Propagation Behavior Of Love Waves Research Articles

Propagation behavior of ultrasonic Love waves in functionally graded piezoelectric-piezomagnetic materials with exponential variation

The current research is devoted to studying the propagation behavior of Love waves in a functionally graded piezoelectric film perfectly bound to a homogeneous piezomagnetic substrate named FGPPM. All the material properties are supposed to be exponential through the piezoelectric film. Using the stiffness matrix method (SMM), the phase and group velocities are numerically calculated for magneto-electrically open and shorted cases. A detailed investigation of the gradient coefficient effect on the dispersion curve, the magneto-electromechanical coupling factor, the cutoff wave-number, and the modal shape is undertaken. It is found that quite a high magneto-electromechanical coupling factor for the structure at some appropriate wave number can be achieved by a simple adjustment of the gradient coefficient. As the variation of magneto-electromechanical properties of the film changes gradually with depth, and since the initial stress is supposed negligible during the manufacturing process, this calculation model could serve as a perfect match for the laminated piezoelectric-piezomagnetic structures used as surface acoustic wave devices (SAW). Thus, it can provide a theoretical basis for the design of the SAW devices with high performance.

Love waves in a layered functionally graded piezoelectric structure under initial stress

To study the effect of initial stress on the propagation behavior of Love waves in a layered functionally graded piezoelectric structure, a mathematical model is established. The piezoelectric layer is taken as exponentially graded material where as half-space is taken as simply elastic substratum. The coupled electromechanical field equations are solved analytically to obtain the mechanical displacements and electrical potential functions for the piezoelectric layer and elastic substrate. The dispersion relations are obtained for electrically open and short cases. The higher mode Love wave propagation has been considered. For numerical interpretation of the results, four sets of piezoelectric layer and elastic substrate have been taken into consideration. Graphical representation reveals about the effect of initial stress and the effect of inhomogeneity parameter on the phase velocity against wave number for electrically open and electrically short cases, respectively.

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 shear-lag model, especially for long waves when the piezoelectric layer is relatively thin.

Effect of gradient dielectric coefficient in a functionally graded material (FGM) substrate on the propagation behavior of love waves in an FGM-piezoelectric layered structure

The propagation behavior of Love waves in a layered structure that includes a functionally graded material (FGM) substrate carrying a piezoelectric thin film is investigated. Analytical solutions are obtained for both constant and gradient dielectric coefficients in the FGM substrate. Numerical results show that the gradient dielectric coefficient decreases phase velocity in any mode, and the electromechanical coupling factor significantly increases in the first- and secondorder modes. In some modes, the difference in Love waves' phase velocity between these two types of structure might be more than 1%, resulting in significant differences in frequency of the surface acoustic wave devices.

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.

Effect of initial stress on Love waves in a piezoelectric structure carrying a functionally graded material layer

The effect of initial stress on the propagation behavior of Love waves in a piezoelectric half-space of polarized ceramics carrying a functionally graded material (FGM) layer is analytically investigated in this paper from the three-dimensional equations of linear piezoelectricity. The analytical solutions are obtained for the dispersion relations of Love wave propagating in this kind of structure with initial stress for both electrical open case and electrical short case, respectively. One numerical example is given to graphically illustrate the effect of initial stress on dispersive curve, phase velocity and electromechanical coupling factor of the Love wave propagation. The results reported here are meaningful for the design of surface acoustic wave (SAW) devices with high performance.

Transverse surface waves in an FGM layered structure

The existence and propagation behavior of Love waves in a functionally graded material (FGM) layered structure are theoretically investigated in this paper based on the three-dimensional equations of linear electricity. The Wentzel–Kramers–Brillouin (WKB) method is applied to obtain the analytical solutions in the FGM layer. The dispersion equation for a Love surface wave in this kind of structure is obtained in a simple mathematical form, where the material property variation of the FGM layer is arbitrary. First, the solution is used to study the effect of the gradient coefficients on the dispersion curves and the phase velocities of Love waves. Then, the influence of gradient coefficients on the stress and displacement fields is discussed in detail. The reported results are important in the design of surface acoustic wave (SAW) devices with high performance.

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.

Effect of Initial Stress on the Behavior of Love Waves in an Elastic Half-Space with a Functionally Graded Layer

The propagation behavior of Love waves in a functionally graded material layered half-space with initial stress is taken into account. The Wentzel-Kramers-Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of mechanical displacement and stress along thickness direction in the layered structure. Firstly, these solutions are used to study effects of the initial stress on the dispersion relations and phase velocities, then influences of the initial stress on the distributions of mechanical displacement and shear stresses along thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of Love wave increases with the increase of the magnitude of the initial tensile stress, while decreases with the increase of 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 100MPa. Some other results are shown for 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.

