Asymptotic modeling of the effect of a thin slab in the framework of linear elasticity with voids
Abstract
The aim of this paper is to model the effect of a planar thin layer in the framework of linear elasticity with voids by using the notion of impedance boundary condition. We start from a transmission model problem which models the wave propagation between an elastic body with small distributed voids $\Omega _{-}$\ \ and a thin coating slab $\Omega _{+}^{\delta }$ ($\delta$ is supposed to be small enough). We show how to model the effect of the thin coating by an impedance boundary condition on the junction of the elastic two bodies. To this end, we use the technique of asymptotic expansion with scaling. We also prove an error estimate.
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DOI: https://doi.org/10.52846/ami.v52i2.1987