Elastic wave and vibration bandgaps in planar square metamaterial-based lattice structures

Abstract

In this work, a new type of planar square lattice structures for the attenuation of elastic wave propagation is proposed and designed. To obtain a high vibration attenuation in low frequency ranges, the internal resonance mechanism of the acoustic metamaterials (AMs) is introduced into the continuous square lattice system with a cross-type core consisting of two segments with a radius jump discontinuity in each unit-cell. The wave propagation and vibration bandgap properties of the AM-based lattice structures are studied by using a spectral element method (SEM) which can provide accurate dynamic characteristics of a lattice structure due to its analytical spectral element matrix. The band structures calculated show that the phononic bandgaps induced by the local resonance and destructive interference co-exist in the considered systems. The effects of the structural and material parameters on the bandgaps are investigated in detail by the frequency response analysis of a spectral element model subjected to a dynamic excitation. Finally, in order to obtain lower and wider frequency bandgaps, the mechanism to optimize the unit-cell of the AM-based lattice structures is illustrated and a composite lattice model is suggested.