Bleustein–Gulyaev waves in 6 mm piezoelectric materials loaded with a viscous liquid layer of finite thickness

In this paper, we analyze the propagation of Bleustein–Gulyaev waves in an unbounded piezoelectric half-space loaded with a viscous liquid layer of finite thickness within the linear elastic theories. Exact solutions of the phase velocity equations are obtained in the cases of both electrically open circuit and short circuit by solving the equilibrium equations of piezoelectric materials and the diffusion equation of viscous liquid. A PZT-5H/Glycerin system is selected to perform the numerical calculation. The results show that the mass density and the viscous coefficient have different effects on the propagation attenuation and phase velocity under different electrical boundary conditions. In particular, the penetration depth of the waves is of the same order as the wavelength in the case of electrically short circuit. These effects can be used to manipulate the behavior of the waves and have implications in the application of acoustic wave devices.     

PMN-PT夹层弹性半空间结构中SH波的传播Propagation of SH waves in sandwich structures consisting of PMN-PT single crystal layer and elastic half-spaces

分析了弹性上下半空间和PMN‐PT单晶层组成的夹层结构中SH波的传播性质,PMN‐PT单晶沿[011]c方向极化,宏观上呈mm2对称,且晶体沿角度θ方向切割。基于正交各向异性压电材料和各向同性弹性材料的基本方程,得到了夹层结构中SH波传播时行列式形式的频散方程。通过对数值算例进行分析可以看出,PMN‐PT单晶的切割角度和弹性材料属性对结构中的相速度有很大影响,因此波的某些传播性能可以通过材料的设计以及晶体切割的方向来实现,这些结论为声表面波器件的开发和应用提供了理论依据。     

Effects of covering layer thickness on Love waves in functionally graded piezoelectric substrates

An analytical approach is used to investigate the effects of covering layer thickness on the propagation behavior of Love waves in functionally graded piezoelectric materials (FGPMs) covered with a dielectric layer. The piezoelectric substrate is polarized in the direction perpendicular to the wave propagation plane, and its material parameters change continuously along the thickness direction. The dispersion equations for the existence of Love waves with respect to phase velocity are obtained for electrically open and shorted cases, respectively. A detailed investigation of the effects of the covering dielectric layer thickness on dispersion curve, phase velocity, group velocity, and electromechanical coupling factor is carried out. Numerical results show that for a given FGPM, the covering dielectric layer thickness affects significantly the fundamental mode of Love waves but has only negligible effects on the high-order modes. The changes in phase velocity, group velocity, and electromechanical coupling factor due to the change of gradient coefficient of FGPMs could be approached approximately by changing the thickness of the covering dielectric layer, which imply a potential factor for designing new-type surface wave devices with FGPMs.     

Propagation characteristics of thermoelastic waves in piezoelectric (6 mm class) rotating plate

The propagation of Lamb waves in a homogeneous, transversely isotropic (6 mm class), piezothermoelastic plate rotating with uniform angular velocity about normal to its boundary has been investigated. The generalized (non-classical) theories of thermoelasticity in contrast to Sharma and Pal [Sharma, J.N., Pal, M., 2004. Lamb wave propagation in transversely isotropic piezothermoelastic plate. J. Sound Vib. 270, 587–610] have been used to investigate the problem. The surfaces of the plate are subjected to stress free, thermally insulated/isothermal and electrically shorted boundary conditions. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. After obtaining the complex characteristic roots with the help of Descartes' algorithm, the transcendental secular equations have been solved by functional iteration numerical technique to compute phase velocity and attenuation coefficient. Finally, in order to illustrate the analytical development, numerical solution of secular equations is carried out for PZT-5A piezo-thermoelastic material. The corresponding simulated results of various physical quantities such as phase velocity, attenuation coefficients, specific loss factor of energy dissipation, thermo-mechanical coupling factor and relative frequency shifts have been presented graphically for both rotating and non-rotating plates for comparison purpose. There is a scope for extension of the present work to other classes of piezo/pyroelectric crystals. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric surface acoustic wave (SAW) devices.     

