Experimental Dispersion Curves Research Articles

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.

Silicon wafer characterisation by laser ultrasonics and neural networks

Lamb waves propagating in plate like structures, have been investigated to characterise a silicon wafer in a non destructive way. A laser ultrasonic technique was first used for the generation and the detection of these guided acoustic waves. A two-dimensional Fourier transform was next performed on the whole experimental data to obtain the dispersion curves, revealing the propagation of symmetric and antisymmetric modes. The sample characterisation was carried out in an original way, directly comparing the experimental results to theoretical ones. A feedforward neural network, specifically trained to recognize the same propagation behaviours, achieved to fit the experimental dispersion curves with a theoretical anisotropic model. Knowing the wafer thickness and density, the elastic constants were then determined without any user intervention. This non contact method showed very good agreement with the results obtained in the literature, and was found to be prompt and easy to automate.

Kinerja dan Verifikasi Teknik Seismik Gelombang Permukaan Terintegrasi untuk Pengukuran Modulus Elastisitas Tanah Dasar

An integrated-spectral analysis of surface waves (ISASW) test has been recently proposed as an alternative technique in pavement evaluation and monitoring. ISASW technique is developed from the spectral analysis of surface wave (SASW) method which has been a well known nondestructive testing (NDT) for geotechnical and pavement structures. Surface wave propagation between a set of receivers were transformed to frequency domain using fast Fourier transform (FFT). Therefore, a phase spectrum was produced for measuring the time lag between receivers. A wavelet filtering on impulse response was used for constructing an enhanced phase spectrum. Using phase different method, an experimental dispersion curve was generated. Inversion analysis based on the 3-D stiffness matrix method was then performed in order to produce the shear wave velocity profile. The elastic modulus of pavement layer was calculated based on the linear elastic theory. In this paper, the performance of ISA SW measurement for determining the elastic modulus of pavement subgrade is presented in this paper. Verification on its elastic modulus obtained from ISASW technique was also conducted by using falling weight deflectometer (FWD) test. The result shows that the dispersion curves obtained in the ISASW test are sensitive to indicate the stiffness change in each layer of a pavement structure. Stiffer layer, i.e., pavement surface layer, can be indetified by the parameter of high frequency and phase velocity range; and vice versa. ISASW technique is also able to comprehensively investigate the elastic modulus of subgrade layer in exisiting pavement without any destruction. A good agreement of elastic modulus of subgrade layer from ISASW and FWD test was also pres ented.

Notes on fk analysis of surface waves

The dispersive nature of Rayleigh waves is the basis of many identification procedures to infer the site stiffness profile from surface measurements. This article presents some important aspects related to fk analysis of seismic gathers, which is one of the procedures commonly used to obtain the experimental dispersion curve, focusing on the great influence that the scale of the survey has in the global process. At a short distance from the source, the seismic signal contains information related to different modes of propagation in a composite form. As the wave travels away, the different modal group velocities produce a separation of such information. Hence only if the testing array is sufficiently long is it possible to assume mode separation and to invert the dispersion curve for modal velocities. Otherwise the effects of mode superposition need to be carefully accounted for. To clarify this concept, the results of some numerical simulations are reported, together with some experimental results.

Band gaps in the spectra of terahertz surface plasmons on metallic diffraction gratings

The effect of the appearance of band gaps in the energy spectra of terahertz surface plasmons has been experimentally observed and investigated. The band gaps are formed due to the interference interaction of the surface plasmons excited by pulsed terahertz radiation on metallic diffraction gratings. It has been shown that the experimental dispersion curves of terahertz plasmons are in good agreement with the dispersion curves obtained in the numerical simulation.

Influence of the anisotropy on zero-group velocity Lamb modes

Guided waves in a free isotropic plate (symmetric S(n) and antisymmetric A(n) Lamb modes) exhibit a resonant behavior at frequencies where their group velocity vanishes while their phase velocity remains finite. Previous studies of this phenomenon were limited to isotropic materials. In this paper, the optical generation and detection of these zero-group velocity (ZGV) Lamb modes in an anisotropic plate is investigated. With a circular laser source, multiple local resonances were observed on a silicon wafer. Experiments performed with a line source demonstrated that the frequency and the amplitude of these resonances depend on the line orientation. A comparison between experimental and theoretical dispersion curves for waves propagating along the [100] and [110] directions of the silicon crystal verified that these resonances occur at the minimum frequency of the S(1) and A(2) Lamb modes. Simulations indicated that it is possible to deduce the three elastic constants of the plate material with good accuracy from these measurements.

