TY - CHAP
T1 - Locally Resonant Structures for Low Frequency Surface Acoustic Band Gap Applications
AU - Khelif, Abdelkrim
AU - Achaoui, Younes
AU - Aoubiza, Boujemaa
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2024.
PY - 2024/11/17
Y1 - 2024/11/17
N2 - In this chapterResonantweFrequencyinvestigateAcousticstheBand gappropagationAcoustic band gap of acousticAcousticswavesWaves 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 acousticAcousticswavesWaves. 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 acousticAcousticswaveWavestransmissionTransmission across a finite arrayArray of pillars corroborates the signature of the locally resonantResonantband 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.
AB - In this chapterResonantweFrequencyinvestigateAcousticstheBand gappropagationAcoustic band gap of acousticAcousticswavesWaves 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 acousticAcousticswavesWaves. 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 acousticAcousticswaveWavestransmissionTransmission across a finite arrayArray of pillars corroborates the signature of the locally resonantResonantband 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.
UR - http://www.scopus.com/inward/record.url?scp=85211119760&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-60015-9_2
DO - 10.1007/978-3-031-60015-9_2
M3 - Chapter
AN - SCOPUS:85211119760
T3 - Springer Series in Materials Science
SP - 53
EP - 71
BT - Springer Series in Materials Science
PB - Springer Science and Business Media Deutschland GmbH
ER -