On the elastodynamics of thin microperiodic plates

The aim of this paper is to propose and investigate a new modelling approach to thin elastic plates having micro-periodic structure in planes parallel to the midplane. The main feature of this approach is that it describes the effect of the microstructure length dimensions on the macro-behaviour of the plate. This effect is neglected in the asymptotic homogenization approaches leading to the known effective stiffness models. It is shown that in micro-dynamic problems the aforementioned length scale effect plays a crucial role and cannot be neglected.