Dispersion Of Acoustic Waves Research Articles

Local Decay of Acoustic Waves in the Low Mach Number Limits on General Unbounded Domains Under Slip Boundary Conditions

We discuss several aspects of the problem of propagation and dispersion of acoustic waves arising in the low Mach number asymptotic limits of compressible fluid systems. A general approach is proposed based on analysis of the spectral measures associated to the corresponding wave propagator. In particular, the local decay estimates based on a result of Tosio Kato and on RAGE theorem are obtained as limit cases. The approach is applied to problems on domains their shape may vary with the Mach number.

Dynamics of mechanical waves in periodic graphene nanoribbon assemblies

We simulate the natural frequencies and the acoustic wave propagation characteristics of graphene nanoribbons (GNRs) of the type (8,0) and (0,8) using an equivalent atomistic-continuum FE model previously developed by some of the authors, where the C-C bonds thickness and average equilibrium lengths during the dynamic loading are identified through the minimisation of the system Hamiltonian. A molecular mechanics model based on the UFF potential is used to benchmark the hybrid FE models developed. The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures. We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length). We also show the dependence of the wave dispersion characteristics versus the aspect ratio and edge configurations of the nanoribbons, with widening band-gaps that depend on the chirality of the configurations. The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures.PACS 62.23.Kn · 62.25.Fg · 62.25.Jk

Analysis of dispersion characteristics of phononic structures

A general theory for calculating the dispersion of bulk acoustic waves in 3D and 2D phononic crystals made of anisotropic materials is presented, which is based on the plane-wave expansion method. Two approaches to separating acoustic modes in the dispersion diagrams are proposed. The pattern of the acoustic field distribution is studied as depending on the wavevector direction for various types of modes. Degeneracy of acoustic modes in directions different from the axes of symmetry of the phononic crystal is demonstrated. Possibilities of the proposed method are illustrated by the application to 3D and 2D silicon-based phononic crystal structures.

Laser-based surface acoustic wave dispersion spectroscopy for extraction of thicknesses, depth, and elastic parameters of a subsurface layer: Feasibility study on intermetallic layer structure in integrated circuit solder joint

Laser beam deflection in combination with optical heterodyne diffraction is used to detect surface acoustic waves that are generated by impulsive laser light on a Sn–CuxSny–Cu–Si multilayer structure with layer thicknesses of the order of 1 μm. The acoustic phase velocity dispersion curves of the lowest two-surface acoustic wave modes are determined by spectral analysis of the experimental signals. The sensitivity of the dispersive behavior to the thickness and elastic properties of the individual layers is analyzed on the basis of the experimental data and of simulated data with noise added. The elastic parameters of the CuxSny intermetallic alloy are determined. Statistical least squares and most squares uncertainties on all best fitting material parameters are determined, giving a quantitative measure of the feasibility of parameter extraction by this method. The feasibility of solving the inverse problem of elastic depth profiling of a multilayer by the proposed wideband and multimode SAW dispersion spectroscopy method is confirmed.

Thin Nano- and Microcrystalline CVD Diamond Films for Micro-channel Cooling: Thermal and Elastic Properties

ABSTRACTThin nano- to microcrystalline diamond (N/MCD) films were deposited on silicon substrates using plasma enhanced microwave chemical vapor deposition. Selected layers were covered with a thin metal layer of Cr to enhance their optical absorption characteristics for photothermal and photoacoustic experiments. A heterodyne diffraction method was used to investigate the thermoelastic signatures of the N/MCD layers. While the dispersion of surface acoustic waves turned out to be difficult to determine due to high optical scattering from the diamond crystallites, it was found that a diamond film of ~ 2 μm thick is enhancing the thermal diffusion along the surface.

Corrections to the Magnitude of Cross-Correlation Functions for Dispersion of Solar Acoustic Waves

The cross-correlation function is a useful tool in helioseismology. The magnitude of the cross-correlation function has been used to represent the power of wave packets. Dispersion causes a decrease in amplitude and an increase in width of wave packets. This leads to a decrease in magnitude and an increase in width of cross-correlation functions. The effect of dispersion on the magnitude of cross-correlation functions needs to be adequately corrected for in order to use the magnitude of cross-correlation functions to represent the power of wave packets. In this study, we investigate how the magnitude of cross-correlation functions changes with the number of skips owing to dispersion and the method to correct it. Our study, using simulated and observational data, indicates that the correction should be three dimensional instead of the one-dimensional correction adopted in previous studies. Using the three-dimensional correction, the measured dissipation rate in the quiet Sun is smaller than the value of previous studies.

Dispersion and damping of two-dimensional dust acoustic waves: theory and simulation

A two-dimensional generalized hydrodynamics (GH) model is developed to study the full spectrum of both longitudinal and transverse dust acoustic waves (DAW) in strongly coupled complex (dusty) plasmas, with memory-function-formalism being implemented to enforce high-frequency sum rules. Results are compared with earlier theories (such as quasi-localized charge approximation and its extended version) and with a self-consistent Brownian dynamics simulation. It is found that the GH approach provides a good account, not only of dispersion relations, but also of damping rates of the DAW modes in a wide range of coupling strengths, an issue hitherto not fully addressed for dusty plasmas.

