An equivalent lattice-modified model of interfering Bragg bandgaps and Locally Resonant Stop Bands for phononic crystal made from Locally Resonant elements

The design and development of advanced devices based on metamaterials to control the transmission of acoustic waves is a hot topic. An important class of these metamaterials is based on phononic crystals with Locally Resonant Structure, included in those commonly known as Locally Resonant Sonic Materials. In these metamaterials, wave control is basically performed by two mechanisms: internal (or local) resonances in the scatterers that form the phononic crystal, and Bragg bandgaps due to structural periodicity. Their main control feature is the resonance peaks forming additional stop-bands away from the Bragg frequency, mainly in the low frequency regime. For some applications, coupling of the two phenomena is necessary to create a broad transmission gap. However, when both are located in close frequency ranges, some destructive interferences can occur. In this paper, the authors develop a comprehensive numerical model of periodic arrays of Hemholtz resonators, which explains in detail the physical mechanisms of this destructive interference and, simultaneously, allows the reproduction of the consequences of the interference. The numerical results are supported by experimental tests.