Dispersive Wave Modes Research Articles

Partially embedded metabarrier to suppress surface waves in granular mediaa).

The gravity-induced depth-dependent elastic properties of a granular half-space result in multiple dispersive surface modes and demand the consideration of material heterogeneity in metabarrier designs to suppress surface waves. Numerous locally resonant metabarrier configurations have been proposed in the literature to suppress Rayleigh surface waves in homogeneous media, with little focus on extending the designs to a heterogeneous half-space. In this work, a metabarrier comprising partially embedded rod-like resonators to suppress the fundamental dispersive surface wave modes in heterogeneous granular media known as first order PSV (PSV1; where P is the longitudinal mode and SV is the shear-vertical mode) and second order PSV (PSV2) is proposed. The unit-cell dispersion analysis, together with an extensive frequency-domain finite element analysis, reveals preferential hybridization of the PSV1 and PSV2 modes with the longitudinal and flexural resonances of the resonators, respectively. The presence of the cutoff frequency for the longitudinal-resonance hybridized mode facilitates straightforward suppression of the PSV1 mode, while PSV2 mode suppression is possible by tailoring the hybridized flexural resonance modes. These PSV1 and PSV2 bandgaps are realized experimentally in a granular testbed comprising glass beads by embedding 3D-printed resonator rods. Also explored are novel graded metabarriers capable of suppressing both PSV1 and PSV2 modes over a broad frequency range for potential applications in vibration control and seismic isolation.

Turbulence, Waves, and Taylor’s Hypothesis for Heliosheath Observations

Magnetic field fluctuations measured in the heliosheath by the Voyager spacecraft are often characterized as compressible, as indicated by a strong fluctuating component parallel to the mean magnetic field. However, the interpretation of the turbulence data faces the caveat that the standard Taylor’s hypothesis is invalid because the solar wind flow velocity in the heliosheath becomes subsonic and slower than the fast magnetosonic speed, given the contributions from hot pickup ions (PUIs) in the heliosheath. We attempt to overcome this caveat by introducing a 4D frequency-wavenumber spectral modeling of turbulence, which is essentially a decomposition of different wave modes following their respective dispersion relations. Isotropic Alfvén and fast mode turbulence are considered to represent the heliosheath fluctuations. We also include two dispersive fast wave modes derived from a three-fluid theory. We find that (1) magnetic fluctuations in the inner heliosheath are less compressible than previously thought, an isotropic turbulence spectral model with about 25% in compressible fluctuation power is consistent with the observed magnetic compressibility in the heliosheath; (2) the hot PUI component and the relatively cold solar wind ions induce two dispersive fast magnetosonic wave branches in the perpendicular propagation limit, PUI fast wave may account for the spectral bump near the proton gyrofrequency in the observable spectrum; (3) it is possible that the turbulence wavenumber spectrum is not Kolmogorov-like although the observed frequency spectrum has a −5/3 power-law index, depending on the partitioning of power among the various wave modes, and this partitioning may change with wavenumber.

Applications of Linear Scanning Magnetostrictive Transducers (MST) for Finding Hard-to-Detect Anomalies in Structural Components

Guided wave testing is now a widely accepted method for detection of structural damage in many different types of components, from pipelines to pressure vessels to tanks. Torsional wave modes (T modes) in pipes and shear horizontal (SH) mode guided waves in plates are good candidates for finding areas with generalized corrosion, due to the absence of fluid coupling effects and their lack of dispersion. However, from our field test experience, certain types of defects are difficult to detect with conventional T mode or SH mode guided wave probes. Gradual wall thinning is one such type of defect; another is crack-like defects in or close to welds or penetrations in the pipe. Recently, Southwest Research Institute (SwRI) has developed a new sensor configuration and scanning system that overcomes these limitations. We have recently developed a linear scanning magnetostrictive transducer (MsT) probe system, in which a FeCo strip wound with radio frequency (RF) coils is attached to the structure under test with shear wave couplant, and a moving permanent magnet driven by a motor is used to excite SH guided waves at predefined positions along this strip. The probe is designed to operate over a wide frequency range (20 – 500 kHz) and can be used to generate dispersive shear wave mode (SH1) in addition to the nondispersive SH0 mode. The use of different modes with the sensor at multiple positions allows detection of a range of defect types. In this paper, the performance of linear scanning MsTs is presented, including experimental evaluation of detection of gradual wall thinning patches of different depths and locations on a steel pipe and plate mockups. Another set of experiments evaluates detection of notches in seam welds. Indications from real-time B-scan and SAFT (synthetic aperture focusing technique) processing will be presented.