Evaluation of film adhesion to substrates by means of surface acoustic wave dispersion

For thin film structures acoustically classified as slow-on-fast systems, modeling and evaluation of their interfacial condition are known to be very complex and difficult due to dispersion and multi-mode excitation of acoustic waves. This paper presents a quantitative model and a reliable measurement procedure established for adhesion evaluation of such film structures. An effective interface model employing a virtual intermediate layer is utilized for the dispersion prediction of the surface acoustic wave, which is affected by various interfacial conditions. Through acoustic microscopy experiments, this model presents a potential method to classify the bonding condition. Comparisons with a destructive scratch test and an acoustic imaging verify the failure mode of the film structure.

Surface Roughness of Laser-Shock-Peened Aluminum Alloys and Its Effect on the Dispersion of Surface Acoustic Waves

The experimental dispersion curves of laser-shock-peened aluminum samples were obtained from the phase spectra of the laser induced surface acoustic waves (SAWs) and the results indicated that the more the peening times, the greater the dispersion. The change in phase velocity resulting from the surface roughness was obtained by comparing the dispersions of the samples before and after being polishing. It was found that the surface roughness decreased the phase velocity, and the change in velocity depended on the frequency of the SAW as expected from the theoretical analysis of the case when the lateral correlation length is much smaller than the wavelength of the SAWs. Furthermore, the experimental dispersion results of the SAWs for three samples with different peening times showed that the more the peening times, the smaller the roughness, which was verified by the values measured with a roughmeter.

Approximating the wave moduli of double porosity media at low frequencies by a single Zener or Kelvin-Voigt element

SUMMARY The analytic transient acoustic wave solution and dispersion characteristics for the doubleporosity model are obtained over the whole frequency range for a homogeneous medium. The solution is also obtained by means of approximating the double porosity model with a uniform poro-viscoacoustic model based on a single Zener and a single Kelvin-Voigt (KV) element, respectively. We choose the relaxation function of both mechanical elements which just approximates the dispersion behaviour of the double porosity model around source centre frequencies of 5, 50, 200 and 1000 Hz, respectively. The comparison between the results of the three models shows that if the frequency is much lower than the peak attenuation frequency (4470 Hz) of the example double porosity model, then wave propagation can be well described by the poro-viscoacoustic model with a single Zener element. However, if the frequency is less than 50 Hz, then a single KV element gives an even better result. Therefore, this paper investigates the validity and range of applicability of different single mechanical elements in solving for transient acoustic wave modelling in heterogeneous, double porosity media. The primary attraction of using a Zener model or a KV model is that it allows the convolution integral to be replaced by memory equations by which the field quantities calculated at every time step need not be stored.

Quantum effects on the dispersion of ion acoustic waves

The longitudinal response function for an isotropic, nonrelativistic, thermal plasma with the quantum recoil included exactly is used to generalize the dispersion relation for ion acoustic waves and the absorption coefficient for Landau damping to include the quantum recoil. The results are compared to recent treatment of the dispersion relation derived using a fluid theory with the quantum effects included through the Bohm potential.

Dispersion and attenuation of surface acoustic waves of shear horizontal polarization on a free surface of a hexagonal crystal with a structurally damaged isotropic surface layer

The phase velocity dispersion and the inverse attenuation length of surface acoustic waves of shear horizontal polarization propagating along a free flat (smooth) surface of a hexagonal crystal (Z cut) in the presence of a thin (compared to the wavelength) structurally damaged surface layer are found in the analytical form. It is shown that, in the long-wavelength limit (the wavelength is large compared to the characteristic size of layer inhomogeneities), which is of the greatest interest to experimenters, the change in the phase velocity dispersion and the change in the inverse attenuation length are proportional to the third and sixth powers of the wave frequency, respectively. The inverse attenuation length is numerically calculated.

Theoretical analysis of acoustic waves propagating in materials with continuous variations of near-surface elastic constants

The near-surface elastic properties (NSEPs) of materials take on continuous distribution after surface modification such as surface polishing. In this paper, the influence of the continuous variations of NSEPs on the ultrasonic waves propagating in finite-thick and semi-infinite-thick plates is investigated. An orthogonal polynomial extended method is presented to study the acoustic waves propagating in metals with continuous distribution of NSEPs. By this method, the near-surface layer of the materials does not need to be discrete sublayers, which can avoid the presence of pseudoacoustic waves. The velocities of different ultrasonic wave modes in finite-thick and semi-infinite-thick plates with continuous distributions of NSEPs are obtained. In addition, the influence of the near-surface layer’s thickness and the distribution of the NSEPs on the relative velocity dispersion of Lamb waves and surface acoustic waves are discussed, providing further theoretical foundation for the inversion of near-surface properties.

