Calculation Of Phase Velocities Research Articles

Analytical study of ion-acoustic soliton in single temperature nonisothermal electron

In presence of warm negative ion, propagation of ion-acoustic solitary waves has been investigated analytically in a plasma consisting of warm positive ion, warm positron and single-temperature non-isothermal electron. The necessary and sufficient conditions for the existence of compressive solitary waves are discussed critically along with the calculation of phase velocity, kinetic energy (K.E) and force (F) found out in this paper by this new analytical method. Some important general observations and Theorems related with this problem are highlighted that supports the results of previous authors. The Sagdeev potential function ψ(𝜙) [= - L(𝑢𝛼 )] against ϕ depicted graphically under the variation of different plasma parameters is the most important and interesting situations by this analytical method.

Behavior of Love-Wave Fields Due to the Reinforcement, Porosity Distributions, Non-Local Elasticity and Irregular Boundary Surfaces

Investigations are carried out to predict the characteristic behavior of Love-wave fields propagating in a non-local elastic model under the effects of irregular boundary surfaces, reinforcement, and porosity distributions. The model includes an anisotropic fiber-reinforced medium lying over an anisotropic porous half-space. Two different porosity distributions are investigated within the porous half-space, namely uniform porosity and asymmetrical porosity. Analytical solutions to the displacement fields for both the upper layer and the lower porous half-space are calculated. Solutions to the latter porosity distribution are obtained by using the asymptotic expansions of the Kummer hypergeometric functions of the second kind. Both the interface and the upper surface of the two-layered media are subjected to irregular boundary conditions, which leads to a complex form of the dispersion relation. We analyze the phase velocity and damped velocity behavior of the traveling Love-wave fields separately by using the real and imaginary components of the velocity dispersion relation. The calculated phase velocity curves obtained at the same parameters have been compared to demonstrate the accuracy of the established model. The effects of corrugation parameters, porosity distributions, non-local elasticity, and reinforcement on the phase velocity and the damped velocity curves are analyzed in detail using MATLAB software.

In-Situ Modulus Determination Using Dispersion Curves Developed From the Deflection-Time History Data

The advanced non-destructive tests (NDT) have become increasingly popular in the structural performance evaluation of transportation infrastructures including pavements. Among them, Falling Weight Deflectometer (FWD) and Spectral Analysis of Surface Waves (SASW) are the two most widely used methods in modulus measurement. Although popularly used, FWD methods base the analysis purely on the deflection characteristics of the pavement and the back-calculated modulus values are usually not unique for different data processing methods. SASW is based on fundamental spectral analysis of the Rayleigh waves but is practically limited in field operation due to its efficiency concern. On the other hand, the impact loading applied by the FWD will generate the Rayleigh wave, and the geophones used in FWD can capture Rayleigh wave fluctuation and measure the particle motion for phase velocity calculations. It is theoretically possible to use the deflection-time history collected by FWD to perform dispersion analysis based on the Rayleigh wave propagation theory, as used in the SASW method. Inspired from that, the main objective of this paper is to propose a new approach of using the deflection-time history collected by FWD to develop the dispersion curves and thus obtain the in-situ modulus of the layered asphalt pavement. This approach is referred as the FWD dispersion curve method. Two in-service semirigid base asphalt pavement segments were used as case studies to explain the new methodology. The results of layered modulus from the FWD dispersion curve method were compared with the traditional FWD and SASW method, as well as the laboratory Indirect Tensile (IDT) testing results using field cores. Findings demonstrated the feasibility of the FWD dispersion curve method in accurately capturing the layered modulus profile of the asphalt pavements.

Theoretical and experimental investigation of circumferential guided waves in orthotropic annuli

The fiber composite materials fabricated by stacking the lamina structure obtain increasing attention in the industry, and at the same time, damage analysis is essential for safe operation. A proposed way to detect defects such as debonding and delamination is to induce circumferential guided waves. Accurate determination of the dispersion characteristics and wave fields is a prerequisite for using acoustic guided waves. The aim of this work is to provide such an accurate dispersion results in an arbitrarily thick cylindrically orthotropic homogeneous cylindrical shell of uniform thickness. Compared with the traditional SAFE method, the proposed method, which combines the two numerical methods, namely Floquet Boundary Condition (Floquet BC) Method and Sweeping Frequency Finite Element Modeling (SFFEM) method has obvious advantages. Through Floquet BC method, a theoretical result can be easily obtained without tedious code writing. Then SFFEM helps to verify the theoretical result in an experimental way. Besides, the slight gap between the theoretical and experimental results works as a basis for calibrating the elastic constants of composite materials provided in the manual. Simulations in COMSOL Multiphysics FE software supported by both methods and experiments by the latter have been carried out in this work. The calculated phase velocity dispersion curves demonstrated the efficiency of those two methods. The developed method can be adapted to other complex pipeline structures to extract circumferential guided wave dispersion characteristics by both simulation and experimental measurements.

