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Research Papers

Angular Band Gaps in Sonic Crystals: Evanescent Waves and Spatial Complex Dispersion Relation

[+] Author and Article Information
V. Romero-García

e-mail: virogar1@gmail.com

R. Picó

e-mail: rpico@fis.upv.es

A. Cebrecos

e-mail: alcebrui@epsg.upv.es
Instituto de Investigación para la Gestión Integrada de Zonas Costeras,
Universitat Politècnica de València,
Paranimf 1, 46730, Gandia, Spain

K. Staliunas

Institució Catalana de Recerca i Estudis Avançats (ICREA),
Pg. Lluis Companys, 23,
ES-08010, Terrassa, Spain
e-mail: kestutis.staliunas@icrea.es

V. J. Sánchez-Morcillo

Instituto de Investigación para la Gestión Integrada de Zonas Costeras,
Universitat Politècnica de València,
Paranimf 1, 46730, Gandia, Spain
e-mail: victorsm@fis.upv.es

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 30, 2012; final manuscript received November 9, 2012; published online June 6, 2013. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 135(4), 041012 (Jun 06, 2013) (6 pages) Paper No: VIB-12-1165; doi: 10.1115/1.4023832 History: Received May 30, 2012; Revised November 09, 2012

Phononic crystals are artificial materials made of a periodic distribution of solid scatterers embedded into a solid host medium with different physical properties. An interesting case of phononic crystals, known as sonic crystals (SCs), appears when the solid scatterers are periodically embedded in a fluid medium. In SCs only longitudinal modes are allowed to propagate and both the theoretical and the experimental studies of the properties of the system are simplified without loss of generality. The most celebrated property of these systems is perhaps the existence of spectral band gaps. However, the periodicity of the system can also affect to the spatial dispersion, making possible the control of the diffraction inside these structures. In this work we study the main features of the spatial dispersion in SCs from a novel point of view taking into account the evanescent properties of the system, i.e., studying the complex spatial dispersion relations. The evanescent behavior of the propagation of waves in the angular band gaps are theoretically and experimentally observed in this work. Both the numerical predictions and the experimental results show the presence of angular band gaps in good agreement with the complex spatial dispersion relation. The results shown in this work are independent of the spatial scale of the structure, and in principle the fundamental role of the evanescent waves could be also expected in micro- or nanoscale phononic crystals.

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Figures

Grahic Jump Location
Fig. 1

Analysis of the eigenvalue problem using EPWE. (a) Real part of the complex band structure for a square array of rigid cylinders embedded in air. Horizontal dashed line represents the studied frequency. Real (b) and imaginary (c) parts of the isofrequency contours at ν. Analysis of the scattering problem at the selected frequency.

Grahic Jump Location
Fig. 2

Analysis of the scattering problem using multiple scattering theory. (a), (b), and (c) represent the pattern of the absolute value of the pressure for a linear source, a linear source inside (in the middle of the SC) a 6 × 6 PC and a linear source inside a 16 × 16 PC, respectively. (d), (e), and (f) show the polar profiles of the absolute value of the pressure for different radial distances from the source in each SC.

Grahic Jump Location
Fig. 3

Geometrical interpretation of diffraction of waves propagating along the z axis (a) positive, or normal diffraction in propagation through homogeneous materials (b) negative, or anomalous diffraction (c) zero diffraction. The area of negligible diffraction (for evaluation of the minimum size of the nondiffractive beam) is indicated [35]. (d) Different regimes considered: a broad beams with spatial spectra inside the parabolic area of the spatial dispersion curve, b beams of intermediate width, with spatial spectra filling the full width of the isoline of the given band, c narrow beams with the spatial spectra extending over isolines from the neighboring bands, and thus overlapping the band gaps in angular domain. The region denoted by d corresponds to the forbidden angles (band gaps in space spectra domain). (d) Schematic representation of the angular BG.

Grahic Jump Location
Fig. 4

Experimental analysis of the angular band gaps. We have analyzed three cases, 5, 7, and 9 rows. (a) Experimental polar map of the sound pressure level spectrum for the case of 9 rows. Color scale represents the sound pressure level. (b) Cuts at the analyzed frequency for the three analyzed cases.

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