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As to an ideally layered structure with a functionally graded piezoelectric substrate (material parameters change continuously along the thickness direction) and a hard dielectric layer, the existence and propagation behavior of transverse surface waves is studied by analytical technique. The dispersion equations for the existence of the transverse surface waves with respect to phase velocity are obtained for electrically open and short circuit conditions, respectively. A detailed investigation of the effect of gradient coefficient on dispersion relation, electromechanical coupling factor and penetration depth is carried out. It is found by numerical examples that adjusting gradient coefficient makes the electromechanical coupling factor of the transverse surface waves achieve quite high values at some appropriate ratio values of the layer thickness to the wavelength, and at the same time, the penetration depth can be reduced to the same order as the wavelength.

An analytical study on transverse surface waves propagating in a functionally graded material carrying a piezoelectric layer is carried out by Wentzel–Kramers–Brillouin technique. Dispersion relations for the existence of the waves are obtained for material gradient of arbitrary functions and the effects of material gradient on wave propagation are quantified. Numerical examples show the presence of material gradient significantly affects long waves but has only negligible effects on short waves. Depending on whether the surface wave velocity is smaller or greater than the bulk-shear-wave velocity in the piezoelectric layer, two different types of dispersion behavior are discussed.

The propagation of transverse surface waves in a piezoelectric material carrying a prestressed metal layer of finite thickness is investigated analytically. The dispersion equation is solved in closed form for class 6 mm piezoelectric materials and the conditions for the existence of various wave modes are obtained. Numerical examples are presented for an aluminum, gold, or zinc layer on a PZT-4 ceramic substrate. The presence of initial stress can extend or shorten the range of phase velocity within which a nonleaky but dispersive mode exists. The dependence of phase velocity on initial stress opens a new window for designing acoustic wave devices.

An analytical study on transverse surface waves propagating in a functionally graded piezoelectric substrate carrying a metal layer of finite thickness was carried out. Dispersion relations for the existence of the waves were obtained and the effects of material gradient on wave propagation were quantified. Numerical examples show that the presence of the material gradient affects significantly the fundamental mode but has only negligible effects on the higher order modes. Depending on whether the surface wave velocity is smaller or greater than the bulk shear wave velocity in the metal layer, three different types of the dispersion behavior are discussed.

For a functionally graded piezoelectric substrate with exponential variation, the existence and propagation behavior of transverse surface waves is studied by analytical technique. The dispersion equations for the existence of the transverse surface waves with respect to phase velocity are obtained for both electrically open and short conditions. A detailed investigation of the effect of gradient coefficient on dispersion relation, phase velocity, group velocity and electromechanical coupling factor is carried out. It is found by numerical examples that adjusting gradient coefficient makes the electromechanical coupling factor of the transverse surface waves achieve quite high values at some appropriate wavenumber, and at the same time, the penetration depth can be reduced to the same order as the wavelength under electrically short case. Because of the negligible initial stress in functionally graded piezoelectric materials, this model could serve as an excellent substitute for the typical layered piezoelectric structures used in surface acoustic wave (SAW) devices, thus providing a theoretical foundation for designing SAW devices with high performance.

The scattering behavior of elastic P-waves by a transversely isotropic piezoelectric cylinder embedded in an infinite polymer matrix is studied. The method of wavefunction expansion is used to formulate the problem. Numerical calculations are carried out for the distribution of stresses, mechanical displacements and electrical potential around the piezoelectric cylinder, respectively. Effects of normalized frequency and incident angle of incident waves, radius of the cylinder on the dynamic stress and electric field concentrations are investigated in detail. It is found that the effect of the incident angle on the dynamic stress concentration is markedly only for the low frequency waves and the maxima of the magnitudes of stresses shift toward the incident side of the piezoelectric cylinder as the normalized frequency increases. This study is useful in designing piezoelectric composites, especially for the case of piezoelectric cylinders aligned sparsely in a matrix medium.

In this paper, we analyze the propagation of Bleustein–Gulyaev waves in an unbounded piezoelectric half-space loaded with a viscous liquid layer of finite thickness within the linear elastic theories. Exact solutions of the phase velocity equations are obtained in the cases of both electrically open circuit and short circuit by solving the equilibrium equations of piezoelectric materials and the diffusion equation of viscous liquid. A PZT-5H/Glycerin system is selected to perform the numerical calculation. The results show that the mass density and the viscous coefficient have different effects on the propagation attenuation and phase velocity under different electrical boundary conditions. In particular, the penetration depth of the waves is of the same order as the wavelength in the case of electrically short circuit. These effects can be used to manipulate the behavior of the waves and have implications in the application of acoustic wave devices.