Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure

The propagation behavior of Love waves in a layered piezoelectric structure with an initial stress is investigated in this article. It involves a thin piezoelectric layer bonded perfectly to an elastic substrate. Solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate by solving the coupled electromechanical field equations. The phase velocity equations of the Love wave propagation and the stress fields in the layered piezoelectric structure are obtained for electrical open and short cases on the free surface, respectively. The effect of the initial stress on the phase velocity, the stress fields and the coupled electromechanical factor are discussed, respectively. Three sets of piezoelectric layer–elastic substrate systems are considered, i.e. BaTiO₃ ceramic layer–borosilicate glass substrate, PZT-5H ceramic layer–borosilicate glass substrate, and PZT-5H ceramic layer–SiO₂ glass substrate. It is seen that the phase velocity of the Love wave propagation decreases with the increase of the magnitude of the initial stress. The coupled electromechanical factor increases remarkably, as the magnitude of the initial the stress is greater than 100 MPa. This is useful for the design of acoustic surface wave devices.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

Propagation of Love waves in a functionally graded piezoelectric material (FGPM) layered composite system

In this theoretical study, we investigate the propagation of Love waves in a layered structure consisting of two different homogenous piezoelectric materials, an upper layer and a substrate. A functionally graded piezoelectric material (FGPM) buffer layer is in between the upper layer and the substrate. We employ the power series technique to solve the governing differential equations with variable coefficients. The influence of the gradient coefficients of FGPM and the layer thicknesses on the dispersion relations, the electro-mechanical coupling factor, and the stress distributions of Love waves in this structure are investigated. We demonstrate that the low gradient coefficient raises the significant variation of the phase velocity within a certain range of ratios of upper layer thickness to equivalent thickness. The electro-mechanical coupling factor can be increased when the equivalent thickness equals one or two wavelengths, and the discontinuity of the interlaminar stress can be eliminated by the FGPM buffer layer. The theoretical results set guidelines not only for the design of high-performance surface acoustic wave (SAW) devices using the FGPM buffer layer, but also for the measurement of material properties in such FGPM layered structures using Love waves.     

Properties of Love waves in layered piezoelectric structures

Love waves propagating in a layered structure with an elastic layer deposited on a piezoelectric substrate are analytically investigated. We present a general dispersion equation that describes the properties of Love waves in the structure. A detailed discussion regarding the dispersion equation is presented, and the parameters for Love-mode sensors are also introduced. The properties of Love waves are illustrated by means of sample results for a layered structure with an SiO₂ layer sputtered on an ST-cut 90°X-propagating quartz substrate. Interestingly, we found that a threshold-normalized layer thickness existed for the fundamental Love mode in such a structure.     

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.     

SH Waves in(1-x)Pb(Mg_(1/3)Nb_(2/3))O_(3-x)PbTiO_3 Piezoelectric Layered Structures Loaded with Viscous Liquid

The velocity dispersion and attenuation of shear horizontal(SH) waves in a layered piezoelectric structure loaded with viscous liquid is studied,where the(1- x)Pb(Mg_(1/3)Nb_(2/3))O_(3-x)PbTiO_3[PMN-xPT]single crystal is chosen as the piezoelectric layer.The PMN-xPT is being polarized along[011]_c and[001]_c so that the macroscopic symmetries are mm 2 and 4 mm,respectively.For the nonconductive liquid,the electrically open and shorted conditions at the interface between the liquid and the piezoelectric layer are considered.The phase velocity equations are derived analytically.The effects of the electrically boundary condition,the viscous coefficient and mass density of liquid as well as the thickness of the PMN-xPT layer on the phase velocity and attenuation are graphically illustrated.The results show that the phase velocity for the[011]_c polarized PMN-0.29 PT is much smaller than that for the[001]_c polarized PMN-0.33 PT,and the effects of viscous coefficient and piezoelectric layer thickness on the phase velocity for the[011]_c case are stronger than that for the[001]_c case.In addition,the electrical boundary conditions have an obvious influence on the propagation behaviors.These results can be useful for the designs and applications of acoustic wave devices and liquid biosensors.     

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.     

