Mode computation of immersed multilayer plates by solving an eigenvalue problem

Abstract

The aim of this paper is to compute modes of immersed multilayer plates by writing and solving an eigenvalue problem. The method can be applied to any kind of material with layers, i.e., fluid, anisotropic and viscoelastic. The two external interfaces of the plate can be described as either vacuum/vacuum, fluid/vacuum, or fluid/fluid with a single fluid or fluid/fluid with two different fluids. The method is based on the discretization of the plate by using a finite differences scheme in its vertical direction. One global state vector is associated with inner discretized positions of each layer, and two local state vectors characterize the physical state at its bounds. Interfacial state vectors are introduced in certain situations at external and internal plate interfaces. With these state vectors and after pertinent algebraic manipulations, an eigenvalue system is built. Its solutions are searched by fixing the slowness, wavevector or frequency of guided waves. These three parameterizations correspond to three different physical models. For each case, discussions of dispersion curves and attenuation curves are given for guided modes in a plate loaded by fluids at one or two sides. This numerical tool is shown to provide convenience and accuracy.