Optimal unidirectional generation of a dispersive wave mode with dual-array transducer

Array transducers are commonly used to generate several types of waves, such as ultrasonic guided waves. They consist of a series of periodic wave source elements, and thus define a nominal or dominant wavelength of generated waves. A common approach to generating waves in a single direction is to use two identical wave sources, or two arrays of sources forming a dual-array transducer, that are separated by a quarter wavelength. Then, one source is activated a quarter of a time period after the other. In this way, constructive interference arises in one direction, whilst destructive interference arises in the opposite direction, making the total wave source unidirectional. This principle assumes that the frequency content of the generated wave is monochromatic. When there is some frequency bandwidth to the wave generated, such as with finite-length pulses, one cannot satisfy simultaneously constructive and destructive interference in opposite directions with dual-array transducers. For a non-dispersive wave mode, ideal destructive interference for pulsed waveform is obtained if one of the sources is inverted relative to the other, so that, in theory, complete cancellation can be achieved. Moreover, most guided wave modes are dispersive, meaning that, different frequencies propagate at different phase speeds. This limits the amount of wave cancellation in one direction and constructive interference in the other. Here, we describe the operation of the dual-array transducer in the frequency–wavenumber domain and use it to propose two new excitation methods, based on a frequency-dependent phase-shift strategy, that is designed through the dispersion relationship of the wave mode of interest. These provide ideal constructive or destructive interferences for dispersive waves, and achieve optimal unidirectional generation behaviour for dispersive wave modes. The new methods were experimentally assessed with shear horizontal ultrasonic waves, generated by a dual periodic permanent magnet electromagnet acoustic transducer. The optimal excitation signal yielded up to 30 dB unidirectionality, when generating the dispersive SH1 wave mode in an aluminium plate.

Phase velocity measurement of dispersive wave modes by Gaussian peak-tracing in the f-k transform domain

The measurement of guided wave phase velocity is vital for the successful implementation of the guided wave technique for defect detection and material characterization. In this paper, an algorithm for quantitative phase velocity measurement based on f-k (frequency-wavenumber) transformation with a Gaussian fit peak-tracing is proposed. The versatility of the algorithm is demonstrated using numerically simulated data for a wide range of case studies, including non-dispersive, dispersive, dispersive with viscoelasticity, overlapping modes, and highly attenuative materials. It is further validated utilizing two experimental datasets. The maximum error in measuring phase velocity using experimental and numerical data is less than 0.8% when compared to the analytical value obtained using DISPERSE. The phase velocity values obtained with the proposed f-k transformation with a Gaussian fit peak-tracing algorithm are also compared with the conventional methods and found to be superior. Further, the proposed algorithm is suitable for evaluating the phase velocity of the coexistence of forward and reflected wave modes. Hence, the proposed algorithm is appropriate for measuring phase velocity where separation of modes or reflected signal is difficult to achieve, such as for a smaller specimen or even longer specimens with higher-order faster mode.

Estimation of nighttime ionospheric D-region parameters using tweek atmospherics observed for the first time in the North African region

Dispersive wave modes called tweek atmospherics produced by lightning strokes were observed using Stanford University designed AWESOME VLF receiver system installed at the University of Tunis El Manar, Tunisia (Geog. lat. 36.50° N; lon. 10.08° E). About 84 tweek atmospherics were analyzed during geomagnetically quiet days to provide important clues for estimating the effective ionospheric reflection height and electron density using the cut-off frequency of first modes. Variations of nighttime Wait ionospheric parameters (h′ and β) have been studied using tweeks observed for the first time at the low latitude station in the North African region. The distance of the lightning located in a range of 500–5000 km and the accuracy obtained by single-site technique had been estimated by a comparison with independent data from the World-Wide Lightning Location Network (WWLLN).