A three-layer structure model for the effect of a soft middle layer on Love waves propagating in layered piezoelectric systems

A three-layer structure model is proposed for investigating the effect of a soft elastic middle layer on the propagation behavior of Love waves in piezoelectric layered systems, with "soft" implying that the bulk-shear-wave velocity of the middle layer is smaller than that of the upper sensitive layer. Dispersion equations are obtained for unelectroded and traction-free upper surfaces which, in the limit, can be reduced to those for classical Love waves. Systematic parametric studies are subsequently carried out to quantify the effects of the soft middle layer upon Love wave propagation, including its thickness, mass density, dielectric constant and elastic coefficient. It is demonstrated that whilst the thickness and elastic coefficient of the middle layer affect significantly Love wave propagation, its mass density and dielectric constant have negligible influence. On condition that both the thickness and elastic coefficient of the middle layer are vanishingly small so that it degenerates into an imperfectly bonded interface, the three-layer model is also employed to investigate the influence of imperfect interfaces on Love waves propagating in piezoelectric layer/elastic substrate systems. Upon comparing with the predictions obtained by employing the traditional shear-lag model, the present three-layer structure model is found to be more accurate as it avoids the unrealistic displacement discontinuity across imperfectly bonded interfaces assumed by the shearlag model, especially for long waves when the piezoelectric layer is relatively thin.     

Love waves in functionally graded piezoelectric materials

To investigate the features of Love waves in a layered functionally graded piezoelectric structure, the mathematical model is established on the basis of the elastic wave theory, and the WKB method is applied to solve the coupled electromechanical field differential equation. The solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate. The dispersion relations of Love waves are deduced for electric open and short cases on the free surface respectively. The actual piezoelectric layer–elastic substrate systems are taken into account, and some corresponding numerical examples are proposed comparatively. Thus, the effects of the gradient variation about material constants on the phase velocity, the group velocity, the coupled electromechanical factor and the cutoff frequency are discussed in detail. So the propagation behaviors of Love waves in inhomogeneous medium is revealed, and the dispersion and the anti-dispersion are analyzed. The conclusions are significant both theoretically and practically for the surface acoustic wave devices.     

初应力对压电层状结构声表面波传播性能的影响

研究了压电层状结构中初应力对广义Ｒａｙｌｅｉｇｈ波传播相速度和机电耦合性能的影响,通过求解含初应力的运动微分方程,对自由界面电学开路和短路两种情况得到了相应的相速度方程。给出了具体的数值算例,所得结果对于提高和改善声表面波器件性能有参考意义。     

Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space

The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson’s half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity.     

Effect of a viscous liquid loading on Love wave propagation

This paper describes a theory of surface Love waves propagating in a layered elastic waveguide loaded on its surface by a viscous (Newtonian) liquid. An analytical expression for the complex dispersion equation of Love waves has been established. The real and imaginary parts of the complex dispersion equation were separated and resulting system of nonlinear algebraic equations was solved numerically. The influence of the viscosity of liquid on the dispersion curves of phase velocity, the wave attenuation and the distribution of the Love wave amplitude is analyzed numerically. The propagation loss is produced only by the viscosity of liquids. Elastic layered waveguide is assumed to be loss-less. The numerical solutions show the dependence of the phase velocity change, the wave attenuation and the wave amplitude distribution in terms of the liquid viscosity and the wave frequency. The results of the investigations are fundamental and can be applied in the design and development of liquid viscosity sensors and biosensors, in Non-Destructive Testing (NDT) of materials, in geophysics and seismology.     

Love wave dispersion in pre-stressed homogeneous medium over a porous half-space with irregular boundary surfaces

The paper investigates the existence of Love wave propagation in an initially stressed homogeneous layer over a porous half-space with irregular boundary surfaces. The method of separation of variables has been adopted to get an analytical solution for the dispersion equation and thus dispersion equations have been obtained in several particular cases. Propagation of Love wave is influenced by initial stress parameters, corrugation parameter and porosity of half-space. Velocity of Love waves have been plotted in several figures to study the effect of various parameters and found that the velocity of wave decreases with increases of non-dimensional wave number. It has been observed that the phase velocity decreases with increase of initial stress parameters and porosity of half-space.     

