On the non-conventional vibro-acoustic behaviour of highly contrasted plates, by Claude Boutin (ENTPE / CNRS - Université de Lyon) 25 janvier 2017
DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017
Session on New trends in vibroacoustics (i.e. elastic metamaterials and metasurfaces)
Speaker: Claude Boutin (ENTPE / CNRS - Université de Lyon)
We investigate two types of highly contrasted plates that exhibit non-conventional vibro-acoustic behaviour. These correspond to highly contrasted stratified (HCS) plates, and to cellular plates consisting of a plate held in a lattice frame. The effective HCS plate behaviour is derived from the 3D constitutive law of the materials combined with an asymptotic expansion formulation and an appropriate scaling of the stiffness contrast. The different regimes of behaviour are specified, according to the mechanical and geometrical parameters of the layers, and to the loading. The method provides a synthetic bi-torsor representation that facilitates the understanding of the coupling between the shear and bending mechanisms. Some analytical solutions under basic loading are derived. In addition, the theory is validated with experiments conducted on laminated glass with a viscoelastic interlayer. The dynamic behaviour of a cellular plate with local resonance is investigated. The unit cell is made of a beam frame on which a plate is clamped. The model is established by up-scaling the linear local description of the plate and the beams coupled together Such up-scaled model is obtained using the multiscale asymptotic method and allows investigating the atypical dispersion relationship with respect to the geometrical and mechanical contrasts of the structure components. The validity and feasibility of the model are also verified by comparing theoretical predictions with numerical FEM simulations.