A detailed investigation of low latitude tweek atmospherics observed by the WHU ELF/VLF receiver: I. Automatic detection and analysis method

As a dispersive wave mode produced by lightning strokes, tweek atmospherics provide important hints of lower ionospheric (i.e., D-region) electron density. Based on data accumulation from the WHU ELF/VLF receiver system, we develop an automatic detection module in terms of the maximum-entropy-spectral-estimation (MESE) method to identify unambiguous instances of low latitude tweeks. We justify the feasibility of our procedure through a detailed analysis of the data observed at the Suizhou Station (31.57°N, 113.32°E) on 17 February 2016. A total of 3961 tweeks were registered by visual inspection; the automatic detection method captured 4342 tweeks, of which 3361 were correct ones, producing a correctness percentage of 77.4% (= 3361/4342) and a false alarm rate of 22.6% (= 981/4342). A Short-Time Fourier Transformation (STFT) was also applied to trace the power spectral profiles of identified tweeks and to evaluate the tweek propagation distance. It is found that the fitting accuracy of the frequency–time curve and the relative difference of propagation distance between the two methods through the slope and through the intercept can be used to further improve the accuracy of automatic tweek identification. We suggest that our automatic tweek detection and analysis method therefore supplies a valuable means to investigate features of low latitude tweek atmospherics and associated ionospheric parameters comprehensively.

Numerical simulation of solitary wave attenuation by vegetation with non-hydrostatic model

In this paper solitary wave attenuation by vegetation is investigated by using numerical simulation. To take into account effects of dispersion, we use a dispersive and nonlinear wave mode; the non-hydrostatic with 1 vertical layer. The damping by vegetation is modelled by using mean drag force using Morison’s formula. The dissipative term is added in the momentum equation. The wave model is implemented numerically using finite volume with momentum conservative staggered grid scheme. To test the numerical scheme implementation, we simulate a physical experiment of solitary wave attenuation by vegetation of Huang et al. 2011. Comparison with experimental data shows that the results of simulation agree quite well.

Enhancement of Ultrasonic Guided Wave Signals Using a Split-Spectrum Processing Method

Ultrasonic guided wave (UGW) systems are broadly utilised in several industry sectors where the structural integrity is of concern, in particular, for pipeline inspection. In most cases, the received signal is very noisy due to the presence of unwanted wave modes, which are mainly dispersive. Hence, signal interpretation in this environment is often a challenging task, as it degrades the spatial resolution and gives a poor signal-to-noise ratio (SNR). The multi-modal and dispersive nature of such signals hampers the ability to detect defects in a given structure. Therefore, identifying a small defect within the noise level is a challenging task. In this work, an advanced signal processing technique called split-spectrum processing (SSP) is used firstly to address this issue by reducing/removing the effect of dispersive wave modes, and secondly to find the limitation of this technique. The method compared analytically and experimentally with the conventional approaches, and showed that the proposed method substantially improves SNR by an average of 30 dB. The limitations of SSP in terms of sensitivity to small defects and distances are also investigated, and a threshold has been defined which was comparable for both synthesised and experimental data. The conclusions reached in this work paves the way to enhance the reliability of UGW inspection.

Spin wave excitations in the tetragonal double perovskiteSr2CuWO6

Sr$_2$CuWO$_6$ is a double perovskite proposed to be at the border between two and three dimensional magnetism, with a square lattice of $S=\frac{1}{2}$ Cu$^{2+}$ ions. We have used inelastic neutron scattering to investigate the spin wave excitations of the system, to find out how they evolve as a function of temperature, as well as to obtain information about the magnetic exchange interactions. We observed well defined dispersive spin wave modes at $6$~K, which partially survive above the magnetic ordering temperature, $T_N=24$~K. Linear spin wave theory is used to determine the exchange interactions revealing them to be highly two-dimensional in nature. Density functional theory calculations are presented supporting this experimental finding, which is in contrast to a previous \emph{ab-initio} study of the magnetic interactions. Our analysis confirms that not the nearest neighbour, but the next nearest neighbour interactions in the tetragonal $ab$ plane are the strongest. Low incident energy measurements reveal the opening of a $0.6(1)$~meV gap below $T_N$, which suggests the presence of a very weak single ion anisotropy term in the form of an easy axis along $\hat{\mathbf{a}}$.

Dynamic modeling of Kevlar KM2 single fiber subjected to transverse impact

In this paper, the transverse impact onto a Kevlar KM2 single fiber is studied using analytical and numerical models. The impact response of fibers with reduced longitudinal shear moduli (‘string’ model) is studied with a 3D finite element model and the wave propagation results converge to the classic 1D analytic solution that supports only axial loads. A dispersive flexural wave mode is predicted numerically for the single fiber during transverse impact due to its finite longitudinal shear modulus. The numerical results are confirmed with an analytical solution derived for the response of an infinitely long Euler–Bernoulli beam subjected to a constant velocity impact. Fiber bounce is predicted for impact with a cylindrical projectile with fiber velocity exceeding impact velocity by 60–80%. At short time scales significant transverse compressive stresses and strains develop in the fiber and the magnitude depends on the impact velocity. The breaking speed predicted by the 3D model based on maximum principal stress criterion for a single fiber is between 26% (membrane failure) and 76% (combined membrane and flexure failure) less than the 1D analytical solution. The flexural wave and projectile fiber interactions induce curvatures in the fiber significant enough to induce compressive fiber failure and fibrillation.