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and a dielectric layer

The existence and behaviour of electro-elastic surface Love waves in a structure consisting of a piezoelectric substrate of crystal classe 6, 4, 6 mm, 4 mm, 622 or 422, an elastic layer and a dielectric medium is considered. The mathematical model obtained includes all the above crystal classes, i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The dispersion equation for the existence of Love surface waves with respect to phase velocity is obtained. A detailed investigation of the electromechanical coupling coefficient is carried out depending on the dielectric and piezoelectric parameters of the problem. Geometrical investigation of the solutions of the dispersion equation is carried out.     

Propagation behavior of Love waves in a functionally graded half-space with initial stress

The propagation behavior of Love waves in a functionally graded material layered non-piezoelectric half-space with initial stress is taken into account. The Wentzel–Kramers–Brillouin (WKB) technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of the mechanical displacement and stress along the thickness direction in the layered structure. First, these solutions are used to study the effects of the initial stress on the dispersion relations and the group and phase velocities, then the influences of the initial stress on the distributions of the mechanical displacement and shear stresses along the thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of the Love waves increases with the increase in the magnitude of the initial tensile stress, while decreases with the increase in the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100 MPa. Some other results are obtained for the distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.     

Rayleigh and Love surface waves in isotropic media with negative Poisson’s ratio

The behavior of Rayleigh surface waves and the first mode of the Love waves in isotropic media with positive and negative Poisson’s ratio is compared. It is shown that the Rayleigh wave velocity increases with decreasing Poisson’s ratio, and it increases especially rapidly for negative Poisson’s ratios less than ?0.75. It is demonstrated that, for positive Poisson’s ratios, the vertical component of the Rayleigh wave displacements decays with depth after some initial increase, while for negative Poisson’s ratios, there is a monotone decrease. The Rayleigh waves are characterized by elliptic trajectories of the particle motion with the change of the rotation direction at critical depths and by the linear vertical polarization at these depths. It is found that the elliptic orbits are less elongated and the critical depths are greater for negative Poisson’s ratios. It is shown that the stress distribution in the Rayleighwaves varies nonmonotonically with the dimensionless depth as (positive or negative) Poisson’s ratio varies. The stresses increase strongly only as Poisson’s ratio tends to?1. It is shown that, in the case of an incompressible thin covering layer, the velocity of the first mode of the Love waves strongly increases for negative Poisson’s ratios of the half-space material. If the thickness of the incompressible layer is large, then the wave very weakly penetrates into the halfspace for any value of its Poisson’s ratio. For negative Poisson’s ratios, the Love wave in a layer and a half-space is mainly localized in the covering layer for any values of its thickness and weakly penetrates into the half-space. For the first mode of the Love waves, it was discovered that there is a strong increase in the maximum of one of the shear stresses on the interface between the covering layer and the half-space as Poisson’s ratios of both materials decrease. For the other shear stress, there is a stress jump on the interface and a more complicated dependence of the stress on Poisson’s ratio on both sides of the interface.     

Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces

The effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces are studied in this paper. First, the secular equations in the traverse isotropic piezoelectric half space are derived from the general dynamic equation with initial stress taken into consideration. Then, the interface conditions that displacement, stress, electric potential, and electric displacement are continuous across interface are required to be satisfied by three sets of coupled waves, namely, quasi-longitudinal wave, quasi-transverse wave and the electric–acoustic wave. The algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and the effects of initial stress are discussed.     

Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium

The frequency of the Love-type surface waves in a bedded structure consisting of a porous piezoelectric(PP) medium and a functionally graded material(FGM)substrate is approximated. The FGM layer is assumed to have a constant initial stress.The Wentzel-Kramers-Brillouin(WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses(tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.     

Scattering of love waves by an interface crack between a piezoelectric layer and an elastic substrate

The scattering of Love waves by an interface crack between a piezoelectric layer and an elastic substrate is investigated by using the integral transform and singular integral equation techniques. The dynamic stress intensity factors of the left and the right crack tips are determined. It is found from numerical calculation that the dynamic response of the system depends significantly on the crack configuration, the material combination and the propagating direction of the incident wave. It is expected that specifying an appropriate material combination may retard the growth of the crack for a certain crack configuration. Project supported by the National Natural Science Foundation of China (No. 19891180), the Fundamental Research Foundation of Tsinghua University (JZ 2000.007) and the Fund of the Education Ministry of China.     

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.