PROPAGATION OF LOVE WAVES IN PRESTRESSED PIEZOELECTRIC LAYERED STRUCTURES LOADED WITH VISCOUS LIQUID

We investigate analytically the effect of initial stress in piezoelectric layered structures loaded with viscous liquid on the dispersive and attenuated characteristics of Love waves, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of initial stress in the piezoelectric layer and the viscous coefficient of the liquid on the phase velocity of Love waves are analyzed. Numerical results are presented and discussed. The analytical method and the results can be useful for the design of chemical and biosensing liquid sensors.     

Propagation of Bleustein–Gulyaev wave in 6 mm piezoelectric materials loaded with viscous liquid

The influence of a viscous liquid on acoustic waves propagating in elastic or piezoelectric materials is of particular significance for development of liquid sensors. Bleustein–Gulyaev wave is a shear-type surface acoustic wave and has the advantage of not radiating energy into the adjacent liquid. These features make the B–G wave sensitive to changes in both mechanical and electrical properties of the surrounding environment. The Bleustein–Gulyaev wave has been reported to be a good candidate for liquid sensing application. In this paper, we investigate the potential application of B–G wave in 6 mm crystals for liquid sensing. The explicit dispersion relations for both open circuit and metalized surface boundary conditions are given. A numerical example of PZT-5H piezoelectric ceramic in contact with viscous liquid is calculated and discussed. Numerical results of attenuation and phase velocity versus viscosity, density of the liquid and wave frequency are presented. The paper is intended to provide essential data for liquid senor design and development.     

Propagation behavior of SH waves in a piezomagnetic substrate with an orthorhombic piezoelectric layer

The dispersion behavior of the shear horizontal (SH) waves in the coupled structure consisting of a piezomagnetic substrate and an orthorhombic piezoelectric layer is investigated with different cut orientations. The surface of the piezoelectric layer is mechanically free, electrically shorted, or open, while the surface of the piezomagnetic substrate is mechanically free, magnetically open, or shorted. The dispersion relations are derived for four electromagnetic boundary conditions. The dispersion characteristics are graphically illustrated for the layered structure with the PMN-PT layer perfectly bonded on the CoFe₂O₄ substrate. The effects of the PMN-PT cut orientations, the electromagnetic boundary conditions, and the thickness ratio of the layer to the substrate on the dispersion behavior are analyzed and discussed in detail. The results show that, (i) the effect of the cut orientation on the dispersion curves is very obvious, (ii) the electrical boundary conditions of the PMN-PT layer dominate the propagation feature of the SH waves, and (iii) the thickness ratio has a significant effect on the phase velocity when the wave number is small. The results of the present paper can provide valuable theoretical references to the applications of piezoelectric/piezomagnectic structure in acoustic wave devices.     

有限液体负载下压电平板声板波理论分析

主要推导平板声板波受有限液体负载后能量衰减与波速改变情形, 以部分波传理论分析该受液体负载的压电平板波传行为, 并以一128$^{\circ}Y$向切角的铌酸锂芯片为例,分析前20个声板波受水与甘油负载下 的能量衰减,并固定某一平板板波, 针对不同甘油厚度负载下, 计算其相速度与衰减变化,该理论分析对于液体负载下的平板板波传感器应用具有极大的参 考价值.     

