Locally Resonant Structures for Low Frequency Surface Acoustic Band Gap Applications

In this chapterResonant weFrequency investigateAcoustics theBand gap propagationAcoustic band gap of acousticAcoustics wavesWaves in a two-dimensional arrayArray of cylindrical pillars on the surface of a semi-infinite substrate. Through the computation of the acousticAcoustics band diagram and transmissionTransmission spectra of periodicPeriodic pillars arranged in different symmetries, we show that these structures possess acoustic metamaterialAcoustic metamaterial features for surface acousticAcoustics wavesWaves. The pillars on the top of the surface introduce new guided modesGuided modes in the non-radiative region of the substrate outside the soundSound cone. The modal shape and polarization of these guided modesGuided modes are more complex than those of classical surface wavesWaves propagating on a homogeneous surface. Significantly, an in-plane polarized waveWaves and a transverse waveWaves with sagittal polarization appear that are not supported by the free surface. In addition, the band diagram of the guided modesGuided modes defines band gapsBand gap that appear at frequenciesFrequency markedly lower than those expected from the BraggBragg mechanism. We identify them as originating from local resonancesResonance of the individual cylindrical pillar and we show their dependence on the geometrical parameters, in particular with the height of the pillars. The frequencyFrequency positions of these band gapsBand gap are invariant with the symmetry, and thereby the period, of the lattices, which is unexpected in band gapsBand gap based on BraggBragg mechanism. However, the role of the period remains important for defining the non-radiative region limited by the slowest bulk modes and influencing the existence of new surface modes of the structures. The surface acousticAcoustics waveWaves transmissionTransmission across a finite arrayArray of pillars corroborates the signature of the locally resonantResonant band gapsBand gap for surface modes and their link with the symmetry of the source and its polarization. Numerical simulations based on an efficient finite elementFinite element method and considering Lithium Niobate pillars on a Lithium Niobate substrate are used to illustrate the theory.