Wave Propagation in Sandwich Plates with Periodic Auxetic Core

Abstract

The wave propagation in and the vibration of sandwich plates with cellular core are analyzed and controlled. Negative Poisson’s ratio (auxetic) core materials of different geometry placed periodically in the plate introduce the proper impedance mismatch necessary to obstruct the propagation of waves over specified frequency bands (stop bands) and in particular directions. The location and the extension of the stop bands and the directions of wave propagation can be modified by proper selection of the periodicity and of the geometrical and physical properties of the core. A finite element model is developed to predict the dynamic response of three-layered sandwich panels with honeycomb core. The finite element model along with the theory of periodic structures evaluates the influence of core materials of different geometry placed periodically along the two dimensions of the structure. This combined analysis yields the phase constant surfaces for the considered sandwich plates, which define location and extension of the stop bands, as well as the directions of wave propagation at assigned frequency values. The analysis of the phase constant surfaces and the evaluation of the harmonic response at specified frequencies demonstrate the plates’ directional properties, whose spatial patterns strongly depend on the configuration of the periodic core and on the excitation frequency. Auxetic honeycombs are here considered as core materials in order to obtain maximum design flexibility. Their elastic and inertial characteristics in fact vary substantially with their internal geometry. For given configurations they outcast up to five times the corresponding properties of traditional hexagonal honeycombs. The presented numerical results demonstrate the unique characteristics of this class of two-dimensional periodic structures, which behave as directional mechanical filters. The findings of the study suggest that optimal configurations for the periodic cellular core may be identified in order to design passive composite panels, which are stable and quiet over desired frequency bands and which fit desired transmissibility levels in particular directions. Such unique filtering capabilities are achieved without requiring additional passive or active control devices and therefore without compromising the size and the weight of the layered structure.