Solitons in viscous films flowing down a vertical wall

Periodic wave solutions in a film of viscous liquid near optimal regimes have been investigated in the boundary layer approximation by Shkadov et al. [1]. Urintsev [2] has found nonlinear steady solutions near the upper neutral stability curve on the basis of the Navier-Stokes equations. In the present paper, equations are derived that can be used either to make the boundary-layer solution more accurate or estimate its applicability. Soliton type solutions are considered for parameter of the problem in the range δ ε (0, ∞). Asymptotic expansions are considered in the limits δ → 0 and δ → ∞. For finite δ, two numerical algorithms are proposed for solving the problem; one of them is for equations in von Mises variables. The numerical solutions revealed the existence of “singular” sections, at which the velocity profile differs strongly from parabolic. The integral characteristics of the soliton — the phase velocity, amplitude, etc. — are found to be close to the corresponding characteristics obtained earlier by the present author [3] by assuming that the velocity profile is parabolic. The first determination is made of the critical value δ = δ_** of the onset of boundary layer separation in the vertically flowing viscous film. It is interesting that the separation does not occur on the rigid wall but at an interface near the crest of the soliton.     

Diffusion to a particle at large péclet numbers and small Reynolds and Hartmann numbers

A study is made of the influence of a homogeneous magnetic field on the mass transfer for a spherical solid particle and a liquid drop in a flow of a viscous electrically conducting fluid. The previously obtained [1] velocity field of the fluid is used to calculate the concentration distribution in the diffusion boundary layer, the density of the diffusion flux, and the Nusselt number, which characterizes the mass transfer between the particle and the surrounding medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 189–192, January–February, 1980.     

Love waves in a two-layered piezoelectric/elastic composite plate with an imperfect interface

Based on the shear spring model, the propagation of Love wave in two-layered piezoelectric/elastic composite plates under the influence of interfacial defect is investigated. The piezoelectric layer is electrically shorted at both top and bottom surfaces. The wave form solutions of the piezoelectric and elastic layers are obtained, and the dispersion equation is derived by subjecting the boundary conditions and the continuity conditions to the obtained wave form solutions. Numerical results are performed for PZT4/aluminum composite plate. The phase velocities and the mode shapes of mechanical displacement and electric potential are illustrated graphically. The results show that both the interfacial defect and the thickness ratio between the piezoelectric and elastic layers have significant effect on the propagation characteristics of Love wave. One important feature is observed that the interfacial defect always decreases the phase velocities.     

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer–Viscous-Liquid-Layer System

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier–Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.     

覆盖层与基底极化方向相反时压电层状半空间中的B-G波

对于覆盖层与基底介质极化方向相反的压电状半空间,在自由表面电学开路和短路两种情况下,分析用解析的方法以了Ｂｌｅｕｓｔｅｉｎ－Ｇｕｌｙａｅｖ波传播的相速度方程或相速度的表达式;以工程技术中应用的压电材料为例考察了波速随覆盖厚度ｈ的变化规律,为了分析表面金属薄膜对波的传播速度的影响,计算了机电耦合系数ｋ＾２与ｈ的关系,结果表明：层状结构Ｂ－Ｇ波传播时具有很小的穿透深度,同时在ｈ取适当值时依然可使ｋ＾２     

Wave propagation in gaseous small-scale channel flows

The propagation and attenuation of an initial shock wave through a mm-scale channel of circular cross-section over lengths up to 2,000 diameters is examined as a model problem for the scaling of viscous effects in compressible flows. Experimental wave velocity measurements and pressure profiles are compared with existing data and theoretical predictions for shock attenuation at large scales and low pressures. Significantly more attenuation is observed than predicted based on streamtube divergence. Simulations of the experiment show that viscous effects need to be included, and the boundary layer behavior is important. A numerical model including boundary layer and channel entrance effects reproduces the wave front velocity measurements, provided a boundary layer transition model is included. A significant late-time pressure rise is observed in experiments and in the simulations.     

Generalized Bleustein-Gulyaev type waves in layered porous piezoceramic structure

The propagation of a Bleustein-Gulyaev (B-G) type wave in a structure consisting of multiple layers and a half-space of porous piezoelectric materials is theoretically studied. The solutions of the problem in terms of the mechanical displacements and electric potential functions are obtained for each layer and the half-space. The dispersion equation is obtained for electrically open and shorted boundary conditions by use of the transfer matrix method. A peculiar kind of B-G waves is investigated, which can propagate only in the layer over the half-space. The relationship between the piezoelectric constants and the dielectric constants is found for the existence of a peculiar kind of propagation modes. The numerical results in terms of the phase velocity and the electromechanical coupling factor with different thicknesses of the layer stack are presented.     

