Dispersion Curves Of Modes Research Articles

단일 센서와 모드해석을 이용한 박판 음향방출의 위치 표정

It was investigated how to take into account the modal nature of AE (Acoustic Emission) signals to reduce the number of sensors needed in AE source localization. To this end, the theory of the chirplet transform and modal acoustic emission are used to analyze the propagation of elastic waves in thin plates. First, the chirplet transform and the dispersion curves of the fundamental Lamb wave modes are utilized to separate the first-arrived modes and to estimate the distance between a source and a sensor. Then an analytical model is developed to simulate their late-arrived wave packets. Finally the correlations between the experimental and the simulated waveform are used to estimate the location of AE source. To validate the proposed source localization algorithm, experiments were performed on a steel plate using Hsu-Nielsen pencil lead break (PLB) test. Results show that the proposed algorithm can effectively localize AE source regardless of the location of the sources.

Numerical Computation of Dispersion Curves for Both Symmetric and Asymmetric Modes in Metal Coaxial Slow Wave Structures

In the overmoded coaxial slow wave structures (SWSs), the asymmetric mode is easier to be excited by the electron beam. For conveniently studying the high frequency characteristics of coaxial asymmetric modes, we derive and solve the universal dispersion equation for both symmetric and asymmetric modes in coaxial SWSs. In principle, this numerical formula can be applied to arbitrary even-function SWSs, arbitrary corrugated depth and arbitrary transverse dimension. By this dispersion equation, the dispersion curves of asymmetric modes can be calculated more quickly and conveniently than the simulation software based on finite-element method.

Surface wave transference in a piezoelectric cylinder coated with reinforced material

The present study deals with the propagation of a polarized shear horizontal (SH) wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder. The interface of the two media is assumed mechanically imperfect. For obtaining the dispersion relation, the mathematical formulation has been developed and solved by an analytical treatment. The effects of various parameters, i.e., the thickness ratio, the imperfect interface, the initial stress, the reinforcement, and the piezoelectric and dielectric constants, on the dispersion curve are observed prominently. The dispersion curves for different modes have been also plotted. The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.

Quantification of the resolution of dispersion image in active MASW survey and automated extraction of dispersion curve

Multichannel analysis of surface waves is a non-invasive method in the field of geophysics which is used for identifying shear wave velocity profile of the subsurface along its depth. The reliability and accuracy of the obtained profile strictly depends on the resolution of the dispersion image obtained from an active survey. The dispersion image is a representation of the distribution of the energy of propagating waves on a frequency-phase velocity space. Based on the relative energy accumulation in the dispersion image, the fundamental (M0) and higher modes of dispersion can be identified. As there are several parameters that can affect the resolution of dispersion images, it is important to determine the optimum magnitude of each parameter that would contribute in generating dispersion images of higher resolution. Until date, the resolution of dispersion image is described only qualitatively, wherein fundamental mode dispersion curve was extracted based on the best possible visual discretion of the user. Erroneous selections of dispersion points often led to the misidentification of the dispersion mode, leading to incorrect shear wave velocity profile. This paper reports an image-processing based methodology to quantify the resolution of dispersion images and automated extraction of M0 dispersion curve through threshold energy filtering of the dispersion image. Such methodology removes the user discretion-induced subjectivity associated with the manual extraction of dispersion curve, thereby resulting in a robust extraction technique.

On the sound speed dispersion and the frequency dependence of sound attenuation in a fine-grained sediment in the New England Mud Patch