Split-Spectrum Signal Processing for Reduction of the Effect of Dispersive Wave Modes in Long-range Ultrasonic Testing

This paper presents a Split-Spectrum Signal Processing (SSP) with applications to Long Range Ultrasonic Testing (LRUT). The problem of coherent noise due to Dispersive Wave Modes (DWM) in the context of ultrasonic scattering is addressed and a novel solution by utilizing the SSP technique is proposed for reduction of the effects of DWM in the received signal. The proposed technique investigates the sensitivity of SSP performance to the filter bank parameter values such as processing/filter bandwidth, and filter overlap. Therefore, as a result the optimum values are introduced that improve the signal to noise ratio (SNR) significantly. The proposed method has been compared with conventional approaches for synthesized signals for a 6 inch pipe by applying the different recombination SSP techniques. The Polarity Thresholding (PT) and PT with Minimization (PTM) methods were found to give the best result and substantially improve the SNR performance by an average of 10dB.

Krauklis wave in a trilayer

The Krauklis wave is a slow dispersive wave mode that propagates in a fluid layer bounded by elastic media. The guided properties of this wave and its ability to generate very short wavelengths at seismic frequency range predict possibility of resonances in fluid-filled rock fractures. Study of Krauklis wave properties at laboratory scales requires evaluation of its propagation velocities in models with finite and thin elastic walls. Analysis of an exact solution for a fluid-filled trilayer with equal thickness plates reveals existence of the Krauklis waves in such a model, as well as another mode which propagates mostly in the solid part. Both propagation modes exist at all frequencies. We derived and verified various asymptotic solutions by comparing their dependencies on layer thicknesses and frequency with the exact numerical solution. Analytical and computational results demonstrate that in a 60-cm-long model, the first resonant frequency can be below 10 Hz. This result suggests that the Krauklis-wave effects can be studied in a laboratory at seismic range of frequencies avoiding a notorious problem of frequency downscaling. Strong dispersive properties of Krauklis waves and their dominant behavior in fluid-fracture systems are likely phenomena explaining the observed frequency-dependent seismic effects in natural underground reservoirs.

Mapping formation shear-velocity variation by inverting logging-while-drilling quadrupole-wave dispersion data

The logging-while-drilling (LWD) quadrupole wave is a dispersive wave mode guided along the borehole with a drill collar. The wave is sensitive to the formation alteration caused by drilling. We inverted LWD quadrupole-wave dispersion data to estimate a radial shear-velocity profile away from the wellbore. We also explored the nonuniqueness of the inverse problem and solved it by using a constrained inversion method. This was done by constraining the high-frequency portion of the model dispersion curve with another curve calculated using the near-borehole velocity. The constraint condition is based on the physical principle that a high-frequency LWD quadrupole wave has a shallow penetration depth and is therefore sensitive to the near-borehole shear velocity. Particularly, we found that a monotonically continuous velocity profile can be well approximated using a one-zone equivalent model, allowing for a drastic simplification of the inversion process. We used theoretical modeling and real data examples to validate the method for the LWD wave data. The quadrupole dispersion data and the inversion results clearly demonstrated that formation alteration can occur even while the well is being drilled.

Krauklis wave in a stack of alternating fluid-elastic layers

The Krauklis wave is a slow dispersive wave mode that propagates in a fluid layer bounded by elastic media. In a model of alternating fluid and elastic layers, two interface waves can exist at low frequencies: The first wave propagates mostly in the elastic layer and has little dispersion, while the second wave can have strong dispersion and propagates as a Krauklis wave for some parameter combinations. Analytical conditions predict appearance of the Krauklis wave for higher frequencies and low porosities. Interface-wave velocities depend on model porosity, which potentially can be used for fracture mapping.

Seismic interferometry application to improve seismic reflection signals affected by ice-plate flexural noise

Seismic interferometry based on cross-correlation of traces recorded at different positions makes it possible to recover new Green's functions and to obtain signals as if sources were placed at the receiver positions. This case history describes results obtained using sea-bottom hydrophone signals recorded in shallow water below the ice plate in an Alaska seismic survey. The aim was to simulate new shots at the sea-bottom receiver positions and to redatum the surface-generated seismic signals below the ice layer. The application was performed and the method investigated to attenuate the strong noise due to dispersive wave modes (mainly flexural waves) which propagate in the ice layer.

