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.     

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.     

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.     

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。     

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and two isotropic layers

Propagation of electro-elastic surface Love waves in a structure consisting of a piezoelectric half-space substrate of crystal class 6, 4, 6 mm or 4 mm and two layers, one of which (adjacent to the substrate) is a conducting material and the second is either a conducting or a dielectric material, 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. Numerical calculations are carried out for three different layered structures. The effect of the second layer on the propagation behaviour of the surface Love wave in the structure is revealed.     

Surface electro-elastic shear horizontal waves in a layered structure with a piezoelectric substrate and a hard dielectric layer

The existence and behaviour of surface electro-elastic shear horizontal waves in a layered structure consisting of a piezoelectric substrate of crystal class 6, 4, 6mm, or 4mm mechanically bonded at its upper surface to an elastic dielectric layer and bounded by an adjacent dielectric medium is considered when the shear bulk wave velocity in the elastic layer is greater than or equal to that in the substrate. The dispersion equation for the existence of the surface electro-elastic SH waves with respect to the phase velocity is obtained which 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 investigation of the solutions of the dispersion equation is carried out and all the possible cases of the behaviour of the surface electro-elastic SH wave depending on the electro-mechanical coefficients of the layered structure are revealed.     

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.     

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.     

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.     

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.     

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.     

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 SURFACE ACOUSTIC WAVES IN PRESTRESSED ANISOTROPIC LAYERED PIEZOELECTRIC STRUCTURES

The propagation of surface acoustic waves in layered piezoelectric structures withinitial stresses is investigated.The phase velocity equations are obtained for electrically free andshorted cases,respectively.Effects of the initial stresses on the phase velocity and the electrome-chanical coupling coefficient for the fundamental mode of the layered piezoelectric structures arediscussed.Numerical results for the c-axis oriented fihn of LiNbO_3 on a sapphire substrate aregiven.It is found that the fractional change in phase velocity is a linear function with the ini-tial stresses,and the electromechanical coupling factor increases with an increase of the absolutevalues of the compressive initial stresses.The results are useful for the design of surface acousticwave devices.     

Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects

This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate. As one of the most important features of nanostructures, surface effects characterized by surface stresses and surface electric displacements are taken into account through the surface piezoelectricity theory and the nonclassical mechanical and electrical boundary conditions. Concrete expressions of th...     

非均匀压电层状结构中Love波的传播

讨论材料参数沿厚度方向发生连续缓慢变化时的各向同性弹性基底上有一等厚压电覆盖层肘Love波的传播性能．给出了压电层的厚度和基底材料的非均匀性对频散曲线的影响．     

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 biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates

This paper is concerned with the effect of a biasing electric field on the propagation of Lamb waves in a piezoelectric plate. On the basis of three dimensional linear elastic equations and piezoelectric constitutive relations, the differential equations of motion under a biasing electric field are obtained and solved. Due to the symmetry of the plate, there are symmetric and antisymmetric modes with respect to the median plane of the piezoelectric plate. According to the characteristics of symmetric modes (odd potential state) and antisymmetric modes (even potential state), the phase velocity equations of symmetric and antisymmetric modes of Lamb wave propagation are obtained for both electrically open and shorted cases. The effect of a biasing electric field on the phase velocity, electromechanical coupling coefficient, stress field and mechanical displacement of symmetric and antisymmetric Lamb wave modes are discussed in this paper and an accompanying paper respectively. It is shown that the biasing electric field has significant effect on the phase velocity and electromechanical coupling coefficient, the time delay owning to the velocity change is useful for high voltage measurement and temperature compensation, the increase in the electromechanical coupling coefficient can be used to improve the efficiency of transduction.     

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 rigid boundary on propagation of torsional surface waves in porous elastic layer

The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato (Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13(2), 125–147 (1983)). The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. (Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6(4), 241–249 (2003)). The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.     

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.