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Study on the Effects of Acoustic Focusing and Concentrating Based on Acoustic Metamaterials

Author: WangYuRan
Tutor: ZhangShuYi; ZhangHui
School: Nanjing University
Course: Acoustics
Keywords: Phononic crystals Negative refraction Band structure Plane wave expansion method Concentrator Wave vector direction Crystal structure Electromagnetic wave propagation Transmission spectrum Sound Focus Bandgap Structure Media Wave vector space Multiple scattering method Photonic crystals Frequency , etc. crystals Scatterers Periodic array Refraction effect
CLC: O42
Type: Master's thesis
Year: 2012
Downloads: 187
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Abstract

This thesis studies the acoustic focusing and concentrating based on acoustic metamaterials, which mainly includes three parts:(1) The related theories of phononic crystal on the study of the metamaterials;(2) Acoustic dual-negative refraction (ADNR) effect and the effects of crystal structure on ADNR;(3) The theory of transformation acoustics and the model of a two-dimensional cylindrical broadband acoustic concentrator. The contents of each part are described briefly as following:1. The related theories of phononic crystal on the study of the metamaterialsPhononic crystal (PC) is a kind of acoustic artificial materials which are constructed with periodically arranged elastic scatterers and matrix, so it can be seen as the extension of the electronic crystals in the sense of elastic wave. Similar to the photonic crystals, PCs are characterized of bandgap effect, waveguide effect, and defect effect, etc. For all above studies, the band structure of PCs should be precisely known. Therefore, the calculating methods of band structures for PCs with different structures are important for the researches of PCs. The directions of energy flux and phase velocity of the wave propagating in left-handed materials are opposited, so it can be used to fabricate the superlens. Acoustic artificial materials with a special desigin may have the effective negative elastic parameters in the resonance, which can be used to realize the acoustic left-handed materials.In the second chapter of the thesis, firstly the calculating methods of band structure for two-dimensional PCs with two components are presented. Specially, the plane wave expansion method and the finite element method are emphatically analyzed, and then the computed results of two methods are compared to verify the validity of algorithms. Secondly the calculation of transmission spectrum for PCs by the method of multiple scattering indicates that the transmission spectrum can be used to describe the frequency range of the bandgap. Lastly, the basic concept of left-handed materials and the principle of effective negative elastic parameters are analyzed to indicate the feasibility of acoustic left-handed materials.2. Acoustic dual-negative refraction (ADNR) effect and the effects of crystal structure on ADNRBesides the bandgap effect, the negative refraction phenomenon results from the effect of abnormal dispersion could happen in PCs. We could use the acoustic negative refraction (ANR) effect in PCs to design and fabricate the superlens which is used to image for evanescent wave. Moreover, ANR effect also can be used for sound focusing by flat lenses. The ADR effects in PCs have two generation mechanisms which are forward negative refraction and backward negative refraction, and the latter one satisfies the requirement for opposite directions of energy flux and wave vector. The ADNR in PCs is caused by the overlapping bands, and for an incident wave at the particular frequency, two different group velocities and effective refractive indexes are generated in PCs, so it may form two different propagation paths of negative refraction. The pattern of equifrequency contours is an important tool to study the ADR effect, and it reflects the directions of group velocities and phase velocities in the wave vector space. Although the generation mechanism of ADNR effect for the particular PCs has been investigated, the effects of scatterers with different crystal structure on ADNR are not known yet.In the third chapter of the thesis, firstly two generation mechanisms which are forward effect and backward effect for ADR phenomenon are analyzed by the band structure and equifrequency contours. Secondly the generation mechanism of ADNR effect is investigated by the overlapping bands, and it indicates that the ADNR effect can be used for double focusing imaging. The band structures of PCs for eight crystal structures with different filling ratios are calculated by finite element method, and the areas of overlapping bands for normalized frequency are given. Lastly, the potential operating frequency ranges in PCs of these eight crystal structures for ADNR effect are investigated, and it can be used to provide guidance for the optimization design of PCs with ADNR effect.3. Transformation acoustics and acoustic concentratorTransformation acoustics can help us to artificially change the propagation path of the elastic wave based on the equivalence of coordinate transformations and elastic parameters. Acoustic cloak is a device guiding waves around the hidden object as if no disturbance is around the cloak. The technique of transformation acoustics makes acoustic cloak be not a dream. Besides the cloaks, electromagnetic (EM) concentrator, EM rotator, and EM wormhole have been proposed in the field of transformation optics. Some of these models have been equivalent to obtain the corresponding models of transformation acoustics, but the corresponding acoustic concentrators have not been proposed until now. For the concentrator, it can concentrate the incident waves into its central core without producing any scattering.In the fourth chapter of the thesis, firstly the theoretical principle of transformation acoustics which means the coordinate invariance of the acoustic equation is given. Then the theory of two-dimensional (2D) cylindrical acoustic cloak is investigated, and the analogy relations from transformation optics to transformation acoustics in2D cylindrical coordinates are given. Secondly, the theory of simulation between acoustic multilayer structure and acoustic materials with density tensors is investigated. Lastly, a2D cylindrical concentrator is proposed by the analogy, and then we use the method of acoustic multilayer system to discretely construct the concentrator. The performances of scattering and concentrating for acoustic concentrators are calculated by finite-element method.Finally, the conclusions and the prospects of the future work are presented.

Study on the Effects of Acoustic Focusing and Concentrating Based on Acoustic Metamaterials

Abstract

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