Modeling of flexural vibrations of a Kirchhoff plate with a thin-walled elastic inclusion of weak contrast

Abstract

We have proposed a model of the elastodynamic interaction between a thin plate and a thin-walled elastic rectilinear inclusion of weak contrast. The inclusion in the plate is subjected to steady-state flexural vibrations and the conditions of perfect contact. The plate motion is described according to the Kirchhoff hypotheses. The procedure of study is based on the application of methods of the theory of singular perturbations. Using the obtained model, we have studied the spectral characteristics of flexural waves scattered by the inhomogeneity into the far-field zone.

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

“…Note that there are not so many works devoted to study of models of thin inclusions in plates. We mention [7][8][9], in which thin elastic inclusions in pates were studied. Papers [10][11][12][13] are devoted investigations of thin rigid inclusions.…”