Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux

Type de document

COMMUNICATION AVEC ACTES INTERNATIONAL (ACTI)

Langue

anglais

Auteur

CHESNAIS ; BOUTIN ; HANS

Résumé / Abstract

This work investigates the dynamic behaviour of structures obtained by repeating a unit cell made up of interconnected beams or plates forming an unbraced frame. Such structures can represent an idealization of numerous reticulated systems, for example the microstructure of foams, plants, bones, the sandwich panels, stiffened plates and truss beams used in aerospace and marine structures, buildings. As beams are much stiffer in tension-compression than in bending, the propagation of compressional waves with wavelengths much greater than the cell size and the bending modes of the elements can occur in the same frequency range. Thus frame structures can behave as metamaterials and exhibit unusual dynamic properties. Since the condition of scale separation is respected for the compressional waves, the homogenization method of periodic discrete media is used to rigorously derive the macroscopic behaviour at the leading order. The main advantages of the method are the analytical formulation and the possibility to study the behaviour of the elements at the local scale. This provides a clear understanding of the mechanisms governing the dynamics of the material. In the presence of the local resonance, the form of the equations is unchanged but some macroscopic parameters depend on the frequency. In particular, this applies to the mass leading to a generalization of the Newtonian mechanics. As a result, the longitudinal modes of periodic frame beams and the transfer function have unusual properties. The same macroscopic modal shape is associated with several resonant frequencies (but the deformation of the elements at the local scale is different). These atypical behaviours are first established theoretically and then, they are confirmed by numerical simulations.