Abstract
The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.
Highlights
Over the past decades, considerable attention has been focused on the investigation of functionally graded materials (FGMs), because the properties of this kind of heterogeneous composite materials can vary in preferred direction
To demonstrate the influences of the gradient coefficients on the characteristics of surface waves propagating on the free surface of functionally graded piezoelectric material (FGPM) half-space, some numerical analysis results are given based on the solution derived in the previous section
Even though all the gradient functions gi (z) may be different because they are bound with different material properties, here, for the convenience of calculation, it is assumed that the variations of the elastic, piezoelectric, and dielectric coefficients and the mass density are the same along the z-axis direction, and the FGPM properties are controlled by the same gradient function g(z) = (1 + z)n, where n is the gradient coefficient
Summary
Considerable attention has been focused on the investigation of functionally graded materials (FGMs), because the properties of this kind of heterogeneous composite materials can vary in preferred direction. Du et al [7] obtained the dispersion relations of the Love waves in FGPM layered half-space using an analytical approach, assuming that all material properties have the same exponential function distribution. On the problem of wave propagation in FGPM plates, C.Othmani et al proposed a Legendre polynomial method to study the effect of the gradient coefficients on the Lamb phase velocity [15]. In the present contribution, an improved method based on the Laguerre polynomial technique is proposed to investigate the complex Rayleigh waves in the FGPM half-space. The conventional Laguerre orthogonal polynomial approach takes the wave numbers k as independent variables while taking the frequencies ω 2 as eigenvalues, but only one square term is related to ω in the Rayleigh wave governing equation It can only obtain the real wavenumber solutions of propagating waves. The results of this study can be used as the guidance of experimental measurement of Rayleigh surface waves in FGPM half-space
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