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Locally resonant periodic acoustic media
thesisposted on 2010-11-12, 12:27 authored by Luke Chalmers
Phononic crystals are composite media, with two different elastic materials modulated in a periodic fashion. The two-dimensional system under study is comprised of an array of cylindrical tubes arranged in a square Bravais lattice. The propagation of a time-harmonic acoustic Bloch waves is investigated experimentally and the findings compared with those obtained from the finite element method. The band structure, that is a well-known characteristic of Bloch wave dispersion, is also determined. This demonstrates the existence of band gaps of forbidden transmission at certain frequency ranges. These arise due to the interference when the wavelength of the incident wave is comparable to the periodic spacing of the modulated media. A second phononic crystal with slotted steel tubes is also studied. The opening in the tube permitting air to flow to the internal cavity, and constituting a Helmholtz resonator. The band structure of such a structure possesses additional band gaps, which arise due to the excitation of the resonators. Furthermore, it has recently been shown that periodically distributed Helmholtz resonator structures, can exhibit negative refraction phenomena. Using the transmission line technique, as outlined by Y.Cheng et al. we demonstrate this behaviour for our experimental system. It is shown that, at certain frequency ranges, the locally resonant phononic crystal exhibits negative effective density and bulk modulus, the two conditions required to obtain a negative index of refraction.
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NotesA Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.