Elastodynamics of strongly heterogeneous periodic plates using Reissner‐Mindlin and Kirchhoff‐Love models
Eduard Rohan, Bernadette Miara · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2015
The paper deals with the homogenization of strongly heterogeneous elastic plates satisfying the Reissner‐Mindlin or the Kirchhoff‐Love hypotheses. We rigorously justify the limit models obtained by the asymptotic analysis which describe the harmonic waves propagation associated with in‐plane displacement and transversal deflection modes in these two classical plate structures. Large contrasts in the coefficients of the elastic material components may result in existence of band gaps for the limit Reissner‐Mindlin plates while an analogous property is lost for the deflection of the Kirchhoff‐Love model. The different dispersion properties of both the limit plates are related to the changing sign of the limit frequency dependent mass density coefficients.