EDT: An ElastoDynamics Toolbox for MATLAB

The ElastoDynamics Toolbox (EDT) version 2.1 offers an extensive set of MATLAB functions to model elastodynamic wave propagation in horizontally layered media. The toolbox is based on the direct stiffness method and the thin layer method. These methods provide stiffness matrices for a homogeneous layer and a homogeneous halfspace, which are formulated in the frequency-wavenumber domain. EDT 2.1 can be used to solve a variety of problems governed by wave propagation in the soil, such as (1) site amplification, (2) the computation of dispersive wave modes in layered soils, and (3) the calculation of the forced response of the soil due to harmonic and transient loading. The toolbox serves as an electronic learning environment for the simulation and processing of seismic wave propagation in layered media. It has also been used by various authors to model wave propagation in layered soils

Analysis of cross-correlation and wavelet de-noising for the reduction of the effects of dispersion in long-range ultrasonic testing

Long-range ultrasonic testing (LRUT) involves transmitting a guided ultrasonic wave through a structure and receiving echoes caused by changes in acoustic impedance. There are several modes of propagation of the ultrasonic signal (wave modes) that depend on the structure and the test frequency. Some of these wave modes are dispersive: their velocity changes with frequency. Generally, LRUT procedures are designed such that non-dispersive wave modes are transmitted. However, interaction of the ultrasonic wave with the structure leads to mode conversions, some of which will be to dispersive wave modes. The effect of these dispersive wave modes is to reduce the signal-to-noise ratio (SNR) of the received signal. Cross-correlation and wavelet de-noising are considered here for reduction of the effect of dispersive wavemodes. An LRUT signal with dispersive and non-dispersive wave modes has been simulated and used to test these techniques. Experimental data have also been collected and used to evaluate further these techniques. Cross-correlation of the transmitted and received signals did not lead to significant improvement in SNR in either the simulated or experimental signals and led to a decrease in SNR in many of the simulated signals. Wavelet de-noising appeared to work well on some of the simulated LR UT signals, where the amplitude of the non-dispersive mode was greater than that of the dispersive mode. With the experimental data this technique improved the SNR slightly, but led to distortion of the signal. The results show that neither technique appears to be able to effectively discriminate between dispersive and non-dispersive wave modes.

Discrete modes of a ferromagnetic stripe dipolarly coupled to a ferromagnetic film: aBrillouin light scattering study

Spin wave excitations in a magnetic structure consisting of a series of long permalloystripes of a rectangular cross section magnetized along the stripe length and situated abovea continuous permalloy film are studied both experimentally and theoretically. Stripes andcontinuous film are coupled by dipole–dipole interaction across 10 nm thick Cuspacers. Experimental measurements made using the Brillouin light scatteringtechnique (with the light wavevector oriented along the stripe width) provideevidence for one dispersive spin wave mode associated with the continuous film andseveral discrete non-dispersive modes resonating within the finite width of thestripes.To interpret the experimental spectra, an analytic theory based on the spin wave formalismfor finite-width magnetic stripes has been developed, achieving a good qualitative andpartly quantitative description of the experimentally observed spin wave spectrum of thesystem. In particular, it is explained why the presence of a continuous magnetic film nearthe magnetic stripe leads to a substantial decrease of the frequencies of the discrete dipolarspin wave modes localized within the stripes. A more quantitative description of themeasured frequencies and of the spatial profiles of the spin wave eigenmodes has beenobtained by numerical calculations performed using a finite element method.

The synthesis of strong ground motion accelerograms from existing records

AbstractThe paper discusses the synthesis of acceleration time histories primarily for use in structural response estimation. A proposed model for the acceleration time history is based on the summation of dispersive wave modes over the range of frequencies of typical interest to structural response. The values of the modal amplitudes and the travel times (or group velocities) are, for cases examined here, extracted from a target earthquake (or an ensemble of them). The synthetic accelerograms are constructed from these parameters with the inclusion of a probabilistic definition of those or other characteristics of the strong ground shaking and, in particular, the modal phase angle. The probability distributions of the peak acceleration and the integral of the square acceleration of the synthetic records are examined along with comparisons of the pseudo spectral velocity (PSV) response.