Excitation of progressing dust ionization waves on PK-4 facility

We report observation of the dust ionization waves (DIWs) excited by an external oscillating electric field on the Plasma Kristall-4 facility under microgravity conditions. It is shown that at the smallest excitation amplitude, the waves are linear, and the dispersion relation can be deduced from the experimental data. The microparticle oscillations are represented as a superposition of two longitudinal waves propagating in the opposite directions. In the investigated range of excitation frequency, the wavenumber is not directly proportional to the frequency, and the phase velocity is almost proportional to the frequency. We propose an interpretation of DIW assuming that the microparticle effect on the recombination rate rather than the microparticle subsystem compressibility is responsible for the wave propagation. The calculated phase velocity of DIW is compatible with the experimental one.

Common-midpoint spatial autocorrelation analysis of seismic ambient noise obtained from a spatially unaliased sensor distribution

We have introduced a passive surface-wave method using seismic ambient noise obtained from dozens of receivers forming spatially unaliased 2D arrays. The method delineates 2D or 3D S-wave velocity ([Formula: see text]) models to depths of several hundreds of meters, without using any sources. Typical data acquisition uses 50–100 vertical-component 2 Hz geophones on the surface with 5–30 m receiver spacing. Cableless seismographs with GPS record 20–60 min of ambient noise. We establish a 2D grid covering the investigation area and use a common-midpoint spatial autocorrelation (CMP-SPAC) method to calculate phase velocities, resulting in a dispersion curve for each grid point. The method provides dozens of ispersion curves in the investigation area. We use a 1D nonlinear inversion to estimate a 1D [Formula: see text] profile for each grid point, and then we construct pseudo-2D or pseudo-3D [Formula: see text] models from the 1D [Formula: see text] profiles. The precision and accuracy of the CMP-SPAC method were tested with a numerical simulation using a 3D finite-difference method. The results of the simulation demonstrated the applicability of the method to complex velocity structures. We applied the method to an active fault investigation in China. Sixty-four cableless seismographs were deployed in an investigation area of 330 × 660 m (217,800 m2) with 5 and 30 m receiver spacings for dense and sparse grids, respectively. A 3D [Formula: see text] model was obtained to a depth of 150 m from CMP-SPAC analysis. The resultant 3D [Formula: see text] model indicates approximately 50 m of vertical displacement on a known fault.

Sound Pressure Interference and Phase Velocities in Shallow Water: Calculation and Experiment

A study was carried out on the interference structure of sound pressure amplitudes, longitudinal projections of phase gradients, and calculated phase velocities in a plane-parallel waveguide. It has been established that the phase velocity values of the sound pressure field and the effective phase velocities in the zones of interference maxima calculated by various methods are quite stable and agree well both with each other and the experimental data. It is shown that at the frequencies for which an array is located in zones of interference maxima, using an equivalent plane wave model and effective phase velocities instead of the sound speed in water reduces the bearing estimation error.

Three‐Dimensional S Wave Velocity Structure of Central Japan Estimated by Surface‐Wave Tomography Using Ambient Noise

AbstractMany significant geological features in central Japan reflect the history of tectonic events such as volcanic eruptions, fault ruptures, and the collision of the Izu‐Bonin arc. Because most previous studies focused on deep, large‐scale structures at relatively low resolution or on local structures using high‐resolution data (e.g., active source seismic data), tectonic structures over a wide area throughout central Japan have not been characterized in detail. In this study, we estimated 3D S wave velocity structures with high spatial resolution by extracting surface waves from 1‐year‐long ambient seismic data recorded by the Hi‐net high‐sensitivity seismograph network. We computed cross spectra of ambient noise data between station pairs and then extracted phase velocity dispersion curves using a frequency domain method. We developed an algorithm to calculate phase velocity and obtained numerous dispersion data. We then estimated the 3D S wave velocity structure by applying a direct surface‐wave inversion method. Our results clearly mapped heterogeneous features such as tectonic lines, sedimentary plains, and volcanic systems. We observed some low‐velocity anomalies below volcanoes. Active fault zones identified as low‐velocity zones were consistent with features on seismic reflection profiles. Several geological blocks that are related to the Izu collision were observed around the Izu Peninsula. We observed previously unreported geological features of the island of Honshu. Our high‐resolution S wave velocity model can be used for not only interpretation of geological structures but also hazard assessment of earthquake.

