Dispersion Relation For Acoustic Waves Research Articles

Acoustic waves in functionally graded rods: polynomial inhomogeneity

The harmonic acoustic waves in a semi-infinite functionally graded (FG) 1D rod with a longitudinal arbitrary inhomogeneity are analyzed by a combined method based on the modified Cauchy formalism and the exponential matrix method. The closed form dispersion equations for harmonic waves are constructed, yielding the implicit dispersion relations for acoustic waves in FG rods. For longitudinal inhomogeneity of polynomial type the corresponding dispersion relations are constructed explicitly.

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

Estimation of photonic band gap in silicon crystal waveguide through acousto-optic interaction

The photonic band gap through acousto-optic interaction in a face-centred cubic silicon crystal is theoretically studied. The dispersion relation for acoustic wave is obtained using method of potentials with boundary conditions involving the bulk and surface stress of considered materials. The dispersion relation for optical wave is derived by transfer matrix method and boundary conditions based on electromagnetic theory. Observation shows that the central frequency of photonic band gap in silicon crystal can be chosen in any desired infrared optical frequency range by adjusting the frequency of acoustic wave. Also, the size of these band gaps in chosen optical frequency range can be further tuned through incident angle of light wave. This study may provide an efficient method to obtain tuneable photonic crystal.

Effective elastic properties of planar SOFCs: A non-local dynamic homogenization approach

The focus of the article is on the analysis of effective elastic properties of planar Solid Oxide Fuel Cell (SOFC) devices. An ideal periodic multi-layered composite (SOFC-like) reproducing the overall properties of multi-layer SOFC devices is defined. Adopting a non-local dynamic homogenization method, explicit expressions for overall elastic moduli and inertial terms of this material are derived in terms of micro-fluctuation functions. These micro-fluctuation functions are then obtained solving the cell problems by means of finite element techniques. The effects of the temperature variation on overall elastic and inertial properties of the fuel cells are studied. Dispersion relations for acoustic waves in SOFC-like multilayered materials are derived as functions of the overall constants, and the results obtained by the proposed computational homogenization approach are compared with those provided by rigorous Floquet–Bloch theory. Finally, the influence of the temperature and of the elastic properties variation on the Bloch spectrum is investigated.

Dispersion relations for the dust-acoustic wave under experimental conditions

The dust acoustic wave dispersion relation is tested to quantify its sensitivity to many physical processes that are important in laboratory dusty plasmas. It is found that inverse Landau damping and ion-neutral collisions contribute about equally to the growth rate ωi, pointing to the advantage of using a kinetic model for the instability. The growth rate ωi increases the most with an increase of dust number density, followed by an increase in ion-drift speed. The quantities that cause ωi to decrease the most when they are increased are the dust-neutral collision rate followed by the ion-neutral collision rate, ion collection current onto dust particles, and the ion thermal speed. In general, ωi is affected more than ωr by the choice of processes that are included. Strong Coulomb-coupling effects can be included in a compressibility term. The susceptibilities derived here can be combined in various ways in a dispersion relation to account for different combinations of physical processes.

Acoustic Analogue of Graphene: Observation of Dirac Cones in Acoustic Surface Waves

We demonstrate the presence of Dirac cones in the dispersion relation of acoustic waves propagating on the surface of a plate of methyl methacrylate containing a honeycomb lattice of cylindrical boreholes. This structure represents the acoustic analogue of graphene, the cylindrical cavities playing the role of carbon atoms while acoustic surface waves are the equivalent of electronic waves in graphene. Analytical expressions for the Dirac frequency and Dirac velocity in acoustics are given as a function of the radius and depth of boreholes. These parameters have been experimentally determined for a constructed structure and the data are in fairly good agreement with the predicted values.

General formulation for acoustic solitons in three-component nonthermal plasmas

A generalized formulation is developed for nonlinear acoustic solitons in three-component such as dust-ion-electron and electron-positron-ion plasmas with the charge of each species being unspecified. The heavy, cold charged particles (ions or dust particles) are treated as a fluid while the light, hot components are described by the kinetic Vlasov equation with separate velocity distributions which can be of κ function or highly nonthermal (non-monotonic) distributions. The model is also applicable for two-component such as ion-electron plasmas with two different temperatures for electrons. The generalized dispersion relation for acoustic waves and the Korteweg-de Vries equations as well as the Sagdeev potential are derived for various models with different combinations of velocity distributions. The parameter regimes for the existence of acoustic solitons are analyzed and examples of nonlinear solutions are illustrated. The polarity of electric potential is found to exhibit anomaly for highly nonthermal cases.

Dispersion relation of acoustic waves in phononic crystals filled with dielectric or metal

The results of the theoretical study of acoustic properties of globular phononic crystals based on artificial opals consisting of closely packed SiO2 globules ∼200 nm in diameter are presented. Dispersion characteristics of the samples under study were calculated, the group velocity and effective mass of phonons were determined.

Analytic continuation for the generalized Bohm criterion in a two-ion-species plasma

The generalized Bohm criterion in a two-ion-species plasma is analytically investigated. The universal iterative formulas of the approximative solutions have been affirmed for the ion acoustic wave (IAW) dispersion relation and the generalized Bohm criterion in the two-ion-species plasma for the first time. For a weakly collisional two-ion-species plasma, it is indicated that the choice of the initial solution and the repetitious iterative operation for the ion drift velocities is the linchpin of the optimized solution for the ion acoustic wave dispersion relation and the generalized Bohm criterion, considering the more general case and extensive physical characteristics.

Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium

Experimentally determined dispersion relations for acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through nonaffine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure.

