Interferences in locally resonant sonic metamaterials formed from Helmholtz resonators

Abstract

The emergence of materials artificially designed to control the transmission of waves, generally called metamaterials, has been a hot topic in the field of acoustics for several years. The design of these metamaterials is usually carried out by overlapping different wave control mechanisms. An example of this trend is the so-called Locally Resonant Sonic Materials, being one of them the Phononic Crystals with a local resonant structure. These metamaterials are formed by sets of isolated resonators in such a way that the control of the waves is carried out by resonances and by the existence of Bragg bandgaps, which appear due to the ordered distribution of the resonators. Their use is based on the creation of resonance peaks to form additional nontransmission bands mainly in the low frequency regime, usually below the first Bragg frequency. The coupling of both gaps has been made in some cases, but it is not always so. In this work, using a periodic structure formed by Helmholtz resonators, we report the existence of interferences between the resonances and the Bragg bandgaps when they are working in nearby frequency ranges, so that they prevent the coupling of both gaps. We explain their physical principles and present possible solutions to mitigate them. To this end, we have developed numerical models based on the finite element method, and the results have been verified by means of accurate experimental results obtained under controlled conditions.