On the topology of the complex wave spectrum in a fluid-coupled elastic layer

Abstract

The behavior of the complex leaky Lamb wave (LLW) spectrum of a plate immersed in a fluid has been studied as a function of the ratio of fluid-to-solid densities. It has been shown that widely accepted assumptions concerning the similarities between the classical Lamb wave spectrum and the LLW spectrum are not valid as the fluid density approaches that of the solid. Recent experimental and theoretical results demonstrate that there is a strong anomaly in the reflectance of composite plates in water. This anomaly is related to the details of the complex LLW spectrum. The spectrum is composed of both the familiar propagating Lamb wave branches and the mostly imaginary, nonpropagating branches. From the character of the complex spectrum, it is demonstrated that topological changes in the fundamental symmetric mode are related to its nearness to the first complex branch of the spectrum. Increasing the fluid–solid density ratio leads to interaction between these modes and to mutual interchange between portions of their branches. As the density ratio increases from zero to infinity, the complex spectrum is gradually transformed from a classical Lamb wave spectrum to one appropriate for a plate with zero normal surface displacements.