Classical vibrational modes in phononic lattices: theory and experiment

Abstract

Abstract. We present a review, through selected illustrative examples, of the physics of classical vibrational modes in phononic lattices, which elaborates on the theory, the formalism, the methods, and mainly on the numerical and experimental results related to phononic crystals. Most of the topics addressed here, are written in a selfconsistent way and they can be read as independent individual parts.

Band gaps in phononic crystals: Generation mechanisms and interaction effects

“…One type is related to the coupling between scattering resonances of the individual inclusions and the propagating mode of the embedding medium, [5][6][7] which is why they have been called hybridization gaps. 8 In metamaterial systems, such gaps are particularly interesting, since it can be shown that they allow, in some cases, the definition of negative effective material parameters. 9,10 The similarities between the mesoscopic structures which exhibit those two different gap creation mechanisms make it possible to investigate questions raised by their eventual combination.…”

Single phase 3D phononic band gap material

“…The most common one relies on Bragg scattering of the waves in phononic crystals at the periodic inclusions and their destructive interference, hence they are called Bragg gaps 6 . Furthermore, hybridization gaps are caused by coupling of the rigid-body resonances of individual inclusions as well as the propagating mode in the embedding medium and do not need a periodic arrangement of inclusions 3,7 . Another mechanism appears only in systems in which masses are elastically bonded: in such a mechanism the resonant modes of the masses interact via the elastic bonding and passbands are generated Based on theoretical and numerical methods, the existence of phononic band gaps has been predicted in lattice topologies 8,9 , undulated lattices 10 and three-dimensional lattices 9,11,12 .…”

“…A lot of studies have been dedicated to phononic crystal systems with periodic variation of density and large mismatches in wave speed periodically modulated on a length scale comparable to the desired wavelength based on multi-phase systems [1][2][3][4] . We present a novel approach of designing the unit cell of a single phase three-dimensional cellular structure leading to complete and tunable phononic band gaps.…”

Evanescent waves and deaf bands in sonic crystals

“…[3][4][5] The particular dispersion relation of these systems, known as the band structure, reveals several properties depending on the frequency. In the range of wavelength much lower than the distance between the scatterers (subwavelength regime), the heterogeneous periodic material can be considered as an effective medium with effective parameters.…”