Thickness-shear vibrations of rotated Y-cut quartz plates with imperfectly bonded surface mass layers

A solution is obtained from the three-dimensional equations of linear piezoelectricity for the pure thickness-shear vibration of rotated Y-cut quartz or langasite plates with imperfectly bonded surface mass layers. The solution includes a few results in the literature as special cases. It is shown that the mass layers lower the resonant frequencies when they are relatively perfectly bonded to the crystal surface, and that loosely bonded mass layers may raise the frequencies. The results are useful in the analysis of frequency stability of quartz resonators and acoustic wave sensors.     

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 an inhomogeneous piezoelectric plate with an imperfectly bonded interface

The propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfectly bonded interface is investigated. Based on the spring-type relation, the imperfectly bonded interface is dealt with, and the exact solution is obtained from the equations of the linear theory of piezoelectricity. The amplitude ratio between the incident wave and the reflected wave, the displacement component and the stress component are all obtained and plotted. Both theoretical analysis and numerical examples show that the effect of the mechanical imperfection on the wave propagation is more evident than that of the electrical imperfection. When the incident wave frequency and the mechanical imperfect parameter meet some particular relation, no reflected waves can appear in the piezoelectric plate. The results are of fundamental importance to the design of resonators and other devices when imperfect joints are considered.     

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.     

Thickness-shear vibration of rotated Y-cut quartz plates with relatively thick electrodes of unequal thickness

An exact solution is obtained from the three-dimensional equations of linear piezoelectricity for thickness-shear vibrations of rotated Y-cut quartz plates with relatively thick electrodes of unequal thickness at its major faces. Effects of the shear stiffness of the electrodes on resonant frequencies are examined.     

Shear-horizontal surface waves on piezoelectric ceramics with depolarized surface layer

Theoretical analysis and numerical results describing the propagation of SH (shear-horizontal) surface waves on piezoelectric ceramics with a depolarized surface layer are described. SH surface waves propagating in piezoelectric ceramics with a depolarized surface layer are shown to be a mixture of the Bleustein-Gulyaev surface wave, electrical potential, and the Love surface-wave mechanical displacement. Depolarization of the surface layer in piezoelectric ceramics produces strong dispersion and a multimode structure of the SH surface wave. The penetration depth of the SH surface waves propagating on an electrically free surface of a piezoelectric ceramic with a depolarized surface layer can be significantly smaller than that of the Bleustein-Gulyaev surface waves propagating on a free piezoelectric half-space. It is concluded that piezoelectric ceramics with a depolarized surface layer can be used in hybrid piezoelectric semiconductor convolvers of reduced size.     

The anti-plane vibration of a quartz plate with an additional partial non-uniform mass layer for acoustic wave sensing

The anti-plane vibration of a quartz plate having an additional partial non-uniform mass layer is solved by ignoring the effect of small c ₅₆ in comparison with other elastic constants. This analysis is based on the trigonometric series solution, and the convergence is examined. Numerical simulation is conducted for several different types of layers of different thicknesses using linear, cosine, and quadratic functions. The frequency spectrums, in addition to the length and mass fraction of the layer, are discussed separately. Compared with the homogeneous mass layer, the non-homogeneous layer with greater inertia leads to earlier appearance of the higher modes and more modes trapped under the same condition. Especially, there is no energy trapping in the plate with a fully covered uniform mass layer. However, this kind of energy trapping can be obtained again when the surface is non-uniform for some cases.     

Stress-induced frequency shifts in rotated Y-cut langasite resonators with electrodes considered

Stress-induced frequency shifts of the thickness-shear vibration of rotated Y-cut langasite resonators are studied with the electrode considered. The relationship between mass loading and force-frequency coefficients is explored for several kinds of electrode materials. Comparisons between Y-cut langasite and AT-cut quartz resonators are also presented.     

Shear-horizontal piezoelectric waves in an aluminum nitride film on a silicon substrate

The propagation of shear-horizontal waves in a piezoelectric film of aluminum nitride on a silicon substrate is studied. Three different electrode configurations are considered for thin film acoustic wave resonator application. A theoretical analysis is performed. The equations of linear piezoelectricity and anisotropic elasticity are used for the film and the substrate, respectively. Real and imaginary dispersion curves as well as electromechanical mode shapes are obtained. The effects of electrode configuration on the distribution of the electromechanical fields and the dispersion curves of long thickness-twist waves as well as energy trapping are examined.     

Turbulent boundary layer on a plate in an incompressible liquid with mass injection

Within the limits of a semi-empirical theory based on a two-layer system, as proposed in [5], an examination is made of the influence of mass addition, homogeneous with the main flow, on friction and the parameters of the turbulent boundary layer (thickness of the laminar sublayer, velocity at the edge of the laminar sublayer, etc.).     

Shear-horizontal acoustic waves in piezoelectric plates bordered with conductive liquid

The influence of a conductive liquid on the characteristics of shear-horizontal acoustic waves of zeroth order (SH0 mode) propagating in thin piezoelectric plates of lithium tantalate, lithium niobate, and potassium niobate was investigated. Experimental results obtained for SH0 mode devices fabricated on lithium niobate plates are found to be in good agreement with theory. The data presented in this paper is useful for a proper design of various acoustic wave sensors operating in contact with conductive liquids.     

Shear-horizontal surface waves in a layered structure of piezoelectric ceramics

A new existence condition for shear-horizontal (SH) surface waves in a layered structure of piezoelectric ceramics is give. The discussed SH surface wave is not a stiffened Love wave, but a new type surface wave.     

The interaction of shock waves with a boundary layer on a sharp plate and a blunted plate

The interaction of shock waves with a turbulent boundary layer on a sharp plate and a blunted plate is numerically investigated. The shock waves in the flow are generated by wedges installed on the flat plate. The flow is simulated by the dynamic equations of a viscous perfect gas. The effect of the blunting radius of the plate’s leading edge and the wedge angle on the flow field and the local aerodynamic coefficients is shown. The calculated results are in agreement with the experimental data.     

Doubly rotated quartz resonators with a low amplitude-frequencyeffect: the LD-cut

This article deals with a crystal quartz cut with virtually no amplitude-frequency effect (also called "isochronism defect" or "anisochronism"). The cut, called LD-cut (Low isochronism Defect), is set in a BVA-type structure for later use in an Ultra-Stable Oscillator (USO). Various design parameters are presented, along with the properties of the resonator. The resonance frequencies of various modes, the temperature dependence, the motional parameters and the phase noise in relation to the power supplied to the resonator are mainly studied. These properties are compared to those of the SC-cut resonators     

Effects of mass layer dimension on a finite quartz crystal microbalance

In this paper, a gradient crystal plasticity model in a polycrystalline grain structure is investigated. Hereby, the focus is on the influence of the grain boundary conditions. A new type of grain boundary conditions is introduced, the so-called micro-flexible boundary condition. In particular, it is compared to existing grain boundary conditions of plastic slip. Numerical results are given for the stress?Cstrain response as well as for the plastic slip field in the grain structure.     

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.     

Interaction of a turbulent boundary layer with an elastic plate

An approximate method is presented for the determination of the efficiency with which an elastic plate reduces turbulent friction, and experimental results are also presented.Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 2, pp. 220–225, February, 1989.     

Boundary layer at a plate with an arbitrary injection mode

A sufficiently general solution is obtained, applicable to a boundary layer with any injection mode (up to a certain limit).Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 4, pp. 720–726, October, 1972.