Ab initiocalculation of phonons for bulk TiC andTiC(001)(1×1)

We present an ab initio pseudopotential study, within the local density functional approximation, of the structural and elastic properties of rock-salt TiC. The calculated structural and elastic properties of TiC are in good agreement with reported experimental values. Using the density-functional perturbation theory, the phonon spectrum and density of states are calculated. Good agreement has been found between the calculated and reported experimental dispersion curves. Following these bulk properties, we have made theoretical investigations of the atomic geometry and lattice dynamics of the $\text{TiC}(001)(1\ifmmode\times\else\texttimes\fi{}1)$ surface. The calculated surface structural parameters compare very well with available experimental values. Using our calculated surface phonon spectrum, we provide a detailed analysis of available experimental data from electron energy-loss spectroscopy.

Probing the membrane potential of living cells by dielectric spectroscopy

In this paper we demonstrate a quantitative way to measure the membrane potential of live cells by dielectric spectroscopy. We also show that the values of the membrane potential obtained using our technique are in good agreement with those obtained using traditional methods—voltage-sensitive dyes. The membrane potential is determined by fitting the experimental dielectric dispersion curves with the dispersion curves obtained from a theoretical model. Variations in the membrane potential were induced by modifying the concentration of potassium chloride in the solution of the cell suspension in the presence of valinomycin. For exemplification of the method, E. coli was chosen for our experiments.

A Remote, Non-destructive Laser Ultrasonic Material Evaluation System with Simplified Optical Fibre Interferometer Detection

An optical non-contact ultrasonic testing system is presented. It uses broadband surface acoustic wave impulses generated with a cylindrical lens focused laser line source. The detection of the ultrasound is achieved by a simple and yet effective design of optical fibre interferometer which provides good sensitivity and manoeuvrability. The effectiveness of the fibre interferometer is demonstrated by accurately measuring the broadband surface waves on various common metal structures. The measurement system’s ability for surface material evaluation is also demonstrated from fitting experimental surface wave dispersion curves with theoretical simulations. This measurement system can test small localised areas and miniature samples that were previously difficult to examine.

Vibrational properties of graphene and graphene layers

AbstractThe phonon dispersions of graphene and graphene layers are theoretically investigated within fifth‐nearest‐neighbor force‐constant approach. Based on their symmetry groups, the number of Raman‐ and infrared‐active modes at the Γ point is given. Interatomic force constants are recalculated by fitting them to experimental phonon energy dispersion curves. Wavenumbers of optically active modes are presented as a function of number of layers (n). Our calculated results reproduce well the experimental data of G peak for graphene (1587 cm−1) and graphite (1581.6 cm−1) and clearly give the relation that ωG = 1581.6 + 11/(1 + n1.6). Copyright © 2009 John Wiley & Sons, Ltd.

Large vacuum Rabi splitting in ZnO-based hybrid microcavities observed at room temperature

Wide-band gap ZnO semiconductors are attractive materials for the investigation of microcavity exciton polaritons due to the large exciton binding energy and oscillator strength. We report the growth and characterization of bulk ZnO-based hybrid microcavity. The phenomenon of strong exciton-photon coupling at room temperature has been observed in the ZnO-based hybrid microcavity structure, which consists of 30 pair epitaxially grown AlN/AlGaN distributed Bragg reflector (DBR) on the bottom side of the 3/2λ thick ZnO cavity and 9 pair SiO2/HfO2 DBR as the top mirror. The cavity quality factor is about 221. The experimental results show good agreement with theoretically calculated exciton-polariton dispersion curves based on transfer matrix method. From the theoretical and experimental exciton-polariton dispersion curves with two different cavity-exciton detuning values, the large vacuum Rabi splitting is estimated to be about 58 meV in the ZnO-based hybrid microcavity.

Application of the Coupled Local Minimizers Method to the Optimization Problem in the Spectral Analysis of Surface Waves Method

The spectral analysis of surface waves (SASW) method aims to determine the small strain dynamic soil characteristics of shallow soil layers. The method involves an in situ experiment, the determination of an experimental dispersion curve, and the solution of an inverse problem, formulated as a nonlinear least squares problem. The latter is usually solved with a gradient-based local optimization method, which converges fast, but does not guarantee to find the global minimum of the objective function. The method of coupled local minimizers (CLM) combines the advantage of gradient-based local algorithms with the global approach of genetic algorithms. A cooperative search mechanism is set up by simultaneously performing a number of local optimization runs that are coupled by pairs of synchronization constraints. A synthetic example with two design variables (the shear wave velocity of two top layers of a layered half-space consisting of three layers on a half-space), demonstrates that the CLM method succeeds in finding the global minimum of an objective function with multiple minima and can successfully be used to solve the inverse problem in the SASW method. This is further illustrated by a complete inversion of the shear wave velocity profile accounting for seven design variables (the thickness and shear wave velocity of the three layers and the shear wave velocity of the underlying half-space). The inversion algorithm based on the CLM method is subsequently applied to invert the experimental dispersion curve derived from in situ data collected at a test site in Saluggia, Italy, consisting mainly of alluvial sediments. Up to a depth of about 25 m, the results show a reasonably good correspondence with crosshole test results.

