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A dynamic solution is presented for the propagation of harmonic waves in magneto-electro-elastic plates composed of piezoelectric BaTiO 3 (B) and magnetostrictive CoFe 2 O 4 (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. [ABSTRACT FROM AUTHOR]

The Peano-series expansion is used to investigate the propagation of the lowest-order symmetric ( S 0 ) and antisymmetric ( A 0 ) 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 S 0 mode, it is close to six percent, conversely for A 0 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. [ABSTRACT FROM AUTHOR]

Abstract: A novel approach, based on spectral analysis, for determination of the upper frequency bound for the homogenization domain is developed. The method is based on displacement field analysis, which is calculated using the recursive transfer matrix. It makes up a description of the equivalent homogenous material associated to the multilayer in the low frequency area. Inside the homogenization domain the displacements field perpendicular to layers, in term of deepness, are plotted. A fast-Fourier transform (FFT) processing is used to compute the wave numbers propagating in the multilayer. The plot of the dispersion curves show that, for a limiting frequency, we may consider the multilayer as an effective homogeneous anisotropic medium supporting at the most three plane waves. Above this frequency the medium becomes dispersive and has a nonhomogeneous character. Multilayered systems resulting from the stratification of carbon–epoxy cells of the type [0/90] and [0/45/90/−45], are used for the illustrations. [Copyright &y& Elsevier]

The guided wave technique has been widely used for evaluating different structures. Recently, these acoustic waves have been implemented in non-destructive testing (NDT). Accordingly, these waves make up a set of motivated means for detecting defects because of their effectiveness for quickly testing a long series of specimens. On that account, the present article introduces a Legendre polynomial approach, for modeling guided dispersion curves solutions in anisotropic fiber-reinforced composite media. This polynomial approach offers a higher computational efficiency and simplicity in comparison to traditional methods. The validity of the proposed Legendre polynomial approach is illustrated by comparison with available data. The convergence of this method is discussed. Consequently, the computation time of the Legendre polynomial approach increases linearly when the number of truncation order M increases. In the same context, the computation time of this polynomial approach is compared to the ordinary differential equation (ODE) approach in terms of efficiency. In addition, the influence on the fundamental guided wave dispersion curves due to reductions in the material properties such as C 11 , C 12 , C 13 , C 22 , C 23 , C 33 , C 44 , C 55 , C 66 and mass density were analyzed for anisotropic fiber-reinforced single-layered composite media with different propagation angles. The studies were performed by obtaining the behavior guided wave dispersion curves for each single-layered type. This was done by reducing the material properties mentioned above by 50% from the original value. Since the guided wave dispersion curves in a single-layered composite media varies with the propagation direction, the layers were analyzed at 0°, 45° and 90° propagation angles, with all the aforementioned variations. The computer programs in this work are written by using Matlab software. [ABSTRACT FROM AUTHOR]

In this paper, the attenuation of guided waves in damped multilayered arbitrary anisotropic composite laminates is investigated using a Legendre orthogonal polynomial approach. The laminate is made of the graphite–epoxy composite material with the layering sequence [0/ ϕ /0]. The validity of the polynomial approach is illustrated through a comparison with exact solution obtained from the Stiffness matrix method and a comparison with earlier known Lamb wave solution of pure elastic multilayered plate. The dispersion and attenuation of coupled Lamb waves with different layering sequences are investigated. The viscous effect on dispersion curves is shown. The combination of frequencies and modes with minimum attenuation in high and low frequencies are determined. These frequencies and modes are of great importance for NDT applications since they play a critical role in the selection of the optimal inspection frequencies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

In this paper, the propagation of Lamb waves in the functionally graded piezoelectric plates discretized into sub-layers is studied. In this presentation, a Legendre polynomial method is proposed to solve the wave equation. This method has three specificities in comparison to traditional methods. It directly incorporates the boundary conditions into the constitutive equations and it allows a resolution by a non-iterative system to the eigenvalues ​​and eigenvectors. Furthermore, this method takes full account of converged results nature. The convergence of this method is discussed a thorough manner. Here, the converged results are obtained with very low truncation number M. In addition, the effect of the gradient coefficients on the Lamb phase velocities is illustrated. Consequently, the different results also reveal differences between the properties of Lamb waves propagation in the functionally graded piezoelectric plates and the corresponding properties in homogeneous plates. Furthermore, the effect of constituent volume fraction is also considered through gradient models. All the developments performed in this work were implemented in Matlab software. [ABSTRACT FROM AUTHOR]

The propagation of Rayleigh–Lamb waves in bi-layered structures is studied. For this purpose, an extension of the Legendre polynomial (LP) method is proposed to formulate the acoustic wave equation in the bi-layered structures induced by thin film Gallium Antimonide (GaSb) and with Aluminum Antimonide (AlSb) substrate in moderate thickness. Acoustic modes propagating along a bi-layer plate are shown to be quite different than classical Lamb modes, contrary to most of the multilayered structures. The validation of the LP method is illustrated by a comparison between the associated numerical results and those obtained using the ordinary differential equation (ODE) method. The convergency of the LP method is discussed through a numerical example. Moreover, the influences of thin film GaSb parameters on the characteristics Rayleigh–Lamb waves propagation has been studied in detail. Finally, the advantages of the Legendre polynomial (LP) method to analyze the multilayered structures are described. All the developments performed in this work were implemented in Matlab software. [ABSTRACT FROM AUTHOR]

Theoretical analysis of surface acoustic wave (SAW) propagation in a pre-stressed layered piezoelectric structure basing on the modified ordinary differential equation (ODE) is described. Numerical calculations involve a thin piezoelectric layer of ZnO bonded perfectly to an elastic substrate of Al 2 O 3 . ZnO thin films are deposited on Al 2 O 3 substrates using plasma assisted molecular beam epitaxial (MBE). The crystallographic orientation of ZnO thin films and the surface morphology are analyzed by X-ray diffraction (XRD) and atomic force microscopy (AFM) respectively. The density and the thickness of the ZnO films are determined by X-ray reflectivity. The initial stress and strain of ZnO films are measured by X-ray diffraction method. The effect of initial stress on the propagation behavior of Rayleigh and Love waves and on the coupled electromechanical factor is discussed. [ABSTRACT FROM AUTHOR]

Abstract: Piezoelectric thin films on high acoustic velocity non piezoelectric substrates, such as ZnO and AlN, deposited on diamond or sapphire substrates, are attractive for high frequency and low-loss surface acoustic wave devices. In this work, ZnO films were epitaxialy grown on R-Al2O3 and C-Al2O3 substrates using plasma-assisted molecular beam epitaxy (MBE). The surface roughness of the ZnO layers is about 0.2nm for a 2μm×2μm AFM scan area. The absolute epitaxial relationships between ZnO films and α-plane sapphire are investigated by X-ray diffraction techniques. The resulting relationships for ZnO films on R-Al2O3 and C-Al2O3 substrates are found to be and , respectively. An analytical technique to determine residual strain in epitaxial ZnO films by X-ray diffraction (XRD) was studied. Based on piezoelectric constitutive equations and Bragg law, we applied an extended model, in which the elastic, piezoelectric and dielectric constants are introduced, to evaluate the residual stress in these films. [Copyright &y& Elsevier]