Band structures of acoustic waves in phononic lattices (original) (raw)
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.
Engineering Analysis with Boundary Elements, 2020
In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM is presented. In comparison with the traditional plane wave expansion (PWE) method and Pressure Acoustics Module in COMSOL software, the proposed GFDM can provide the similar accurate results with less computational times for calculating the band structures of the simple/complicated shape scatterers in the square/triangular lattice. Three influence factors (Filling fractions (Ff), rotation angles (Ra) and arm widths (Aw) in the unit-cell) of the bandgap properties in 2D phononic crystals are numerically discussed.
Continuum Mechanics and Thermodynamics, 2010
Steady-state and transient processes of elastic wave propagation in infinite 2D massless and materialbond lattices subjected to a local monochromatic excitation are studied. Anti-plane dynamics of rectangular and triangular lattices is considered. Mathematical models of lattices, dispersion properties of free waves, and results of transient problems solution are presented. Resonant excitations of lattices are explored. Asymptotic solutions are compared with the results of computer simulation. Special attention is given to the wave-beaming pattern in the case of the excitation frequency located within a pass-band.
The Phononic Lattice Solid With Fluids For Modelling Non-Linear Solid-Fluid Interactions
Geophysical Journal International, 1994
The phononic lattice solid has been developed recently as a possible approach for modelling compressional waves in complex solids at the microscopic scale. Rather than directly modelling the wave equation, the microdynamics of quasi-particles is simulated on a discrete lattice. It is comparable with the lattice gas approach to model idealized gas particles but differs fundamentally in that lattice solid particles carry pressure rather than mass and propagate through a heterogeneous medium. Their speed may be space and direction dependent while the speed of lattice gas particles is constant. Furthermore, they may be scattered by medium heterogeneities. Lattice sites in the phononic lattice solid approach are considered to be fixed in space for all time. Lattice site movements (i.e. deformations) induced by the passage of a macroscopic wave are particularly important for a fluid-filled porous medium considering that non-linear solid-fluid interactions are thought to play a role in attenuation mechanisms. We take lattice site movements into account in the phononic lattice solid and name the approach 'the phononic lattice solid with fluids (PLSF)' because it could lead to an improved understanding of the effect of solid-fluid interactions in wave propagation problems. The macroscopic limit of the Boltzmann equation for the PLSF yields the acoustic wave equation for heterogeneous media modified by shear and bulk viscosity terms as well as the second-order term in macroscopic velocity (for the PLS) and additional non-linear terms due to the lattice site movements. It is hoped that PLSF numerical simulation studies of waves through digitized rock matrices may lead to an improved understanding of attenuation mechanisms of waves in porous rocks.
Journal of Applied Physics, 2016
In this paper, we report a theoretical investigation of surface acoustic waves propagating in onedimensional phononic crystal. Using finite element method eigenfrequency and frequency response studies, we develop two model geometries suitable to distinguish true and pseudo (or leaky) surface acoustic waves and determine their propagation through finite size phononic crystals, respectively. The novelty of the first model comes from the application of a surface-like criterion and, additionally, functional damping domain. Exemplary calculated band diagrams show sorted branches of true and pseudo surface acoustic waves and their quantified surface confinement. The second model gives a complementary study of transmission, reflection, and surface-to-bulk losses of Rayleigh surface waves in the case of a phononic crystal with a finite number of periods. Here, we demonstrate that a non-zero transmission within non-radiative band gaps can be carried via leaky modes originating from the coupling of local resonances with propagating waves in the substrate. Finally, we show that the transmission, reflection, and surface-to-bulk losses can be effectively optimised by tuning the geometrical properties of a stripe. V