Dispersion of plate acoustic waves in periodically poled lithium niobate.

The phase and group velocity dispersion of the plate acoustic waves (PAWs) in ZX-cut periodically poled lithium niobate (PPLN) wafer is calculated theoretically and verified experimentally. The dispersion curves of eight lowest PAW modes are calculated with the help of the finite element method. The PAWs in PPLN have some peculiarities in comparison with the case of a single crystal waveguide. First, some PAW modes may reflect out of the multidomain structure, and so a band gap may occur in the PAW spectrum. For example, a zero antisymmetric mode A0 has 0.2-MHz-wide band gap at frequency where its wavelength is equal to the period of a domain pattern. Second effect includes a variation of a cutoff frequency of PAW. The experimental dispersion curves are in agreement with calculations. The phononic band gap of A0 mode and the cutoff frequency shift of first antisymmetric mode A1 are confirmed by our experiments. The group velocity is calculated from the experimental phase-velocity dispersion curves. The calculated and measured group velocities are consistent. It is shown that the group velocity of A0 mode approaches zero within the band gap.

Dielectric Cytometry with Three-Dimensional Cellular Modeling

We have developed what we believe is an efficient method to determine the electric parameters (the specific membrane capacitance Cm and the cytoplasm conductivity κi) of cells from their dielectric dispersion. First, a limited number of dispersion curves are numerically calculated for a three-dimensional cell model by changing Cm and κi, and their amplitudes Δɛ and relaxation times τ are determined by assuming a Cole-Cole function. Second, regression formulas are obtained from the values of Δɛ and τ and then used for the determination of Cm and κi from the experimental Δɛ and τ. This method was applied to the dielectric dispersion measured for rabbit erythrocytes (discocytes and echinocytes) and human erythrocytes (normocytes), and provided reasonable Cm and κi of the erythrocytes and excellent agreement between the theoretical and experimental dispersion curves.

Potential Phase Unwrapping Errors Associated with SASW Measurements at Soft-Over-Stiff Sites

Abstract Results from simulations of spectral-analysis-of-surface-waves (SASW) measurements are presented for the common geotechnical condition of soft surficial soils overlying a stiffer half-space. Several recent experimental and numerical studies have demonstrated the dominance of higher-mode surface wave propagation at low frequencies for profile conditions where strong, shallow contrasts in elastic properties exist. This transition to higher-mode propagation has proven problematic for methods utilizing a fundamental-mode forward model in the inversion procedure, resulting in overprediction of the shear wave velocity (VS) profile. The objective of this study is to investigate the effectiveness of the SASW methodology, which uses an effective-velocity forward model, in dealing with the soft-over-stiff profile condition. Specifically, this study focuses on the phase unwrapping procedure used in the SASW method. Nine VS profiles were simulated in this study, representing different conditions of VS contrast and depth to the stiffer layer. The results show that in some cases the phase unwrapping procedure produces an experimental dispersion curve that is inconsistent with both the fundamental mode and the true effective-velocity dispersion curve for the profile. The resulting VS profile is substantially under-predicted. Experimental results from measurements at a soft-over-stiff site are presented that support the findings from the simulated measurements.

Determination of dispersive phase velocities by complex seismic trace analysis of surface waves (CASW)

A method for deriving experimental dispersion curves of surface waves from active source recordings is presented. The method is based on the complex seismic trace analysis of surface waves (CASW) and is applicable when only two receivers are available. Reliable phase velocities are obtained when keeping the geophone interval smaller than one λ, allowing both a velocity structure as local as possible to be derived and to avoid long geophone spreads which are difficult to handle in urban areas. A large number of velocity estimates for each frequency can be estimated, even when using only two sensors, allowing statistical validation of the results, and providing a statistically defined uncertainty interval to be used in the dispersion curve inversion. The method is tested using synthetic seismograms and applied to real-world data, showing that it provides reliable estimates of apparent phase velocities. Although a final conclusion cannot yet be drawn, its application to observed data suggests it has the potential to be a useful method for distinguishing different modes.