Exact and approximate analysis of surface acoustic waves in an infinite elastic plate with a thin metal layer

For an accurate approximation of the effect of a thin layer over a finite substrate, we consider the displacements are continuous across the interface, while the stress components are obtained from derivatives of displacements. As a result, the stress boundary conditions are transformed to a relationship between stresses in the vicinity of the interface of two layers and density of the metal layer. Through this approximation, we eventually have four equations to solve for the surface acoustic wave dispersion relation of the two-layer structure. The approximate and accurate results are compared with good agreement for small thickness of the metal layer. These results are intended for periodic structures with separate solutions for electroded and unelectroded regions, which can be connected by the continuity boundary conditions for the analysis of the complete structure of typical surface acoustic wave resonators.

Dispersion relations for acoustic waves in heterogeneous multi-layered structures contacting with fluids

The paper describes a method and a computer application for the computation of the velocity of acoustic waves excited in complicated multi-layered structures consisting of anisotropic piezoelectric and isotropic layers. The structure assumes to be unbounded in the lateral directions. The top and bottom layers are either semi-infinite in the vertical direction or they contact with media such as fluids, gases or vacuum. A special homogenization technique enables to account for bristle-like layers contacting with a fluid. The program is supplied with a user friendly graphical interface and can be useful for researchers working on acoustic sensors.

Non-principal surface waves in deformed incompressible materials

The Stroh formalism is applied to the analysis of infinitesimal surface wave propagation in a statically, finitely and homogeneously deformed isotropic half-space. The free surface is assumed to coincide with one of the principal planes of the primary strain, but a propagating surface wave is not restricted to a principal direction. A variant of Taziev’s technique [R.M. Taziev, Dispersion relation for acoustic waves in an anisotropic elastic half-space, Sov. Phys. Acoust. 35 (1989) 535–538] is used to obtain an explicit expression of the secular equation for the surface wave speed, which possesses no restrictions on the form of the strain energy function. Albeit powerful, this method does not produce a unique solution and additional checks are necessary. However, a class of materials is presented for which an exact secular equation for the surface wave speed can be formulated. This class includes the well-known Mooney–Rivlin model. The main results are illustrated with several numerical examples.

Measurement and Modelling for the Dispersion Relations of Acoustic Waves Propagating in a Free Piezoelectric Plate

ABSTRACTThis research is focused in the measurement and modelling of the dispersion relations of Lamb waves propagating in a piezoelectric plate. A theoretical model based on a partial wave analysis is used to provide numerical calculations for the dispersion relations of Lamb waves propagating in an LiNbO3 plate with different propagating directions. The dispersion relations are presented in an innovative image format. A non-contact laser ultrasound technique operated in B-scan mode with the aid of double Fast Fourier transform signal-processing scheme is used to measured multi-mode dispersion realtions. Among all the propagation angles, the measured dispersion curves show good agreement with the theoretical calculations. The Rayleigh wave speeds are extracted from the measured and calculated dispersion curves, showing favorable comparison with classical theory by Campbell.

Band structures of acoustic waves in phononic lattices

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.

Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch

The finite-difference time-domain method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional (2D) 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.

Longitudinal collective modes of strongly coupled dusty plasmas at finite frequencies and wavevectors

Dusty plasmas offer a unique method for testing dynamical wave theories in the strong Coulomb coupling regime. Recently, there have been many theoretical models, based on either a generalized hydrodynamic or on kinetic descriptions, developed to describe dust acoustic waves under conditions of strong coupling. These theories attempt to extend the usual acoustic wave dispersion relation to the strong coupling regime and, in some cases, to finite frequencies and wave vectors beyond the hydrodynamic limit. Here a multicomponent kinetic theory is used to obtain the dust acoustic wave dispersion relation in terms of an approximate dynamic local field correction, and comparison is made with the viscoelastic Navier–Stokes description.

Shear horizontal acoustic waves at the periodically corrugated interface between two isotropic elastic media

On the basis of the Rayleigh method we have obtained two equivalent exact dispersion relations for acoustic waves of shear horizontal polarization propagating across the periodically corrugated interface between two different isotropic elastic media. These dispersion relations have been solved numerically, and the dispersion curve of the corresponding surface acoustic waves obtained. These waves exist for only a limited range of wave vectors in the immediate vicinity of the boundary of the one-dimensional first Brillouin zone of the periodically corrugated interface, in agreement with the results of earlier, perturbative studies of this problem. By continuing the solutions into the radiative region of the frequency-wave vector plane, we also calculate the attenuation of these shear horizontal interface acoustic waves.

Acoustic wave propagation in a flowing liquid-vapour mixture

The two-fluid equations describing transient nonequilibrium liquid-vapour flow have been used to derive a general dispersion relation for acoustic waves. The analysis is valid in principle for both dispersed and separated flow regimes. In contrast to previous work, the predicted sound speeds and attenuations depend only on measurable properties of the flow. The model can apply over a wide range of angular frequencies (up to 1–10 6 Hz for steam and water), under conditions where the scattering of waves by individual bubbles and droplets is unimportant. Predictions are made for sound speeds and attenuations in both bubbly and annular flow at low Mach numbers. Agreement of the theory with available data is shown to be reasonable.

Kinetic theory of parametric excitation of acoustic waves in piezoelectric semiconductors

Using a kinetic description for electrons and the usual equation of motion for lattice displacement we have derived a general dispersion relation for acoustic waves in a piezoelectric semiconductor, in the presence of a strong high frequency electric field oscillating near the electron plasma frequency. Earlier hydrodynamic results valid forkλ e≪1 (wherek is the wave number of the acoustic wave andλ ethe electron mean free path) are rederived as a special case. Forkλ e≫1, two instability branches are discovered and magnitudes of the threshold electric field required to drive the acoustic wave unstable in each case, are obtained.