Modeling of Rayleigh-type waves in a viscoelastic piezoelectric fiber-reinforced composite layered Structure

Abstract The propagation of Rayleigh-type surface waves in a viscoelastic piezoelectric fiber-reinforced composite (VRFRC) layer bonded to an isotropic elastic half-space through a mechanically imperfect interface is investigated. Both constituents of the composite are dissipative: the PZT fibers are treated as viscoelastic piezoelectric solids and the epoxy matrix as a viscoelastic dielectric, each described by Kelvin–Voigt elements acting on the stress–strain and on the electric field–electric displacement pairs, so that every phase, and the homogenized composite, is passive. The complex , frequency-dependent effective constants are obtained by introducing the complex constituent constants into the strength-of-materials/rule-of-mixtures (SM/RM) relations through the elastic–viscoelastic correspondence principle. The imperfect bond is represented by normal and tangential linear-slip conditions, the upper surface is traction-free and electrically open, and the metallic substrate grounds the interface. An exact 8 × 8 complex dispersion relation is derived and solved, without any small-loss approximation, for the phase velocity and the normalized attenuation of the fundamental mode. The results show that the fiber volume fraction controls the dispersion through the layer stiffness and piezoelectric stiffening, the viscous relaxation times of the matrix (chiefly η c,q 33 and η c,q 44) control the attenuation while leaving the phase velocity almost unchanged, fiber viscoelasticity becomes significant only at high fiber content, and interfacial compliance, in particular the normal compliance, lowers the phase velocity and the attenuation in the dispersive range. Mode shapes, particle orbits, the electric potential distribution and a velocity-based electromechani-cal coupling measure are also analysed; the group velocity shows a pronounced Airy-phase minimum that is sensitive to the fiber content and the bond quality, and the velocity-based coupling measure K 2 = 2(c open − c short)/c open reaches about 3.3% for fiber-rich layers.