Band Structure of Phononic Crystal Consist of Hollow Aluminum Cylinders in Different Media; Finite Element Analysis (original) (raw)
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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.
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...
Finite Element Modeling of Acoustic Shielding via Phononic Crystal structures
2016
Quality factor of Contour Mode Resonators (CMR) are mainly affected by energy losses due to acoustic waves leaving the resonator through the anchors. An engineering of the anchors in order to create a periodic variation in the acoustic impedance of the material, structures known as Phononic Crystals (PnCs), can help improve the Q factor by reflecting part of the acoustic waves. During this project, FEM models have been validated for both 1D and 2D PnCs. The behavior of the band diagram and quantification of transmission has been studied for three different PnC geometries: circle, cross and square unit cell. Parameters such as unit cell size, filling factor, material composition, thickness and number of repetitions have been varied and comparisons between transmission graph and band diagram allowed to understand better the nature of the modes. It has been found that a linear approximation can predict with a good precision the position of the band gap as a function of the unit cell si...
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.
Optical and Quantum Electronics, 2019
Locally resonant phononic crystals (LRPC) are a new type of sound insulating material. Using the plane wave expansion method based on the Bloch theorem, we compute the band structure of two dimensional (2D) phononic crystals (PC) with square and triangular lattices. Such PC typically consists of infinitely long carbon rods coated with silicon rubber and embedded in an elastic background. Computational results show that gaps appear at the lower frequency range, which are lower than those expected from the Bragg mechanism. Those gaps are generated due to local resonances; the optimum gap is obtained by tuning the thickness ratio of the coating layer. The gap created by the LRPC depends on the filling fraction of the coating cylinders.
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 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.
Designing Acoustic Filters on 2D Phononic Crystal Platforms
Two-dimensional phononic crystals (PnCs) are composite materials made of periodic distributions of infinitely long bars of mass density ρ A embedded in a matrix of mass density ρ B . All mechanical properties of such PnCs follow the lattice periodicity. Mechanical waves propagate throughout these periodic structures as elastic or acoustic waves. For a given crystal structure, there may exists a phononic bandgap over a frequency range in which normally incident mechanical waves cannot propagate. Existence and the size of this phononic bandgap depend on the density contrast Δρ=(ρ B −ρ A ), sound velocity contrast, lattice fill factor and topology. Employing plane wave expansion (PWE) method, we have studied the filtering properties 2D PnCs made of periodic arrays of solid cylindrical rods of radius r o in a solid background arranged in both square and triangular lattices. In order to see how lattice topology would affect the filter property, we have replaced the solid cylindrical rods by hollow cylinders of the same outer radii and various inner radii 0.1 r o ≤r i ≤0.75.
Journal of Applied Physics, 2014
We study both theoretically and experimentally the interaction of surface elastic waves with 2D surface phononic crystal (PnC) on a piezoelectric substrate. A rigorous analysis based on 3D finite element method is conducted to calculate the band structure of the PnC and to analyze the transmission spectrum (module and phase). Interdigital transducers (IDTs) are considered for electrical excitation and detection, and absorbing boundary conditions are used to suppress wave's reflection from the edges. The PnCs are composed of an array of 20 Nickel cylindrical pillars arranged in a square lattice symmetry, and deposited on a LiNbO 3 substrate (128 Y cut-X propagating) between two dispersive IDTs. We investigate by means of band diagrams and transmission spectrum the opening band-gaps originating from pillars resonant modes and from Bragg band-gap. The physical parameters that influence and determine their appearance are also discussed. Experimental validation is achieved through electrical measurement of the transmission characteristics, including amplitude and phase. V
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.