The effect of body waves on phase-velocity determined by the spatial autocorrelation (SPAC) method, evaluated using full-wave modelling

Body waves may affect phase velocity obtained from microtremor array surveys in some rare cases. Fitting theoretical phase velocities based on a surface-wave theory to observed phase velocities affected by body waves would therefore result in distorted images of subsurface S-wave velocity structure. In this study, we present a method for the theoretical calculation of phase velocities in which the full-wave field (i.e. a wavefield including not only surface waves but also body waves) is taken into account. In numerical experiments conducted in this study, in which we considered the full-wave field, we generated synthetic microtremors by randomly distributing point vibration sources on the surface of a horizontally stratified velocity model. We then determined the phase velocities by applying the spatial autocorrelation (SPAC) method to the synthetic vertical-component wave data. The phase-velocity dispersion curve thus obtained exhibited a shape with a clear peak, with a peak value (peak phase velocity) exceeding the S-wave velocity of a bedrock in the model, which was not explainable with a surface-wave (Rayleigh-wave) theory. We conducted systematic numerical experiments and clarified the following two features of the peak phase velocity: (1) the peak phase velocity becomes large as the contrast of the S-wave velocities between the surface layer and the bedrock, or the P-to-S-wave velocity ratio (related to the Poisson’s ratio) in the surface layer gets large, and (2) the frequency at which peak phase velocity occurs (peak frequency) lies in the vicinity of the S-wave resonance frequency of the ground. Both the peak phase velocity and the peak frequency were theoretically reproduced by the calculation method that we propose in this study, based on a SPAC method modified to consider the full-wave field. These results imply the possible improvement in the accuracy of microtremor array survey analysis for velocity-structure inference, by applying a full-wave theory to the peak phase velocity.

Determination of Phase Jumps in the Measurement of Phase Velocity of Samples Obeying a Frequency Power-Law Attenuation Coefficient Using Kramers-Kronig Relations.

Ultrasonic phase velocity spectroscopy is a very sensitive technique used in the measurement of material properties. In a phase velocity calculation, ambiguities can arise in the spectral phases, in the form of integer multiples of 2π rad, which, if not corrected, results in large errors. In this work, we propose a method for determining these ambiguities, more specifically, the number of 2π rad phase jumps, using the Kramers-Kronig relations, for samples exhibiting a frequency power-law attenuation coefficient. The method is based on a first estimate of the phase velocity from group velocity and attenuation coefficient that are not affected by phase jumps. This estimated phase velocity is used to obtain the number of 2π rad phase jumps, which in turn is used to calculate the corrected phase velocity. The method was tested with samples of liquids with a frequency power-law attenuation coefficient (exponent y varying from 1.5 to 2) and a solid [polymethyl methacrylate (PMMA)] with y ∼ 1 , and velocity dispersions ranging from 0 to 34 (cm/s)/MHz.

Calculation of Phase Velocities in the Field of Sea Surface Waves

Specific features of phase velocities of sea waves due to the angular distribution of wave energy and the second harmonic of a dominant wave with a velocity differing from the phase velocity of a free wave at the same frequency have been analyzed. The presence of wave components with different velocity projections on a given direction or different propagation velocities leads to a deviation in the estimates of phase velocities from the values resulting from a variance relationship for gravitational waves in deep water. It has been shown that the phase spectrum in field of sea waves varies nonlinearly with increasing distance between the relevant points. As a consequence, the estimates for phase velocity are functions of distance. The deviations of the estimates for phase velocity from the linear theory have been shown to depend on the stage of wave field development.

Long‐Period Rayleigh Wave Phase Velocity Tomography Using USArray

AbstractSeismic models show that the shallow mantle beneath the contiguous United States is characterized by low velocities west of the Rocky Mountain Front, high velocities beneath the North American craton, and moderate wave speeds along the eastern seaboard. However, numerous questions remain, including the distribution of temperature and partial melt in the mantle that may explain the slower velocities in the west; the origin and depth extent of the western edge of the cratonic lithosphere; and explanations for slower velocities observed along the eastern seaboard. To investigate these questions, we have measured teleseismic Rayleigh wave phase and amplitude at USArray stations for periods of 25–180 s and calculated phase velocity using the Helmholtz tomography method. Notably, the new long‐period maps represent an opportunity to resolve mantle structure at sublithospheric depths and show differences relative to shorter periods in both the distribution of slow velocities in the west and the extent of fast velocities in the central United States. The maps are then used as a basis for comparing six recent 3‐D shear velocity models of the contiguous United States, from which we predict phase velocities. While predictions from surface‐wave models agree best with our observations at short and intermediate periods, the longest‐period maps are most similar in amplitude to body‐wave models.