The study on the sound speed dispersion and the frequency dependence of sound attenuation in marine sediments is of great importance in understanding the physics of sound propagation in the sea bottom. Modal dispersion curves (MDC) have only been utilized to estimate the low-frequency sound speed. At higher frequencies (i.e., above a few hundred hertz), arrival time difference for different modes generally become smaller and MDC is difficult to extract because of the cross-mode interference. This paper applies time-frequency representations (TFR) with high time-frequency resolution (e.g., optimal-kernel and center-affine-filtered TFR) to broadband acoustic signals (e.g., 31g explosive and combustive source signals) detonated along the 15-km Northwest-Southeast tracks during the Seabed Characterization Experiment in the New England Mud Patch, which has a surface fine-grained sediment layer overlying a sandy bottom. The resulting high-resolution broadband (150–1500 Hz) MDC, in conjunction with TL data, are fed to a previously developed two-step dimension-reduced geoacoustic inversion algorithm including modal dispersion-based inversion for sound speed and energy-based inversion for attenuation [IEEE J. Ocean. Eng., 44, in print, (2019)]. The estimated sound speed and attenuation are compared with the theoretical results from seabed geoacoustic models for fine-grained sediments. [Work supported by ONR Ocean Acoustics (322OA).]The study on the sound speed dispersion and the frequency dependence of sound attenuation in marine sediments is of great importance in understanding the physics of sound propagation in the sea bottom. Modal dispersion curves (MDC) have only been utilized to estimate the low-frequency sound speed. At higher frequencies (i.e., above a few hundred hertz), arrival time difference for different modes generally become smaller and MDC is difficult to extract because of the cross-mode interference. This paper applies time-frequency representations (TFR) with high time-frequency resolution (e.g., optimal-kernel and center-affine-filtered TFR) to broadband acoustic signals (e.g., 31g explosive and combustive source signals) detonated along the 15-km Northwest-Southeast tracks during the Seabed Characterization Experiment in the New England Mud Patch, which has a surface fine-grained sediment layer overlying a sandy bottom. The resulting high-resolution broadband (150–1500 Hz) MDC, in conjunction with TL data, are ...

Normal mode dispersion and time warping in the coastal ocean.

Simple, analytically solvable models of normal mode propagation in the coastal ocean are developed and applied to study the effect of the seafloor bathymetry on modal travel times. Within the adiabatic approximation, horizontal inhomogeneity of the waveguide is found to change the modal dispersion curves in a way that helps separation of the modal components of the acoustic field using the time-warping transform. It is shown that moderate seafloor slopes can lead to surprisingly large errors in retrieved geoacoustic parameters and cause a positive bias in bottom sound speed estimates if horizontal refraction is ignored.

Estimates of Low-Frequency Sound Speed and Attenuation in a Surface Mud Layer Using Low-Order Modes

Whereas there have been numerous theoretical and experimental studies on the properties of marine granular sands, there are significantly fewer studies on sediments classified as muds. The validity of geoacoustic models for muddy sediments has not been successfully tested due to the lack of inverted low-frequency sound speed and attenuation values. The geoacoustic properties of a surface fine-grained mud layer, overlaying three sand transition layers, and a half-space basement within the New England Mud Patch, were studied using explosive signals from long-range along-shelf sound propagation tracks. The sound-speed profile of the mud layer in the low-frequency band (100-500 Hz) was estimated using acoustic normal mode characteristics including the mode shapes and the modal dispersion curves of low-order modes, which mainly propagated in the water column and the surface mud layer. The ambiguity of sound speed at the top of the mud layer and sound-speed gradient was approximately removed. It was found that the resultant sound-speed ratio at the water-sediment interface was close to unity and the sound-speed gradient was 1.8 1/s with a standard deviation of 1.0 1/s. The attenuation in the mud layer was inverted using the attenuation coefficient of the first mode extracted from explosive signals at three source locations. The estimated attenuation at 150 Hz had a mean of 0.006 dB/m and a standard deviation of 0.003 dB/m.

Phonons in chiral nanorods and nanotubes: A Cosserat-rod-based continuum approach

A Cosserat-rod-based continuum approach is presented to obtain phonon dispersion curves of flexural, torsional, longitudinal, shearing, and radial breathing modes in chiral nanorods and nanotubes. Upon substituting the continuum wave form in the linearized dynamic equations of stretched and twisted Cosserat rods, we obtain an analytical expression of a coefficient matrix (in terms of the rod’s stiffnesses, induced axial force, and twisting moment) whose eigenvalues and eigenvectors give us frequencies and mode shapes, respectively, for each of the above phonon modes. We show that, unlike the case of achiral tubes, these phonon modes are intricately coupled in chiral tubes owing to extension–torsion–inflation and bending–shear couplings inherent in them. This coupling renders the conventional approach of obtaining stiffnesses from the long wavelength limit slope of dispersion curves redundant. However, upon substituting the frequencies and mode shapes (obtained independently from phonon dispersion molecular data) in the eigenvalue–eigenvector equation of the above-mentioned coefficient matrix, we are able to obtain all the stiffnesses (bending, twisting, stretching, shearing, and all coupling stiffnesses corresponding to extension–torsion, extension–inflation, torsion–inflation, and bending–shear couplings) of chiral nanotubes. Finally, we show unusual effects of the single-walled carbon nanotube’s chirality as well as stretching and twisting of the nanotube on its phonon dispersion curves obtained from the molecular approach. These unusual effects are accurately reproduced in our continuum formulation.

