Band structures of acoustic waves in phononic lattices (original) (raw)
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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.
Influence of rod diameter on acoustic band gaps in 2D phononic crystal
Archives of materials science and engineering, 2014
Purpose: The purpose of this paper is to investigate influence of changing the fill factor (or rod diameter) on acoustic properties of phononic crystal made of mercury rods inside of water matrix. Change in construction of primary cell without changing the shape of rod may cause shifts in bands leading to widening of forbidden band gaps, which is the basis of modern composite material designing process. Design/methodology/approach: Band structure is determined by using the finite element study known as finite difference frequency domain simulation method. This is achieved by virtual construction and simulation of primary cell of phononic crystal. Phononic crystals are special devices which by periodic arrangement of properties related to the sound can affect the transmission of acoustic waves thru their body. Findings: The fill factor/rod diameter has a significant influence on the acoustic band structure of studied phononic crystal which can be divided in two mainly effects: fissio...
Wave Propagations in Metamaterial Based 2D Phononic Crystal: Finite Element Analysis
Journal of Physics: Conference Series, 2018
In the present work, the acoustic band structure of a two-dimensional (2D) phononic crystal (PnC) containing composite material were investigated by the finite element method. Two-dimensional PC with triangular and honeycomb lattices composed of composite cylindrical rods are in the air and liquid matrix. The existence of stop bands are investigated for the waves of certain frequency ranges. This phononic band gap-forbidden frequency rangeallows sound to be controlled in many useful ways in structures. These structures can be used as sonic filters, waveguides or resonant cavities. Phononic band diagrams ω=ω(k) for a 2D PnC were plotted versus the wavevector k along the Г-X-M-Г 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.
Band gap structure of elliptic rods in water for a 2D phononic crystal
Applied Physics A, 2017
major fields in acoustics. Sonic crystals (SCs) are defined as structured materials formed by a periodic distributions of acoustic scatterers embedded in a host material, with strong periodic modulations in their density and elastic coefficients between the constituent materials. The periodicity of the scatterers in a surrounding material gives rise to the appearance of sonic band gaps, a range of frequencies for which sound propagation is forbidden inside the crystal. These stop bands were observed at frequencies depending on the lattice constant of the array in the band structures of crystals with various lattice geometries [3-5]. The SCs have induced several application proposals and enabled development of many new technologies. Recent studies in this field have attracted a great interest due to the splendid application prospects, such as acoustic filters [6, 7], shield devices [8-10], defect states for acoustic filters and wave guides [11], and so on. Recently, an increased attenuation at low frequencies has been achieved by the locally resonant sonic materials formed by soft and rigid elements [12]. Several theoretical methods have been used to study the elastic/acoustic band structures, such as, the plane-wave expansion (PWE) method [13, 14], the finite difference time domain (FDTD) method [15], the extended plane wave expansion (EPWE) method [16, 17], the multiple scattering theory (MST) [18], perturbative approach [19], and variational method [20]. Among them, the PWE is the most widely used method for calculating the band structures. In the literature, acoustic band gaps of various two-dimensional sonic crystal structures were investigated and these structures mostly consist of circular cross-section scatterers in square, triangular, rectangular lattices, the constituent being either both solids or fluids, or mixed solid-fluid [21]. Practically, band gaps properties of sonic crystal structures or the acoustic dispersion of the branches can be controlled by the lattice filling factor, the constituent Abstract The propagation of acoustic waves in twodimensional sonic crystals (SC) is studied theoretically. Effects of elliptical rod orientations on the acoustic band gaps in periodic arrays of rigid solid rods embedded in a polar liquid are investigated. We have found that the pass bands and forbidden bands of the sonic crystals can be changed by utilizing the rotational anisotropy of the structure factor at different rotation angles of the scatterers. The plane wave expansion (PWE) method is used to calculate the band structure. The variation of the absolute band gap was also investigated as a function of any filling fraction at a fixed orientation of the elliptical columns. The gap-tuning effect can be controlled by the rotational asymmetry and eccentricity of the scatterers.
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.
Physical Review B, 1999
Spatial and frequency distributions of forbidden bands of both surface and bulk acoustic waves are studied theoretically for two-dimensional ͑2D͒ periodic elastic structures consisting of aluminum and polymer. The surface is perpendicular to the 2D periodic arrays of circular cylinders embedded in a background material. The dispersion relations of the surface and bulk modes with wave vectors parallel to the surface are calculated for triangular lattices, and the stop band distributions are plotted in a form relevant to the comparison with ultrasound imaging experiments. ͓S0163-1829͑99͒03043-X͔
Physical Review E, 2002
The propagation of acoustic waves in a two-dimensional composite medium constituted of a square array of parallel copper cylinders in air is investigated both theoretically and experimentally. The band structure is calculated with the plane wave expansion ͑PWE͒ method by imposing the condition of elastic rigidity to the solid inclusions. The PWE results are then compared to the transmission coefficients computed with the finite difference time domain ͑FDTD͒ method for finite thickness composite samples. In the low frequency regime, the band structure calculations agree with the FDTD results indicating that the assumption of infinitely rigid inclusion retains the validity of the PWE results to this frequency domain. These calculations predict that this composite material possesses a large absolute forbidden band in the domain of the audible frequencies. The FDTD spectra reveal also that hollow and filled cylinders produce very similar sound transmission suggesting the possibility of realizing light, effective sonic insulators. Experimental measurements show that the transmission through an array of hollow Cu cylinders drops to noise level throughout frequency interval in good agreement with the calculated forbidden band.
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.
Dispersion features of elastic waves in phononic crystals: finite element analysis
Ferroelectrics, 2019
In this report, we present an investigation of the dispersion properties of the phononic crystal in different lattice, geometries for various piezoelectric materials. We study dispersion properties of the epoxy resin/ piezoelectric based phononic structures in the frequency range by using the finite element method for various lattices, piezoelectric materials and cross-sectional inclusions. The effect of the cross-section of piezoelectric inclusions, lattice geometry and filling factor on the phononic band gap is illustrated. A numerical approach is used to obtain the dispersion properties of the 2D piezoelectric phononic crystals which yields further insight into the phenomenon of the reflection from different families of piezoelectric in relation to the presence of phononic gaps.
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.