Inversion of multimode Rayleigh waves in the presence of a low-velocity layer: numerical and laboratory study

SUMMARY The dispersion and the surface displacement as a function of frequency of multiple modes guided waves in stratified media including a low-velocity layer are studied by numerical simulation and experiment. A method is developed to determine the thickness and the shear wave velocity of individual layers. First, the modal analysis of Rayleigh wave is investigated numerically for three layered media. Then, ultrasonic surface measurements are performed for three specimens: Steel half-space, Lucite/Steel half-space and Aluminum/Lucite/Steel half-space. The Characteristics of the dispersion curves are analyzed using the frequency–wavenumber method. The non-dispersive Rayleigh wave is obtained for the first simple specimen. The dispersion curves for two modes are obtained for the second specimen with a low-velocity layer on a fast substrate. The dispersion curves for the third specimen containing a low-velocity layer are apparently discontinuous and correspond to different mode branches. Further analysis demonstrates that the apparent discontinuity is caused by a rapid change of mode excitation with frequency at the surface. While one mode vanishes from the recorded wavefield, the other appears. This indicates that the surface displacements of the modes should be also accounted for in the inverse problem, especially in stratified media with a low-velocity layer. Finally, shear wave velocity profiles are inverted based on the experimental (maybe discontinuous) dispersion curves of fundamental or/and higher modes using a Genetic Algorithm(GA). Besides the dispersion characteristics of each mode, the surface displacement distribution is also taken into account for the case of a low-velocity layer, and as a result, the mode-misidentification is avoided.

Air coupled Lamb waves evaluation of the long-term thermo-oxidative ageing of carbon-epoxy plates

Thermo-oxidative ageing of carbon-epoxy plates has been done for up to 3500 h at two temperatures. Non-destructive evaluation by means of non-contact ultrasonic methods has been tested to characterize the aged plates. Experimental results obtained using Lamb waves propagation in the plates are presented here. Experimental and theoretical dispersion curves are compared. It is shown that the phase velocity of the A 0 and S 0 Lamb modes is decreasing when ageing duration increases. Assuming the plate to be homogeneous and orthotropic, we demonstrate that this phenomenon is related to an important decrease of the C 55 elastic parameter of the plate.

Experiment and Inversion Studies on Rayleigh Wave Considering Higher Modes

AbstractThe dispersive characteristics of the Rayleigh waves propagating in the layered media are investigated experimentally by ultrasonic detection testing, especially in the presence of a low‐velocity layer. Ultrasonic surface detections are implemented for two layered specimens: Lucite/Steel half‐space and Aluminum/Lucite/Steel half‐space. Characteristics of the multimode dispersion curves are analyzed using the frequency‐wavenumber analysis method. The dispersion curves of the first and second modes are obtained for the first specimen of a slow layer on a fast substrate. The dispersion curves for the second specimen containing a low‐velocity mid‐layer are discontinuous and correspond to different mode branches in different frequency ranges due to the mode jumping. Further analysis based on the experimental data demonstrates that the mode jumping is caused by the different surface displacement distribution with frequency for each mode. This indicates that surface displacement distributions of the modes should be also considered for the inversion problems, especially in the stratified media containing a low‐velocity mid‐layer. Parameters of two specimens are inversed by Genetic Algorithm (GA) using the experimental dispersion curves of surface waves. The displacement distributions of each mode are considered in inversion in the presence of a low‐velocity layer. Mode‐misidentification is avoided by the inversion method presented in this paper and satisfied results are obtained.

A New Inversion Procedure for Spectral Analysis of Surface Waves Using a Genetic Algorithm

A new inversion procedure for spectral analysis of surface waves (SASW) using a genetic algorithm (GA) is presented. The inversion process proposed in this study starts by running a forward solution for the Rayleigh dispersion equation, with sets of random inputs, to find the theoretical phase velocities. Then, it continues by finding new and better sets of inputs through processes that mimic natural mating, selection, and mutation in each generation. The goal of the GA is to find the best match between the theoretical and the experimental dispersion curves. Therefore, with each new generation there is a better agreement between the calculated output theoretical dispersion curve and the input experimental dispersion curve. To start the procedure, two options are available, either requesting the GA-based optimization process to obtain shear-wave velocities and thicknesses for each layer, or providing the thicknesses and requesting the optimization process to obtain the best set of shear- wave velocities. The GA part of the procedure is fast, stable, and accurate, with several advantages compared to the traditional methods. The strength and accuracy of the proposed procedure are presented through two example problems. We show that (1) the inversion process using a GA results in a good agreement between the theoretical and experimental dispersion curves, and (2) the shear-wave velocity pro- files obtained from the approach presented in this study and a downhole seismic survey show a good level of agreement.