Analysis of the Directivity of Glass-Etalon Fabry-Pérot Ultrasound Sensors.

Planar glass-etalon Fabry-Pérot (FP) optical ultrasound sensors offer an alternative to piezoelectric sensors for the measurements of high-intensity focused ultrasound (HIFU) fields and other metrological applications. In this work, a model of the frequency-dependent directional response of the FP sensor was developed using the global matrix method, treating the sensor as a multilayered elastic structure. The model was validated against the experimentally measured directional response of an air-backed cover-slip FP sensor with well-known material properties. In addition, the model was compared with the measurements of an all-hard-dielectric sensor suitable for HIFU measurements. The model was then used to calculate modal dispersion curves for both glass-etalon sensors, allowing the features of the directional response to be linked to specific wave phenomena. The features in the directivity of the air-backed cover-slip sensor are due to guided Lamb waves. Symmetric Lamb modes give rise to regions of high sensitivity, whereas anti-symmetric modes cause regions of low sensitivity. For the all-hard-dielectric sensor, two features correspond to the water-substrate and water-spacer compressional and shear critical angles. A region of high sensitivity close to the shear critical angle is associated with a leaky-Rayleigh wave, which has a frequency-dependent phase speed. At higher frequencies, this feature is counteracted by a region of low sensitivity, which occurs when there is no difference in the vertical displacement of the mirrors forming the FP cavity. The model may be used to improve and optimize the design of FP sensors or could be used to assist with the accurate deconvolution of the directional response from array measurements in metrological and imaging applications.

Surface wave analysis: improving the accuracy of the shear-wave velocity profile through the efficient joint acquisition and Full Velocity Spectrum (FVS) analysis of Rayleigh and Love waves

ABSTRACTSurface wave propagation can be exploited to investigate subsurface conditions in terms of shear wave velocities in a number of possible applications (geotechnical site characterisation, seismic-risk assessment, crustal studies and non-destructive testing). Nowadays, one of the most common methods adopted to analyse the dispersion of surface waves is based on the determination of the Rayleigh wave frequency-dependent phase velocities obtained from multichannel active data. The obtained values represent the dispersion curve, which is inverted to determine the vertical shear-wave velocity (VS) profile. After briefly recalling some fundamental facts and problems regarding surface wave propagation and analysis, we present the Full Velocity Spectrum (FVS) approach which here is used to jointly invert the velocity spectra of the Rayleigh and Love waves acquired by means of a set of horizontal geophones only (Rayleigh waves are in fact analysed while considering their radial component). It is shown that for non-trivial data sets for which modal dispersion curves cannot be soundly extracted, the joint FVS approach may represent an efficient way to properly analyse the data, thus eventually obtaining a robust VS profile free from significant ambiguities that would otherwise inevitably affect the results obtained by following the ordinary approach based on the modal dispersion curve(s) of just one component.

Dyakonov surface waves at the interface of nanocomposites with spherical and ellipsoidal inclusions

The dispersion properties of different types of surface electromagnetic waves which are supported by the interface of two nanocomposite materials with inclusions of different shape are studied theoretically and numerically. Both nanocomposites are made of doped n-type semiconductor inclusions which are evenly distributed in a transparent dielectric matrix. First nanocomposite contains semiconductor inclusions of spherical shape and can be represented as isotropic material with scalar effective dielectric permittivity. Second nanocomposite contains semiconductor inclusions of ellipsoidal shape and can be modeled as a uniaxial anisotropic crystal with two different principal effective permittivity components. Influence of physical and geometrical parameters of the nanocomposites on dispersion properties of surface waves is studied. It is shown that when dissipations in the semiconductor inclusions are taken into account the angular spectrum of Dyakonov surface wave existence becomes wider, and several dispersion curves of surface modes can simultaneously exist.

Surface plasmon polaritons in thin-film Weyl semimetals

We theoretically investigate surface plasmon polaritons propagating in the thin-film Weyl semimetals. We show how the properties of surface plasmon polaritons are affected by hybridization between plasmons localized at the two metal-dielectric interfaces. Generally, this hybridization results in new mixed plasmon modes, which are called short-range surface plasmons and long-range surface plasmons, respectively. We calculate dispersion curves of these mixed modes for three principle configurations of the axion vector describing axial anomaly in Weyl semimetals. We show that the partial lack of the dispersion and the non-reciprocity can be controlled by fine-tuning of the thickness of the Weyl semimetals, the dielectric constants of the outer insulators, and the direction of the axion vector.