Surface acoustic waves with negative group velocity in a thin film structure on silicon

A surface acoustic wave dispersion curve of a thin film structure on silicon measured with the laser-induced transient grating technique displays a local minimum in frequency at nonzero wavenumber. For a range of wavenumbers to one side of this minimum the dispersion curve is of negative slope, implying the existence of surface waves with negative group velocity. Unlike in the well studied case of “backward traveling” Lamb waves in plates, the anomalous behavior here is exhibited by the lowest acoustic mode of the structure. The existence of the local minimum in the dispersion curve is corroborated by numerical simulations.

Acoustic wave propagation in the solar sub-photosphere with localised magnetic field concentration: effect of magnetic tension

Aims. In this paper we analyse numerically the propagation and dispersion of acoustic waves in the solar-like sub-photosphere with localised non-uniform magnetic field concentrations, mimicking sunspots with various representative magnetic field configurations. Methods. Numerical simulations of wave propagation through the solar sub-photosphere with a localised magnetic field concentration are carried out using SAC, which solves the MHD equations for gravitationally stratified plasma. The initial equilibrium density and pressure stratifications are derived from a standard solar model. Acoustic waves are generated by a source located at the height approximately corresponding to the visible surface of the Sun. We analyse the response of vertical velocity to changes in the interior due to magnetic field at the level corresponding to the visible solar surface, by the means of local time-distance helioseismology. Results. The results of numerical simulations of acoustic wave propagation and dispersion in the solar sub-photosphere with localised magnetic field concentrations of various types are presented. Time-distance diagrams of the vertical velocity perturbation at the level corresponding to the visible solar surface show that the magnetic field perturbs and scatters acoustic waves and absorbs the acoustic power of the wave packet. For the weakly magnetised case the effect of magnetic field is mainly thermodynamic, since the magnetic field changes the temperature stratification. However, we observe the signature of slow magnetoacoustic mode, propagating downwards, for the strong magnetic field cases.

Energy storage and dispersion of surface acoustic waves trapped in a periodic array of mechanical resonators

It has been shown previously that surface acoustic waves can be efficiently trapped and slowed by steep ridges on a piezoelectric substrate, giving rise to two families of shear-horizontal and vertically polarized surface waves. The mechanisms of energy storage and dispersion are explored by using the finite element method to model surface acoustic waves generated by high aspect ratio electrodes. A periodic model is proposed including a perfectly matched layer to simulate radiation conditions away from the sources, from which the modal distributions are found. The ratio of the mechanical energy confined to the electrode as compared to the total mechanical energy is calculated and is found to be increasing for increasing aspect ratio and to tend to a definite limit for the two families of surface waves. This observation is in support of the interpretation that high aspect ratio electrodes act as resonators storing mechanical energy. These resonators are evanescently coupled by the surface. The dispersion diagram is presented and shows very low group velocities as the wave vector approaches the limit of the first Brillouin zone.

High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams

We study ultrahigh frequency surface acoustic wave propagation in nickel-on-sapphire nanostructures. The use of ultrafast, coherent, extreme ultraviolet beams allows us to extend optical measurements of propagation dynamics of surface acoustic waves to frequencies of nearly 50 GHz, corresponding to wavelengths as short as 125 nm. We repeat the measurement on a sequence of nanostructured samples to observe surface acoustic wave dispersion in a nanostructure series. These measurements are critical for accurate characterization of interfaces beneath very thin films using this technique.

Numerical simulation of acoustic band gaps in homogenized elastic composites

The dispersion of acoustic or elastodynamic waves in elastic composites are studied using the homogenized model. We consider heterogeneous periodic structures consisting of soft but heavy inclusions embedded in a stiffer matrix. By virtue of the asymptotic homogenization technique in conjunction with an appropriate scaling of the elasticity coefficients in the inclusions, the limit model exhibits the band gaps in wave propagation due to the negative effective mass. This phenomenon can be revealed by studying guided waves in discrete mass–spring structures with scale-dependent parameters. The main purpose of the paper is to justify the applicability of the homogenized model of the heterogeneous elastic continuum for prediction of the band gaps in structures featured by a finite scale of heterogeneities. We show the band gaps numerical identification and discus aspects of anisotropy, microstructure geometry and material contrast between the constituents in the context of the long wave dispersion.

X-Ray Residual Stress Gradient Analysis in Annealed Silver Thin Films Using Asymmetric Bragg Diffraction

Residual stresses were determined in magnetron-sputtered Ag thin films of 400 nm thickness by asymmetric Bragg scattering. The corresponding cos2α sin2ψ plots were nonlinear which indicates a strong residual gradient along the depth of the samples. The in-plane stress was highly compressive at the sample surface and became tensile at the interface. The out-plane stress was compressive and reached its maximum at the sample interface. The stress gradient changed significantly with postannealing temperature. A Young’s modulus of E = 83 GPa and a Poisson ratio of ν = 0.3 were measured by surface acoustic wave dispersion.

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.