Mohamed Hédi Ben Ghozlen

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.

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 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.

X-ray diffraction and surface acoustic wave analysis of BST/Pt/TiO2/SiO2/Si thin films

High dielectric constant and electrostriction property of (Ba, Sr)Ti03 (BST) thin films result in an increasing interest for dielectric devices and microwave acoustic resonator. Barium strontium titanate (Ba0.645Sr0.355TiO3) films of about 300 nm thickness are grown on Pt(111)/TiO2/SiO2/Si(001) substrates by rf magnetron sputtering deposition techniques. X-ray diffraction is applied for the microstructural characterization. The BST films exhibit a cubic perovskite structure with a dense and smooth surface. A laser acoustic waves (LA-waves) technique is used to generate surface acoustic waves (SAW) propagating in the BST films. Young’s modulus E and the Poisson ratio ν of TiO2, Pt and BST films in different propagation directions are derived from the measured dispersion curves. Estimation of BST elastics constants are served in SAW studies. Impact of stratification process on SAW, propagating along [100] and [110] directions of silicon substrate, has been interpreted on the basis of ordinary differential e...

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 layered piezoelectric/piezomagnetic plates

HighlightsThe first order differential equation and stiffness matrix method are developed.The phase velocity of the Lamb wave is calculated for the magneto‐electrically open and short cases.The influence of stacking sequences and thickness ratio on dispersion curves and on magneto electro‐mechanical coupling factor. Abstract 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.

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.

Acoustoelastic effect of textured (Ba,Sr)TiO3 thin films under an initial mechanical stress

Acoustoelastic (AE) analysis of initial stresses plays an important role as a nondestructive tool in current engineering. Two textured BST (Ba0.65Sr0.35TiO3) thin films, with different substrate to target distance, were grown on Pt(111)/TiO2/SiO2/Si(001) substrate by rf-magnetron sputtering deposition techniques. A conventional “sin2 ψ” method to determine residual stress and strain in BST films by X-ray diffraction is applied. A laser acoustic waves (LA-waves) technique is used to generate surface acoustic waves (SAW) propagating in both samples. Youngs modulus E and Poisson ratio ν of BST films in different propagation directions are derived from the measured dispersion curves. Estimation of effective second-order elastic constants of BST thin films in stressed states is served in SAW study. This paper presents an original investigation of AE effect in prestressed Ba0.65Sr0.35TiO3 films, where the effective elastic constants and the effect of texture on second and third order elastic tensor are conside...

Acoustoelastic Effects in Anisotropic Layered Structure of Cu/Si(001)

Theoretical studies are made in order to evaluate the acoustoelastic effect of prestressed layered systems using the ordinary differential equation method (ODE) and the stiffness matrix method (SMM). The modifications for residual stresses consider the change of the density, the influence of residual stress, and the modification of the elastic stiffness tensor by residual strain and by third-order constants. For illustration, we use a layered system of copper deposited on a silicon substrate. The acoustoelastic effect is investigated for both Love and Rayleigh surface acoustic waves. The obtained results demonstrate the importance of the acoustoelasticity studies for the homogeneity examination.

Guided modes modelling in viscoelastic multilayered composites

Due to the periodicity of the composite structure the Floquet wave approach seems well suited for multilayered medium characterization. The pass and stop band domains for [0/45/90/-45] cross ply composites have been plotted. Dispersive guided wave propagation through a lossy composite laminates immersed in water have been investigated. Our interest is focused on a guided mode inside the frequency range from 1.6 MHz to 5 MHz. Within the considered frequency range, these modes have been pointed out by both reflection coefficient and density of energy analysis in term of incident angle. In this paper it is investigated how by fine-tuning the frequency and the incident angle, internal displacement and stress field vary in the multilayer. When the frequency is increased the mode changes from a plate mode to a surface mode. The description includes real Floquet wave numbers as well as complex wave numbers.