Particle filtering with adaptive resampling scheme for modal frequency identification and dispersion curves estimation in ocean acoustics

The goal of this work is to accurately estimate the modal frequencies and dispersion curves from a measured ocean acoustics signal. A particle filtering approach, a class of sequential Monte Carlo methods, is developed for modal frequency identification and dispersion curves estimation from a time-frequency representation of ocean acoustics signal. The adaptive resampling algorithm for enhancing the quality of a set of particles after likelihood calculation is implemented to improve the accuracy of the modal estimates as well as the dispersion curves of the signal. Results demonstrate the advantages in implementing the adaptive resampling into the conventional sequential importance sampling particle filter (SIS-PF) instead of using the sequential importance resampling (SIR) scheme. The noise robustness of the proposed method is demonstrated through examples where the realizations of different Signal-to-Noise Ratio (SNR) levels were used to test the performance of the adaptive resampling method. The results display the evidences that the adaptive resampling particle filter (AR-PF) is superior to the SIR-PF. Via root mean square error (RMSE), the AR-PF delivers smaller errors than those obtained by the SIR-PF for all SNR levels, emphasizing the benefit in incorporating the adaptive resampling into the PF for modal frequency identification and dispersion curves estimation of ocean acoustics signal.

Frequency‐Bessel Transform Method for Effective Imaging of Higher‐Mode Rayleigh Dispersion Curves From Ambient Seismic Noise Data

AbstractIt has been widely recognized that the cross‐correlation function of ambient seismic noise data recorded at two stations approximates to the part of Greens function between two stations. Therefore, the cross‐correlation function should include higher modes, aside from the fundamental mode. However, the problem of measuring or extracting overtones from ambient seismic noise data remains. In this paper, we propose the frequency‐Bessel transform method (F‐J method) for extracting the dispersion curves of higher modes from ambient seismic noise data. We then assess the validity, accuracy, and applicability of the F‐J method by conducting extensive numerical simulations and processing the observed ambient seismic noise data of the USArray. As demonstrated in this study, the F‐J method is a convenient, practical, and accurate method for extracting the dispersion curves of multimodes from ambient seismic noise data and therefore has significant potentiality in the field of ambient seismic noise tomography.

An Ultrasonic Guided Wave Mode Selection and Excitation Method in Rail Defect Detection

Different guided wave mode has different sensitivity to the defects of rail head, rail web and rail base in the detection of rail defects using ultrasonic guided wave. A novel guided wave mode selection and excitation method is proposed, which is effective for detection and positioning of the three parts of rail defects. Firstly, the mode shape data in a CHN60 rail is obtained at the frequency of 35 kHz based on SAFE method. The guided wave modes are selected, combining the strain energy distribution diagrams with the phase velocity dispersion curves of modes, which are sensitive to the defects of the rail head, rail web and rail base. Then, the optimal excitation direction and excitation node of the modes are calculated with the mode shape matrix. Phase control and time delay technology are employed to achieve the expected modes enhancement and interferential modes suppression. Finally, ANSYS is used to excite the specific modes and detect defects in different rail parts to validate the proposed methods. The results show that the expected modes are well acquired. The selected specific modes are sensitive to the defects of different positions and the positioning error is small enough for the maintenance staff to accept.

Trans-Dimensional Inversion of Modal Dispersion Data on the New England Mud Patch

This paper presents single receiver geoacoustic inversion of two independent data sets recorded during the 2017 seabed characterization experiment on the New England Mud Patch. In the experimental area, the water depth is around 70 m, and the seabed is characterized by an upper layer of fine grained sediments with clay (i.e., mud). The first data set considered in this paper is a combustive sound source signal, and the second is a chirp emitted by a J15 source. These two data sets provide differing information on the geoacoustic properties of the seabed, as a result of their differing frequency content, and the dispersion properties of the environment. For both data sets, source/receiver range is about 7 km, and modal time-frequency dispersion curves are estimated using warping. Estimated dispersion curves are then used as input data for a Bayesian trans-dimensional inversion algorithm. Subbottom layering and geoacoustic parameters (sound speed and density) are thus inferred from the data. This paper highlights important properties of the mud, consistent with independent in situ measurements. It also demonstrates how information content differs for two data sets collected on reciprocal tracks, but with different acoustic sources and modal content.

