Love wave propagation in functionally graded piezoelectric material layer

ArticleinUltrasonics 46(1):13-22 · April 2007with54 Reads
DOI: 10.1016/j.ultras.2006.09.004 · Source: PubMed
Abstract
An exact approach is used to investigate Love waves in functionally graded piezoelectric material (FGPM) layer bonded to a semi-infinite homogeneous solid. The piezoelectric material is polarized in z-axis direction and the material properties change gradually with the thickness of the layer. We here assume that all material properties of the piezoelectric layer have the same exponential function distribution along the x-axis direction. The analytical solutions of dispersion relations are obtained for electrically open or short circuit conditions. The effects of the gradient variation of material constants on the phase velocity, the group velocity, and the coupled electromechanical factor are discussed in detail. The displacement, electric potential, and stress distributions along thickness of the graded layer are calculated and plotted. Numerical examples indicate that appropriate gradient distributing of the material properties make Love waves to propagate along the surface of the piezoelectric layer, or a bigger electromechanical coupling factor can be obtained, which is in favor of acquiring a better performance in surface acoustic wave (SAW) devices.
    • The use of layered Love waves waveguides with a nonhomogeneous distribution of physical properties can significantly improve performance (e.g., sensitivity and selectivity) of bio and chemosensors that employ the inhomogeneous elastic waveguides [13]. SH surface acoustic waves (Love and Bleustein–Gulyaev type) may also be used to study spatial profiles changes in mechanical properties (e.g., modulus of elasticity and density) of the Functionally Graded Material (FGM) [14][15][16][17] . These materials are heterogeneous media, in which the mechanical parameters are functions of the distance from the surface into the bulk of the material.
    [Show abstract] [Hide abstract] ABSTRACT: This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices.
    Article · Feb 2016
    • As piezoelectric nanofilms which are nanosized in thickness and possess piezoelectric properties are often attached to a substrate of different physical properties in performances, surface effects on the propagation of elastic waves in the layered structures consisting of a piezoelectric nanofilm and a half-space elastic substrate are vital for the functions of piezoelectric nanofilms. Transverse shear waves in the above structures are referred as Love waves and have been extensively studied when surface effects are neglected[24][25][26][27][28][29][30][31][32]. To the author's knowledge, however, research on the Love waves propagation with surface effects has not yet reported in literature.
    [Show abstract] [Hide abstract] ABSTRACT: The propagation of Love waves in the structure consisting of a nanosized piezoelectric film and a semi-infinite elastic substrate is investigated in the present paper with the consideration of surface effects. In our analysis, surface effects are taken into account in terms of the surface elasticity theory and the electrically-shorted conditions are adopted on the free surface of the piezoelectric film and the interface between the film and the substrate. This work focuses on the new features in the dispersion relations of different modes due to surface effects. It is found that with the existence of surface effects, the frequency dispersion of Love waves shows the distinct dependence on the thickness and the surface constants when the film thickness reduces to nanometers. In general, phase velocities of all dispersion modes increase with the decrease of the film thickness and the increase of the surface constants. However, surface effects play different functions in the frequency dispersions of different modes, especially for the first mode dispersion. Moreover, different forms of Love waves are observed in the first mode dispersion, depending on the presence of the surface effects on the surface and the interface.
    Full-text · Article · Nov 2015
    • Considering the inhomogeneous initial stress, JIN, et al[5], examined the propagation of Love waves in a piezoelectric layered structure. The effects of functionally graded properties, dissipation, and viscosity on Love wave propagation in piezoelectric structures have been systematically studied by DU and co-workers[6][7][8][9]. LU and HE[10]analyzed the properties of Love waves in layered piezoelectric structures.
    [Show abstract] [Hide abstract] ABSTRACT: Research on the propagation of elastic waves in piezoelectric nanostructures is very limited. The frequency dispersion of Love waves in layered piezoelectric nanostructures has not yet been reported when surface effects are taken into account. Based on the surface elasticity theory, the propagation of Love waves with surface effects in a structure consisting of a nanosized piezoelectric film and a semi-infinite elastic substrate is investigated focusing on the frequency dispersion curves of different modes. The results show that under the electrically-open conditions, surface effects give rise to the dependence of Love wave dispersion on the film thickness when the thickness of the piezoelectric film reduces to nanometers. For a given wave frequency, phase velocity of Love waves in all dispersion modes exhibit obvious toward shift as the film thickness decreases or the surface parameters increase. Moreover, there may exist a cut-off frequency in the first mode dispersion below which Love waves will be evanescent in the structure due to surface effects. The cut-off frequency depends on the film thickness, the surface parameters and the bulk material properties.
    Full-text · Article · Oct 2015
    • (9) Obtained results are found in agreement with the results established by Cao et al. [13] and Du et al. [8].
    [Show abstract] [Hide abstract] ABSTRACT: This paper investigates the propagation behavior of Love-type surface waves in three-layered composite structure with initial stress. The composite structure has been taken in such a way that a functionally graded piezoelectric material (FGPM) layer is bonded between initially stressed piezoelectric upper layer and an elastic substrate. Using the method of separation of variables, frequency equation for the considered wave has been established in the form of determinant for electrical open and short cases on free surface. The bisection method iteration technique has been used to find the roots of the dispersion relations which give the modes for electrical open and short cases. The effects of gradient variation of material constant and initial stress on the phase velocity of surface waves are discussed. Dependence of thickness on each parameter of the study has been shown explicitly. Study has been also done to show the existence of cut-off frequency. Graphical representation has been done to exhibit the findings. The obtained results are significant for the investigation and characterization of Love-type waves in FGPM-layered media.
    Full-text · Article · Jul 2015
    • The structure is composed of a piezoelectric layer (PZT-5H) deposited on an elastic substrate (SiO 2 ). The obtained numerical results agree very well with the analytical work given in Ref. [4] as shown inFig. 2 for the fundamental mode.
    [Show abstract] [Hide abstract] ABSTRACT: 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. Copyright © 2015 Elsevier B.V. All rights reserved.
    Full-text · Article · May 2015
    • In this work, we use the ' * ' and ' ' symbols to distinguish the different parameters associated with the outer portions x 1 < 0 and x 1 > H, respectively. In the left region x 1 < 0, the governing equations for u * and ϕ * are [13, 14] c in the x 1 and x 2 directions, respectively; ξ 2 = mπ 2h (m = 0, 2, 4, . . .); ω is the wave frequency; and i 2 = −1.
    [Show abstract] [Hide abstract] ABSTRACT: The effect of functional graded piezoelectric materials on the propagation of thickness-twist waves is investigated through equations of the linear theory of piezoelectricity. The elastic and piezoelectric coefficients, dielectric permittivity, and mass density are assumed to change in a linear form but with different graded parameters along the wave propagation direction. We employ the power-series technique to solve the governing differential equations with variable coefficients attributed to the different graded parameters and prove the correction and convergence of this method. As a special case, the functional graded middle layer resulting from piezoelectric damage and material bonding is investigated. Piezoelectric damaged material can facilitate energy trapping, which is impossible in perfect materials. The increase in the damaged length and the reduction in the piezoelectric coefficient decrease the resonance frequency but increase the number of modes. Higher modes of thickness-twist waves appear periodically along the damaged length. Moreover, the displacement of the center of the damaged portion is neither symmetric nor anti-symmetric, unlike the non-graded plate. The conclusions are theoretically and practically significant for wave devices.
    Full-text · Article · Aug 2013
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