Dynamics of ribbed plates with inner resonance: Analytical homogenized models and experimental validation

Abstract

This paper deals with the theoretical, numerical and experimental behavior of periodic orthogonally ribbed plates. It extends the paper (Fossat et al., 2018) in which a comprehensive homogenized model has been established for flexural and torsional motion of periodic 1D-ribbed plates. New theoretical results describing the out-of-plane behavior of cellular plates involving inner resonance phenomena, are derived using an asymptotic approach. In this aim, the out-of-plane model of beam grids accounting for local bending and torsion is first established through the asymptotic method of homogenization of periodic discrete media. Then, the coupling between the beam grid and the internal plates (fully or partially connected to it) is detailed. This lead to an explicit analytical formulation of the equivalent plate model whose effective parameters arise from the geometry and mechanical properties of the unit cell. The unconventional features of the flexural wave dispersion are shown to be straightforwardly related to inner-resonance phenomena. These theoretical results are successfully compared to numerical computations conducted using WFEM. Furthermore, experiments performed on two prototypes of ribbed plates evidence the ability of the homogenized model to describe their complex dynamic behavior. The latter is characterized by the co-existence of a dynamic regime at both the micro-scale of the period and the macro-scale of the whole structure, that results in an inhomogeneous kinematics where the plate and beam displacements differ at the leading order. These unique features depart from the usual assumptions retained in plate mechanics and generates the observed non-conventional features. In conclusion, it is stressed that the study yields design rules to tailor cellular panels having specific atypical features in a given frequency range.