Control of Wave Propagation in Sandwich Beams with Auxetic Core

Abstract

The wave propagation in sandwich beams with cellular core is analyzed and controlled. The material properties of cellular cores are highly dependent on the geometry of the cell composing the honeycomb structure. Core materials of different geometry placed periodically along the beam length introduce the proper impedance mismatch necessary to impede the propagation of waves along the beam. A theoretical model is developed to describe the wave propagation characteristics and the vibration of the sandwich beam. The model is used to obtain the transfer matrix for a unit cell of the considered periodic structure, which is then used to analyze the dynamics of wave propagation along the beam. The transfer matrix is also properly recast in order to obtain the dynamic stiffness matrix and formulate a spectral finite element model for the periodic sandwich beam. The spectral finite element model employs dynamic shape functions obtained from the solution of the distributed parameter model, which allow predicting the dynamic behavior of the structure with a significantly reduced number of elements as compared to conventional FEM. The transfer matrix of the sandwich beam identifies the location of the frequency bands where traveling waves are attenuated. The influence of core geometry and periodicity on the location and extension of these stop bands is assessed through a series of simulations. The effect of the periodicity of the structure is also evaluated by considering the vibration response of a clamped free beam excited by the harmonic motion of the base. The results demonstrate the simplicity and the effectiveness of the proposed treatment whereby the transmission of waves and the vibration over specified frequency bands can be significantly reduced without requiring additional passive or active control devices. The unique characteristics of cellular solids therefore can be used to design light-weight composite panels that behave as mechanical filters. The filtering capabilities of such passive composite panels may be easily changed and optimized to reduce their transmissibility over a desired frequency range without compromising the size and the weight of the structure.