Scholte‐Gogoladze‐like waves at the interface between a fluid and an anisotropic layered composite

Abstract

It is now well understood that two types of plane harmonic waves can propagate freely along the plane interface between a homogeneous isotropic elastic solid and an acoustic fluid. The first, with decaying amplitude as it propagates along the interface, and which is equivalent to the Rayleigh wave in the solid as the fluid density becomes negligible, is called a leaky or generalized Rayleigh wave. The other, named here the Scholte‐Gogoladze wave after the two researchers who first, independently, uncovered its existence in 1948, propagates unattenuated parallel to the boundary, while decaying exponentially in both directions away from the interface. In the present contribution, the existence of Scholte‐Gogoladze‐like waves at a fluid/layered composite interface is investigated. The composite is made‐up of an arbitrary number of homogeneous anisotropic layers stacked in a unit cell that repeats periodically. An extension of Stroh's sextic matrix formalism to periodically layered media is employed to carry out the analysis. The associated eigenvalue problem is solved in closed form, and the frequency equation for the interface waves is formulated in terms of the surface impedance tensors for both the fluid and the layered composite. In contrast to the homogeneous medium, the Scholte‐Gogoladze‐like waves are now dispersive and, for certain combinations of the material parameters, the dispersion spectrum consists of more than one branch in the frequency‐wavenumber space. [Work supported by ONR.]