Acoustic stop bands of surface and bulk modes in two-dimensional phononic lattices consisting of aluminum and a polymer (original) (raw)
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Surface acoustic waves in two-dimensional periodic elastic structures
Physical Review B, 1998
Acoustic waves localized at the surface of two-dimensional ͑2D͒ periodic elastic structures, or 2D phononic crystals, are studied theoretically by taking account of the elastic anisotropy of constituent materials. The surface considered is perpendicular to the axis of a periodic array of cylinders embedded in a background material. The dispersion relations of the surface modes are calculated for circular cylinders of AlAs which form a square lattice in a GaAs matrix. The folding and anisotropy of the surface wave branches, as well as the existence of pseudosurface waves, are found. The stop band distributions of the surface, pseudosurface, and bulk waves are plotted in a form relevant for comparison with ultrasound imaging experiments. ͓S0163-1829͑98͒00336-1͔
Physical Review B, 2000
The finite-difference time-domain method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional ͑2D͒ phononic lattices, i.e., periodic solid-solid, solid-liquid, and solid-vacuum composites, for which the conventional plane-wave-expansion method fails or converges very slowly. Numerical examples are developed for 2D structures with polyethylene, mercury, and vacuum cylinders forming a square lattice in an aluminum matrix. The implication of the calculated dispersion relations for ultrasound transmission experiments is discussed.
Band structures of acoustic waves in phononic lattices
Physica B: Condensed Matter, 2002
The finite-difference time-domain (FDTD) method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional (2D) phononic lattices, i.e., periodic solid-liquid composites for which the conventional plane-wave-expansion method fails. Numerical examples are developed for 2D structures with mercury cylinders forming a square lattice in an aluminum matrix.
Two-dimensional phononic crystals: surface acoustic waves
Physica B: Condensed Matter, 1999
We study theoretically the surface localized acoustic waves in two-dimensional phononic crystals consisting of circular cylinders of AlAs embedded in a GaAs matrix. The folding and anisotropy of surface wave branches as well as the existence of pseudosurface wave branches are predicted. We present stop band distributions of both the surface and bulk acoustic waves, which would be relevant to compare with the ultrasound imaging experiment.
Acoustic Phononic Crystals with Square-Shaped Scatterers for Two-Dimensional Structures
International Symposium Innovative Technologies Engineering and Science, 2017
Metamaterials are artificial materials that possess unusual physical properties that are not usually found in natural materials. Phononic crystals (PnC) can be constructed by periodic distribution of inclusions embedded in a matrix with high contrast in mechanical properties. They can forbid the propagations of acoustic waves in certain frequencies by creating band gaps. Such band gaps may be independent of the direction of propagation of the incident wave. In present work the acoustic band structure of a two-dimensional phononic crystal consisting of square-shaped rods embedded in air matrix are studied to find the existence of stop bands for the waves of certain energy. The wave band structures of acoustic waves in 2D air/solid phononic structure are investigated theoretically by Finite Element (FE) simulations. A time harmonic analysis of the acoustic wave propagation is performed using the acoustics package of the FE software Comsol Multiphysics v5.3. Phononic band diagrams ω=ω(k) for a 2D PnC were plotted versus the wavevector k along the M-Г-X-M path in the first Brillouin zone. The calculated phonon dispersion results indicate the existence of full acoustic modes in the proposed structure along the high symmetry points.
Journal of Physics: Condensed Matter, 1998
Transmission of acoustic waves in two-dimensional binary solid/solid composite media composed of arrays of Duralumin cylindrical inclusions embedded in an epoxy resin matrix is studied. The experimental transmission spectrum and theoretical band structure of two periodic arrays of cylinders organized on a square lattice and on a centred rectangular network are reported. Absolute gaps extending throughout the first two-dimensional Brillouin zone are predicted. The measured transmission is observed to drop to noise level throughout frequency intervals in reasonable agreement with the calculated forbidden frequency bands.
Physical Review Letters, 2001
Experimental measurements of acoustic transmission through a solid-solid two-dimensional binarycomposite medium constituted of a triangular array of parallel circular steel cylinders in an epoxy matrix are reported. Attention is restricted to propagation of elastic waves perpendicular to the cylinders. Measured transmitted spectra demonstrate the existence of absolute stop bands, i.e., band gaps independent of the direction of propagation in the plane perpendicular to the cylinders. Theoretical calculations of the band structure and transmission spectra using the plane wave expansion and the finite difference time domain methods support unambiguously the absolute nature of the observed band gaps.
Surface guided waves in two-dimensional phononic crystals
Wave Motion, 2007
With FDTD (finite-difference time-domain) calculations we study the acoustic waves propagating in a semi-infinite, two-dimensional (2D) periodic elastic structure, i.e., a 2D phononic crystal, with a flat surface together with a line defect. Specifically we search for the acoustic modes localized near the surface and at the same time confined inside the straight line defect, i.e., the surface guided waves. The surface assumed is perpendicular to the axis of circular cylinders (steel) embedded periodically in a background material (polymer). These surface guided waves found are unstable in general due to the interaction with bulk acoustic waves but can propagate the distances over several hundreds of lattice constants for a certain range of frequencies.
The existence of full gaps and deaf bands in two-dimensional sonic crystals
Journal of Lightwave Technology, 1999
Theoretical and experimental determination of sonic band structures of two-dimensional (2-D) arrays of rigid cylinders in air is reported. We present measurements for square and triangular lattices. A variational method is employed to calculate the acoustic dispersion relation. Experimentally, a transmission technique and the analysis of the phase delay between the incident and scattered waves by the structure are used to construct the acoustic bands. The comparison between theory and experiments allows to fully characterize the band gaps and it has also demonstrated the existence of deaf bands; i.e., bands which cannot be excited due to symmetry reasons. For the case of square lattice we show that the structure with a filling fraction of 0.41 has a full acoustic gap.