Using ambient noise to evaluate the acoustic Green’s function for a passive geoacoustic inversion in a dynamic shallow-water environment

Cross-correlation functions (CCFs) of ambient and shipping noise recorded by two hydrophones approximate the deterministic Green’s function and contain information about the propagation environment. This paper employs the data collected in the Shallow Water 2006 experiment on the New Jersey continental shelf to investigate the factors that affect the emergence of approximate Green’s functions from noise CCF estimates and accuracy of the approximation. One month-long continuous records of noise obtained by moored single-hydrophone receivers are analyzed. Hydrophones are located in 80–100-m deep water at distances of several kilometers from each other. Rapid variations of the water sound speed profile, which are primarily due to propagation of trains of strong nonlinear internal gravity waves, limit useful noise-averaging time. Available water temperature data are used to guide the selection of time windows for noise averaging and improve CCF evaluation and retrieval of information on seafloor properties. Various approaches to coherent stacking of CCFs are compared. Time warping transform is applied to the resultant noise CCF to extract dispersion curves of acoustic normal modes. The results of the geoacoustic inversion based on the passively measured dispersion curves are compared with the earlier results obtained using controlled sound sources. [Work supported by NSF and BSF.]

High-Order Modes Analysis of Complex Plasmonic Surface Using the Field-Network Joint Solution

The plasmonic surface is made of metallic surface with deep sub-wavelength decorations, which are designed to mimic the surface plasmon polaritons at lower frequency. Recently, high-order modes in some special structures are analyzed. In order to analyze the dispersion problem of high-order modes of complex lossless structures faster and simpler, a convenient and simple method using the average input wave impedance obtained by a field-network joint solution is proposed. Meanwhile, based on Forster's reactance theorem, high-order modes of the complex structure always exist. Then, the dispersion curves of the high-order modes calculated using proposed method are in perfect match with the simulated results, which can verify the effectiveness and correctness of the proposed method. Additionally, the simulated and experimentally measured electric field distribution of high-order modes have great agreement. Using the proposed method, one can quickly obtain dispersion curve of a plasmonic structure to verify or estimate structure design. Hence, the proposed method may make a big step forward for obtaining the special dispersion relations.

Influence of volumic fraction of adhesive in elastic and viscous thin bonded Aluminum/Adhesive/Aluminum plate on Lamb modes that have ZGV modes

Before a nondestructive testing process gets set up, the sensitivity of the Lamb waves to the bonded plate’s properties must be well understood. The dispersion and attenuation curves in thin bonded Aluminum/Adhesive/Aluminum plate are calculated by the Stiffness matrix method. The increase in the volumic fraction d caused the appearance of backward mode in the S0 and S2 dispersion curves. The effect of d on forward waves, and on backward waves and associated ZGV-modes, are studied. The frequencies of ZGV-modes decrease when d increases. The effects of d on dispersion and attenuation curves of the damped symmetric modes are shown. From certain values of d, and at the frequencies of the ZGV-modes, the dispersion curves of the symmetric modes are connected. This phenomenon gives rise to a C coupling mode. The attenuation levels of the ZGV-modes for different d values are calculated. The increase in d caused the shift of C-dispersion and C-attenuation curves toward the decreasing direction of the frequency axis, without significant change in the values of the phase velocity, and with slight decreases in the attenuation level of the C coupling mode.

Trans-dimensional geoacoustic inversion on the New England Mud Patch using modal dispersion data

This paper presents trans-dimensional geoacoustic inversion of two low-frequency broadband signals recorded during the Seabed Characterization Experiment (SBCEX). The considered sources are a chirp emitted by a towed J15 source and an underwater impulse created by a combustive sound source (CSS). Corresponding received signals are recorded on single hydrophones, and the two source/receiver configurations are reciprocal, on the same track. Input data for inversion are modal time-frequency dispersion curves, estimated using warping. Inversion is then performed within a Bayesian framework. A trans-dimensional inverse algorithm is used to estimate the model parametrization (i.e., number of seabed layers), and the mode covariance matrices are estimated as a first-order autoregressive error process. Inversion results on the two reciprocal tracks are consistent with the modal information available in each dataset. Results are also consistent with what is known about the area.