边界条件推导了显函形式的频散方程,最后进行了数值计算,分析了界面性态、压电材料性能和正交各向异性程度对频散特性的影响。分析结果表明：Love波的传播速度随着界面约束强度的降低而减小;当不理想程度较高时,正交各向异性程度和压电材料性能对Love波的传播速度影响不大。     

Effects of piezoelectric coupling on Bechmann's number for thickness-twist waves in a plate of hexagonal crystals

Solutions for thickness-twist waves in a piezoelectric plate of 6-mm crystals with surface mass layers are obtained. The solutions are used to determine Bechmann's number for designing electrode size of devices operating with these waves. This generalizes the existing knowledge on Bechmann's number by the inclusion of piezoelectric coupling. It is shown that this coupling plays a role as important as or more important than the electrode inertia. The results are of fundamental importance to resonator design, in particular thin film resonators of ZnO and AlN.     

Study on SH-SAW in imperfectly bonded piezoelectric structures loaded with viscous liquid

We analytically investigate shear horizontal surface acoustic wave (SH-SAW) propagation in layered piezoelectric structures loaded with viscous liquid, which involves a thin piezoelectric layer imperfectly bonded to an unbounded elastic substrate. The coupling wave equations are obtained based on the linear piezoelectric theory. The governing equations are solved by means of the analytical method with consideration of electrically open and shorted cases, respectively. The dispersive relations are obtained, and the effects of the imperfect constant on the properties of waves are presented and discussed. From the numerical results, we can find that the phase velocity decreases with the increase of the interface parameter n, and for a specified viscosity, the attenuation increases with the interface parameter. The results show that the effects of the imperfect constant on the properties of SH-SAW are remarkable.     

Plane harmonic waves in an infinite piezoelectric plate with dissipation

In a previous paper, the three-dimensional equations of linear piezoelectricity with quasielectrostatic approximation were extended to include losses attributed to the mechanical damping in solid and the resistance in current conduction. These equations were used to investigate the plane wave propagation in an unbounded solid and forced thickness vibration of an infinite piezoelectric plate. In the present paper, these equations are used to obtain solutions of plane harmonic wave of arbitrary direction in an infinite and dissipative piezoelectric plate with general crystal symmetry. Dispersion curves are computed and plotted for real frequencies and complex wave numbers. All frequency branches are complex for dissipative plate. There are no longer any pure real or pure imaginary or complex conjugate frequency branches as those existing for nondissipative plates. Effects of dissipation on the wave propagation are examined in detail for AT-cut of quartz as well as barium titanate ceramic plate.     

Mass sensitivity of thickness-twist modes in a rectangular piezoelectric plate of hexagonal crystals

Mass sensitivity of thickness-twist vibration modes in a rectangular plate piezoelectric resonator of 6 mm crystals are obtained from the three-dimensional equations of linear piezoelectricity. The boundary conditions at the finite-plate boundaries all have been taken into consideration. The solutions obtained are exact, which is relatively few for piezoelectric problems over finite domains. The results are fundamental and useful to the understanding and design of piezoelectric resonators and acoustic wave sensors made of polarized ceramics, ZnO and AlN.     

Material symmetries and inhomogeneous waves in piezoelectric media

Summary This study is an experimental investigation on a novel oscillation phenomenon of a water rivulet on a smooth hydrophobic surface. It is found that the water rivulet running down on a smooth Plexiglass plate exhibits all together four distinctive patterns with increasing either the Froude number, the Weber number or the Reynolds number. Once either the Froude number, the Weber number or the Reynolds number exceeds the third critical value, the rivulet on a smooth Plexiglass plate is restabilized, and becomes almost straight. However, in the restable rivulet, several beads of a rosary are formed following immediately downstream of the pipe mouth. This is no more than the novel oscillation phenomenen of the water rivulet on a smooth Plexiglass plate. The oscillatory motion is steady in the hydrodynamical sense, because the phase of the oscillation is always the same at each point in space.It is found that with increasing either the Froude number, the Weber number or the Reynolds number, not only the wave-length and width of the beads in the restable rivulet increase, but also the rivulet itself becomes more straight and stable. On one hand, with increasing distance from the pipe mouth along the central axis of the rivulet, the local maximum width of each of the beads decreases, but its wave-length increases.It is suggested that the oblique surface waves generated at the left and right contact lines of the rivulet play a primary role in the contraction process of the novel oscillation phenomenon of the restable rivulet.     

Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media

A mathematical model for the propagation of harmonic plane waves in an anisotropic piezo-thermoelastic medium is explained through three relations. Two of them relate the stress-induced harmonic variations in temperature and electric potential to mechanical displacement of material particles. The third is a system that defines modified Christoffel equations for wave propagation in the medium. The solution of this system is ensured by a quartic equation whose complex roots explain the existence and propagation of four attenuating waves in the medium. The effects of piezoelectricity and thermoelasticity on the wave propagation are analyzed in the discussion of special cases. An angle between propagation direction and direction of maximum attenuation defines the attenuated wave as inhomogeneous wave. The complex slowness vector for each of the four attenuated waves in the medium is resolved to calculate the phase velocity and the attenuation factor for its propagation as an inhomogeneous wave along a general direction in three-dimensional space. The variations in phase velocities and attenuation factors with propagation direction are computed, for a realistic numerical model.     

Analysis of a rectangular ceramic plate in electrically forced thickness-twist vibration as a piezoelectric transformer

A rectangular ceramic plate with appropriate electrical load and operating mode is analyzed for piezoelectric transformer application. An exact solution from the three-dimensional equations of linear piezoelectricity is obtained. The solution simulates the real operating situation of a transformer as a vibrating piezoelectric body connected to a circuit. Transforming ratio, input admittance, and efficiency of the transformer are obtained.     

Propagation of torsional waves in a viscoelastic layer over an inhomogeneous half space

This paper presents a theoretical study on propagation of torsional surface waves in a homogeneous viscoelastic isotropic layer with Voigt type viscosity over an inhomogeneous isotropic infinite half space. The non-homogeneity in half space is assumed to arise due to exponential variation in shear modulus and density. A closed-form solution has been obtained for the displacement in the layer as well as for a infinite half space. The dispersion and absorption relations for an torsional wave under the assumed geometry have been found. Numerical results are presented for propagation characteristics in terms of a number of non-dimensionalized parameters and have been produced graphically. This study investigates the effect of various parameters, namely non-homogeneity parameter, internal friction, the layer width and complex wave number on dissipation function and phase velocity of the torsional wave. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close agreement.     

Propagation of straight-crested waves in an electroelastic plate under biasing fields

Summary We study wave propagation in an electroelastic plate under uniform initial thermoelectromechanical fields. An exact solution is obtained for materials with general anisotropy. The specific case of crystals with 6mm symmetry is examined as an example.     

Propagation of inhomogeneous plane waves in anisotropic viscoelastic media

A new technique is explained to study the propagation of inhomogeneous waves in a general anisotropic medium. The harmonic plane waves are considered in a viscoelastic anisotropic medium. The complex slowness vector is decomposed into propagation vector and attenuation vector for the given directions of propagation and attenuation of waves in an unbounded medium. The attenuation is further separated into the contributions from homogeneous and inhomogeneous waves. A non-dimensional inhomogeneity parameter is defined to represent the deviation of an inhomogeneous wave from its homogeneous version. Such a partition of slowness vector of a plane wave is obtained with the help of an algebraic method for solving a cubic equation and a numerical method for solving a real transcendental equation. Derived specifications enable to study the 3D propagation of inhomogeneous plane waves in a viscoelastic medium of arbitrary anisotropy. The whole procedure is wave-specific and obtains the propagation characteristics for each of the three inhomogeneous waves in the anisotropic medium. Numerical examples analyze the variations in propagation characteristics of each of the three waves with propagation direction and inhomogeneity strength.     

Propagation of Iamb waves in adhesively bonded multilayered media

The effect of introducing attenuation on Lamb wave dispersion curves is studied in this paper. Attenuation is introduced to a three-layered composite plate by an adhesive bond layer with viscous behavior. No changes are required to the transfer matrix formulation for the propagation of elastic waves. By introduction of a complex wavenumber, the model can be used to the propagation of attenuative Lamb waves. Numerical examples for a three-layered aluminium-epoxy-aluminium plate show that attenuation values of each mode in plates are related not only to attenuation, but also to the thickness of the bonded layer, which is in agreement with practical situations.     

Control of thermally induced elastic displacement of an isotropic structural plate bonded to a piezoelectric ceramic plate

Summary The present paper deals with a thermoelastic problem in an isotropic structural plate to which a piezoelectric ceramic plate of crystal class 6mm is perfectly bonded. It is assumed that the combined plate is subjected to a thermal load and then is deformed. In this case, we try to control the deformation of the isotropic structural plate by applying an electric potential to the piezoelectric ceramic plate. By analyzing the piezothermoelastic problem in the combined plate, we obtain an appropriate applied electric potential which alters the isotropic structural plate to a prescribed deformation. Finally numerical calculations are carried out for an isotropic steel plate to which a cadmium selenide plate is perfectly bonded, and the results are illustrated graphically.