THERMAL MODEL FRO SAW CALCULATIONS IN THE LAYERED SYSTEMS

The calculation of surface acoustic wave (SAW) parameters in the layered systems consists of half infinite substrate and one or several layers when the temperature is variable have been considered. SAW phase velocity calculation with temperature dependent material constants have been discussed. Expressions for the temperature coefficients of delay (TCD) and the temperature coefficients of frequency (TCF) of the first and the second order with taking into account SAW dispersion have been evaluated. Numerical procedures for TCD and TCF calculation have been proposed.

Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) timoshenko nano-beams considering surface effects and residual surface stress

This research deals with wave propagation of the functionally graded (FG) nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The FG nano-beam is resting in Winkler-Pasternak foundation. It is assumed that the material properties of the nano-beam changes continuously along the thickness direction according to simple power-law form. In order to include coupling of strain gradients and electrical polarizations in governing equations of motion, the nonlocal non-classical nano-beam model containg flexoelectric effect is used. Also, the effects of surface elasticity, di-electricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory (FSDBT) and also considering residual surface stresses. The analytical method is used to calculate phase velocity of wave propagation in FG nano-beam as well as cut-off frequency. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface, bulk and residual surface stresses, Winkler and shear coefficients of foundation, power gradient index of FG material, and geometric dimensions on the wave propagation characteristics of FG nano-beam. The numerical results indicate that considering surface effects/flexoelectric property caused phase velocity increases/decreases in low wave number range, respectively. The influences of aforementioned parameters on the occurrence cut-off frequency point are very small.

On terahertz pulsed broadband Gauss-Bessel beam free-space propagation

Terahertz pulse time-domain holography is the ultimate technique allowing the evaluating a propagation of pulse broadband terahertz wavefronts and analyze their spatial, temporal and spectral evolution. We have numerically analyzed pulsed broadband terahertz Gauss-Bessel beam’s both spatio-temporal and spatio-spectral evolution in the non-paraxial approach. We have characterized two-dimensional spatio-temporal beam behavior and demonstrated all stages of pulse reshaping during the propagation, including X-shape pulse forming. The reshaping is also illustrated by the energy transfer dynamics, where the pulse energy flows from leading edge to trailing edge. This behavior illustrates strong spatio-temporal coupling effect when spatio-temporal distribution of Bessel beam’s wavefront depends on propagation distance. The spatio-temporal and spatio-spectral profiles for different spectral components clearly illustrate the model where the Bessel beam’s wavefront at the exit from the axicon can be divided into radial segments for which the wave vectors intersect. Phase velocity via propagation distance is estimated and compared with existing experimantal results. Results of the phase velocity calculation depend strongly on distance increment value, thus demonstrating superluminal or subluminal behavior.

Simulation of breaking waves using the high-order spectral method with laboratory experiments: Wave-breaking onset

This study investigates a wave-breaking onset criteria to be implemented in the non-linear potential flow solver HOS-NWT. The model is a computationally efficient, open source code, which solves for the free surface in a numerical wave tank using the High-Order Spectral (HOS) method. The goal of this study is to determine the best method to identify the onset of random single and multiple breaking waves over a large domain at the exact time they occur. To identify breaking waves, a breaking onset criteria based on the ratio of local energy flux velocity to the local crest velocity, introduced by Barthelemy et al. (2017) is selected. The breaking parameter is uniquely applied in the numerical model in that calculations of the breaking onset criteria ratio are not made only at the location of the wave crest, but at every point in the domain and at every time step. This allows the model to calculate the onset of a breaking wave the moment it happens, and without knowing anything about the wave a priori. The application of the breaking criteria at every point in the domain and at every time step requires the phase velocity to be calculated instantaneously everywhere in the domain and at every time step. This is achieved by calculating the instantaneous phase velocity using the Hilbert transform and dispersion relation. A comparison between more traditional crest-tracking techniques shows the calculation of phase velocity using Hilbert transform at the location of the breaking wave crest provides a good approximation of crest velocity.The ability of the selected wave breaking criteria to predict single and multiple breaking events in two dimensions is validated by a series of large-scale experiments. Breaking waves are generated by energy focusing and modulational instability methods, with a wide range of primary frequencies. Steep irregular waves which lead to breaking waves, and irregular waves with an energy focusing wave superimposed are also generated. This set of waves provides a wide range of breaking-wave strengths, types and scales for validation of the model. A comparison of calculations made using HOS-NWT with experimental measurements show that the model is successful at predicting the occurrence of wave breaking, as well as accurately calculating breaking onset time and location.Although the current study is limited to a unidirectional wave field, the success of the wave-breaking model presented provides the basis for application of the model in a multidirectional wave field. By including wave breaking onset with the addition of an appropriate energy dissipation model into HOS-NWT, we can increase the application range of the model, as well as decrease the occurrence of numerical instabilities that are associated with breaking waves in a potential flow solver. An accurate description of the wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures and the general physics of ocean waves, for example.

