Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers

Abstract

The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: ε is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and ω is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters ε²ω. If this value is small, then the limit model is the standard homogenized one-dimensional wave equation. On the contrary, if ε²ω is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and “co-existing” at every point. The proof of these results uses the milticomponent homogenization method.