Love waves propagation in functionally graded piezoelectric materials with quadratic variation

The propagation behavior of Love waves in a semi-infinite functionally graded piezoelectric material (FGPM) with a quadratic variation is addressed. The coupled electromechanical field equations are solved, and the dispersion relations, displacement, electric potential, and stress fields are obtained analytically for both electrically open and short conditions. The effects of gradient coefficient on phase velocity, group velocity, and electromechanical coupling factor are plotted and discussed. It is shown that the phase velocity associated with the non-piezoelectric case coincides with that of the corresponding piezoelectric material under electrically open conditions. Because of gradual variation in electromechanical properties, the initial stress during manufacturing process is negligible. Therefore, this model serves as an excellent substitute for the typical layered piezoelectric structures used in surface acoustic wave (SAW) devices. This work provides with a theoretical foundation for the design and practical applications of SAW devices with high performance.

Propagation of Love waves in a smart functionally graded piezoelectric compositestructure

In this paper, the propagation behavior of Love waves in a smart functionally gradedpiezoelectric structure is analyzed. The smart structure consists of three layers, in whichthe piezoelectric plate serves as the upper layer accompanied by a sandwiched graded layerand a metal substrate. In the graded layer, all the parameters and the elastic modulus arerespectively assumed to vary after two mathematical forms, i.e. an exponential functionand a linear function. The WKB method is adopted to analytically solve thepropagation problem of Love waves for both electrical open and short cases on the freesurface, respectively. The phase velocity curves demonstrate that the numberof modes is greater than in the non-graded layer structure. Furthermore, theinfluence of graded variation on coupled electromechanical factor is presented.

Propagation behavior of Love waves in a piezoelectric layered structure withinhomogeneous initial stress

For the piezoelectric layer/substrate structure with slowly varying inhomogeneous initialstress in the layer, the influence of the initial stress on the properties of Lovewave propagation is studied. The Wentzel–Kramers–Brillouin (WKB) approximateapproach is adopted for analytical derivations. Numerical results obtained for theBaTiO3 layer/borosilicate glass substrate combination system indicate that, under certainconditions, initial stress in the layer can markedly affect the propagation of the Love wave.The analysis is meaningful for the theoretical analysis and engineering applications of Lovewaves.

The propagation behavior of Love waves in a functionally graded layered piezoelectricstructure

The propagation behavior of Love waves in a functionally graded layered piezoelectricstructure is investigated in this paper. It involves a thin piezoelectric layer, in which theparameters vary linearly in the thickness direction, bonded perfectly to an elastic substrate.By the WKB method, the phase velocity equations are obtained for both electrical openand short cases on the free surface, respectively. The results show that the circularfrequency and cut-off frequency increase as the elastic modulus and dielectric constant varylinearly respectively; meanwhile, the number of vibration modes decreases, and the coupledelectromechanical factor increases with the decrease of the dielectric constant.Undoubtedly, this is useful for the design of surface acoustic wave (SAW) devices.

Love waves propagation in a piezoelectric layered structure with initial stresses

The propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress is studied. Solutions of the mechanical displacement and electrical potential function are obtained for the isotropic elastic layer and transversely isotropic piezoelectric substrate, respectively, by solving the coupled electromechanical field equations. Firstly, effects of the inhomogeneous initial stress on the dispersion relations and phase velocity of Love wave propagation are discussed. Then the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail. The results reported in this paper are not only meaningful for the design of surface acoustic wave (SAW) devices with high performance, but also effective for evaluating the residual stress distribution in the layered structures.

Influence of Imperfect Interface on the Propagation of Love Waves in Piezoelectric Layered Structures

Layered structures, especially thin film/coating substrate system play important roles in micro-electro-mechanical system (MEMS) and microelectronics packages. Many surface acoustic wave (SAW) devices/sensors adopt the layered structures to achieve high performance that with a piezoelectric layer deposited on the substrate. Recently, much work has been carried out concerning the propagation behavior of surface waves in piezoelectric layered structures, in which the piezoelectric layers are bonded perfectly with the substrate materials. Actually, due to the thermal mismatch, the unavoidable initial stress in the piezoelectric layer and the brittleness nature of piezoelectric ceramics, imperfections exist in the interfaces of these layered structures. Due to the penetration properties of surface waves, the imperfect interfaces may influence the propagation behavior of surface waves. Up to now, little attention has been paid to the propagation behavior of surface waves in layered piezoelectric structures that the imperfect interfaces are taken into account. The propagation behavior of Love waves in a piezoelectric layered structure with imperfect interface is taken into account. Solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and substrate, respectively, by solving the coupled electromechanical field equations. Effect of imperfect interface on the phase velocity of Love wave propagation is discussed in detail. Results obtained indicate that imperfect interface can greatly influence the propagation of Love waves under some certain conditions. The potential application of these results in the field of mechanical behavior of materials is also shown.

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. BaTiO 3 ceramic layer–borosilicate glass substrate, PZT-5H ceramic layer–borosilicate glass substrate, and PZT-5H ceramic layer–SiO 2 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.

The Propagation Behavior of Love Waves in a Pre-stressed Piezoelectric Layered Structure

The Propagation Behavior of Love Waves in a Pre-stressed Piezoelectric Layered Structure