Homogenization of layered media based on scattering response and field integration

The stress wave scattering off of any finite slab may be used as a physical approach to determining some or all of the overall dynamic constitutive parameters of such a specimen. In this paper, this approach is applied to normal incidence of symmetric and asymmetric layered structures with elastic or viscoelastic layers. The method determines all of the overall constitutive constants of a Willis-type material (including zero and non-zero coupling parameters) for all frequencies, even in stop bands of elastic structures, exactly. The ambiguity in phase velocity calculation is overcome using continuity considerations. Symmetries in coupling constants and the restrictions due to energy conservation and dissipation are presented. Integrating the wave equations directly leads to a proposed micro-structural scheme for determination of the overall constitutive parameters. The results of this method are identical to those derived based on the scattering response for all frequencies, including stop bands, and beyond the long wavelength limit of traditional homogenization techniques. The proposed approach has the potential to be applied to 3D-structured unit cells, oblique incidences, and simultaneous scattering of multiple waves.

A theoretical framework for the changing spectral properties of meter‐scale Farley‐Buneman waves between 90 and 125 km altitudes

AbstractStimulated by recent observations described in a companion paper, we have revisited existing theories of the Farley‐Buneman instability throughout the altitude range 90 to 125 km. We have assumed that the irregularities detected by radars at a given altitude are dominated by structures moving at the threshold speed in a direction associated with maximum linear growth rate conditions. We included recent nonisothermal electron and ion theories, which can modify threshold speeds by considerable amounts. We included altitude‐dependent models of ion and electron temperature and of the ion motion in the phase velocity calculations. Our treatment of the instability explains why some spectra are slow (Doppler shifts typically 200 m/s) and narrow, while others are fast (1500 m/s or close to the E × B) and narrow. These narrow spectra have all the characteristics of what has been labeled as “Type III” and “Type IV” in the past. Our calculations also offer an explanation for the observation of a strong asymmetry in the number of events with positive Doppler shifts near the nominal ion‐acoustic speed and those with negative Doppler shifts of the same magnitude.

Proper orthogonal and dynamic mode decompositions of time-resolved PIV of confined backward-facing step flow

The unsteady flow field past a backward-facing step in a rectangular duct is investigated by adopting time-resolved particle image velocimetry (PIV) in the Reynolds number range of 2,640–9,880 based on step height and the inlet average velocity. The PIV realizations are subjected to post-processing techniques, namely, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). At low Reynolds numbers, the second spatial POD modes indicate the presence of the shear layer mode, whereas this feature shifts to higher modes at higher Reynolds numbers. The corresponding temporal modes are Fourier-transformed to obtain the dominant frequency, whose Strouhal number corroborates the above observation. Short-time windows in the transverse velocity component along the shear layer are selected to investigate the temporal stability of the flow field by DMD to quantify the growth rate of the shear layer mode. The higher harmonics of this mode are also observed to grow, albeit at lesser rate. By relating to POD analysis, the most energetic structures were found to correspond to the unstable modes. The correlation between these unstable DMD modes and the Fourier-filtered flow fields for the same frequencies indicate better match for the lower operating Reynolds number case as compared to higher ones. The spatial stability analysis demonstrates the growth of the shear layer vortices, which is combined with the temporal stability analysis to evaluate the phase velocity of the identified shear layer structures. The calculated phase velocity magnitude of the shear layer is found to be reasonably below the local velocity as expected.

Calculation of Phase Velocities of Traveling Waves in a Cylindrical Shell Based on the Solution Analysis of Boundary Problem of Forced Oscillations

Calculation of Phase Velocities of Traveling Waves in a Cylindrical Shell Based on the Solution Analysis of Boundary Problem of Forced Oscillations