2. Phononic crystals with local resonances: towards acoustic metamaterials

2.1 Brief history and motivations

The notion of phononic bandgap, as defined above, is based on the principle of interference. This means that the grating period must be commensurate with the working wavelength, and obtaining usable band gaps requires structures with a certain number of periods, generally of the order of ten or so. The resulting dimensional constraints may prove prohibitive in the context of low-frequency applications, particularly in the field of sound insulation, which was initially seen as the key application for these artificial structures. Audible frequencies typically range from 20 Hz to 20 kHz, so the wavelengths involved range from a few centimetres to a few metres. A sound insulator based on a conventional phononic crystal would therefore be too bulky for...