Lamb waves propagation in layered piezoelectric/piezomagnetic plates.

A dynamic solution is presented for the propagation of harmonic waves in magneto-electro-elastic plates composed of piezoelectric BaTiO3(B) and magnetostrictive CoFe2O4(F) material. The state-vector approach is employed to derive the propagator matrix which connects the field variables at the upper interface to those at the lower interface of each layer. The ordinary differential approach is employed to determine the wave propagating characteristics in the plate by imposing the traction-free boundary condition on the top and bottom surfaces of the layered plate. The dispersion curves of the piezoelectric-piezomagnetic plate are shown for different thickness ratios. The numerical results show clearly the influence of different stacking sequences as well as thickness ratio on dispersion curves and on magneto-electromechanical coupling factor. These findings could be relevant to the analysis and design of high-performance surface acoustic wave (SAW) devices constructed from piezoelectric and piezomagnetic materials.

Love waves propagation in a transversely isotropic piezoelectric layer on a piezomagnetic half-space.

A theoretical approach is taken into consideration to investigate Love wave propagation in a transversely isotropic piezoelectric layer on a piezomagnetic half-space. The magneto-electrically open and short conditions are applied to solve the problem. The phase and group velocity of the Love wave is numerically calculated for the magneto-electrically open and short cases, respectively. The variations of magneto-electromechanical coupling factor, mechanical displacements, electric and magnetic potentials along the thickness direction of the layers are obtained and discussed. The numerical results clearly show the influence of different stacking sequences on dispersion curves and on magneto-electromechanical coupling factor. This work may be relevant to analysis and design of various acoustic surface wave devices constructed from piezoelectric and piezomagnetic materials.

Effect of a functionally graded soft middle layer on Love waves propagating in layered piezoelectric systems.

Numerical examples for wave propagation in a three-layer structure have been investigated for both electrically open and shorted cases. The first order differential equations are solved by both methods ODE and Stiffness matrix. The solutions are used to study the effects of thickness and gradient coefficient of soft middle layer on the phase velocity and on the electromechanical coupling factor. We demonstrate that the electromechanical coupling factor is substantially increased when the equivalent thickness is in the order of the wavelength. The effects of gradient coefficients are plotted for the first mode when electrical and mechanical gradient variations are applied separately and altogether. The obtained deviations in comparison with the ungraded homogenous film are plotted with respect to the dimensionless wavenumber. The impact related to the gradient coefficient of the soft middle layer, on the mechanical displacement and the Poynting vector, is carried out. The numericals results are illustrated by a set of appropriate curves related to various profiles. The obtained results set guidelines not only for the design of high-performance surface acoustic wave (SAW) devices, but also for the measurement of material properties in a functionally graded piezoelectric layered system using Love waves.

Lamb waves propagation in functionally graded piezoelectric materials by Peano-series method.

The Peano-series expansion is used to investigate the propagation of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb wave modes in a functionally graded piezoelectric material (FGPM) plate. Aluminum nitride has been retained for illustration, it is polarized along the thickness axis, and at the same time the material properties change gradually perpendicularly to the plate with an exponential variation. The effects of the gradient variation on the phase velocity and the coupling electromechanical factor are obtained. Appropriate curves are given to reflect their behavior with respect to frequency. The highest value of the electromechanical coupling factor has been observed for S0 mode, it is close to six percent, conversely for A0 mode it does not exceed 1.5%. The coupling factor maxima undergo a shift toward the high frequency area when the corresponding gradient coefficient increases. The Peano-series method computed under Matlab software, gives rapid convergence and accurate phase velocity when analysing Lamb waves in FGPM plate. The obtained numerical results can be used to design different sensors with high performance working at different frequency ranges by adjusting the extent of the gradient property.

A theoretical study of the propagation of Rayleigh waves in a functionally graded piezoelectric material (FGPM).

An exact approach is used to investigate Rayleigh waves in a functionally graded piezoelectric material (FGPM) layer bonded to a semi infinite homogenous solid. The piezoelectric material is polarized when the six fold symmetry axis is put along the propagation direction x(1). The FGPM character imposes that the material properties change gradually with the thickness of the layer. Contrary to the analytical approach, the adopted numerical methods, including the ordinary differential equation (ODE) and the stiffness matrix method (SMM), treat separately the electrical and mechanical gradients. The influences of graded variations applied to FGPM film coefficients on the dispersion curves of Rayleigh waves are discussed. The effects of gradient coefficients on electromechanical coupling factor, displacement fields, stress distributions and electrical potential, are reported. The obtained deviations in comparison with the ungraded homogenous film are plotted with respect to the dimensionless wavenumber. Opposite effects are observed on the coupling factor when graded variations are applied separately. A particular attention has been devoted to the maximum of the coupling factor and it dependence on the stratification rate and the gradient coefficient. This work provides with a theoretical foundation for the design and practical applications of SAW devices with high performance.

Love waves in functionally graded piezoelectric materials by stiffness matrix method.

A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO(2), the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour.

Elastic constants measurement of anisotropic Olivier wood plates using air-coupled transducers generated Lamb wave and ultrasonic bulk wave.

A hybrid elastic wave method is applied to determine the anisotropic constants of Olive wood specimen considered as an orthotropic solid. The method is based on the measurements of the Lamb wave velocities as well as the bulk ultrasonic wave velocities. Electrostatic, air-coupled, ultrasonic transducers are used to generate and receive Lamb waves which are sensitive to material properties. The variation of phase velocity with frequency is measured for several modes propagating parallel and normal to the fiber direction along a thin Olivier wood plates. A numerical model based mainly on an optimization method is developed; it permits to recover seven out of nine elastic constants with an uncertainty of about 15%. The remaining two elastic constants are then obtained from bulk wave measurements. The experimental Lamb phase velocities are in good agreement with the calculated dispersion curves. The evaluation of Olive wood elastic properties has been performed in the low frequency range where the Lamb length wave is large in comparison with the heterogeneity extent. Within the interval errors, the obtained elastic tensor doesn't reveal a large deviation from a uniaxial symmetry.

Influence of attenuation on the behavior of refracted elastic waves at the interface between anisotropic media.

During the ultrasonic non-destructive evaluation of complex materials, like multilayer or composite materials, the behavior of the ultrasonic waves at the interface of samples is strongly dependent upon the anisotropy as well as the attenuation characteristics of the propagation media. In the generally arbitrary case, the incident wave is assumed to be inhomogeneous. Therefore the application of the Snell-Descartes laws requires to consider the real as well as the imaginary parts of all the quantities encountered during the study. In that aim, we use a representation of the complex slowness curves so-called slowness interface curves which point out the evolution of the interaction of the waves at the interface with the inhomogeneity factors, i.e. the imaginary part of the slowness vectors. The continuous distortion of the curves with the inhomogeneity factor increasing is an interesting approach of these complicated phenomena.