Constitutive modeling of textured body-centered-cubic (bcc) polycrystals

A new latent hardening model for body-centered-cubic (bcc) single crystals motivated by the inapplicability of the Schmid law (Critical Resolved Shear Stress Criterion) is presented. This model is based on the asymmetry of shearing resistance of the {112} slip planes depending on the shearing direction in the sense of ‘twin’ and ‘anti-twin’. For the interpretation of deformation of polycrystalline aggregates depending upon initial texture, a constitutive law for bcc single crystals is developed. This law is based on a rigorous constitutive theory for crystallographic slip that accounts for the effects of strain hardening, rate-sensitivity and thermal softening. The deformation response of textured polycrystal is investigated by means of a Taylor type averaging scheme and an established numerical procedure. Results for textured tungsten polycrystals at low and high strain rates for two different textures [001] and [011] are presented and compared with experimental results. The predictions compare well with experimental observations for the [001] texture. In the [011] texture, due to the reduced symmetry of deformation, lateral tensile stresses develop even under uniaxial compression. These lateral tensile stresses are responsible for observed lack of ductility and transgranular failure in the [011] texture.     

Magnetohydrodynamic lubrication theory for a cylindrical bearing

Liquid metal, which is a conductor of electric current, may be used as a lubricant at high temperatures. In recent years considerable attention has been devoted to various problems on the motion of an electrically conducting liquid lubricant in magnetic and electric fields (magnetohydrodynamic theory of lubrication), Thus, for example, references [1–3] study the flow of a conducting lubricating fluid between two plane walls located in a magnetic field. An electrically conducting lubricating layer in a magnetohydrodynamic bearing with cylindrical surfaces is considered in [4–8] and elsewhere.The present work is concerned with the solution of the plane magnetohydrodynamic problem on the pressure distribution of a viscous eletrically conducting liquid in the lubricating layer of a cylindrical bearing along whose axis there is directed a constant magnetic field, while a potential difference from an external source is applied between the journal and the bearing. The radial gap in the bearing is not assumed small, and the problem reduces to two-dimensional system of magnetohydrodynamic equations.An expression is obtained for the additional pressure in the lubricating layer resulting from the electromagnetic forces. In the particular case of a very thin layer the result reported in [4–8] is obtained. SI units are used.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

Flutter of infinite elastic plates in the boundary-layer flow at finite Reynolds numbers

The stability of an infinite elastic plate in supersonic gas flow is investigated taking into account the presence of the boundary layer formed on the plate surface. The effect of viscous and temperature disturbances of the boundary layer on the behavior of traveling waves is studied at large but finite Reynolds numbers. It is shown that in the case of the small boundary layer thickness viscosity can have both stabilizing and destabilizing effect depending on the phase velocity of disturbance propagation.     

Singularly perturbed solution for weakly nonlinear equations with two parameters

A class of singularly perturbed boundary value problems of weakly non- linear equation for fourth order on the interval[a,b]with two parameters is considered. Under suitable conditions,firstly,the reduced solution and formal outer solution are con- structed using the expansion method of power series.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near x=a is constructed which possesses exponential attenuation behavior.Then,using the stronger transfor- mation of stretched variable,the second boundary layer corrective term near x=a is constructed,which also possesses exponential attenuation behavior.The thickness of second boundary layer is smaller than the first one and forms a cover layer near x=a. Finally,using the theory of differential inequalities,the existence,uniform validity in the whole interval[a,b]and asymptotic behavior of solution for the original boundary value problem are proved.Satisfying results are obtained.