Free Vibrations of Thin Periodic Plates

The aim of this contribution is to apply a new modelling approach to the thin linear-elastic Kirchhoff plates with a periodic structure proposed in [2] to investigate free vibrations. Using this approach we can describe the length-scale effect on the dynamic plate behaviour. This approach leading to the structural model is compared with the asymptotic homogenization approach, which neglects the length-scale effect and leads to the local model. It is shown under what conditions the local model is sufficient to analyse free vibrations of microperiodic plates and why we have to take into account the length-scale effect using the structural model. The physical correctness of this model is also discussed.