Asymptotic Behavior of Forced Vibrations of Layered Plates

This article delves into dynamic three-dimensional elasticity problems specifically tailored for layered plates. In contrast to classical and existing refined theories of plates and shells, which prove unsuitable for this particular class of issues, our investigation led to the discovery of fundamentally different asymptotics for stress tensor components and displacement vectors. This breakthrough enabled the formulation of an asymptotic solution to address the intricacies of the 3D problem. The study identifies specific scenarios where the derived solution attains mathematical exactness, providing a comprehensive understanding of the conditions under which the proposed approach proves particularly effective. By exploring these dynamic 3D elasticity problems with layered plates, this work contributes novel insights and solutions, extending beyond the limitations of classical plate theories.