Abstract
The dynamic behavior of a periodic ribbed plate with local resonances is investigated in this paper. The behavior of the unit cell comprises a beam clamped along a plate edge is analyzed via a multi-scale asymptotic method. This allows to derive the governing effective equations that describe the mechanical behavior of the material. This approach allows obtaining a relevant representation of the bending mechanisms at both global and local scales. A bending model is derived first from linear elasticity constitutive laws applied to the plate-beam coupled system. The resolution of the problem in frequency domain leads to dispersion relations and enables to investigate the band gaps associated with the structure. This model permits to identify suitable conditions for which inner resonances exist. Such conditions are determined by the geometrical and mechanical contrasts of the structural components. The validity and feasibility of the model are verified by comparing its theoretical predictions with numerical simulations (FEM/WFEM). This approach can be used to describe the motion of ribbed panels of industrial interest and/or design structures having specific atypical features in a given frequency range.
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