Calculated Dispersion Curves Research Articles

Calculation of wave dispersion curves in multilayered composites using semi-analytical finite element method

The enormous potential of Guided waves have a significant use for non-destructive evaluation(NDE) and structural health monitoring(SHM). It is common to use different solution approaches to predict dispersion curves depending on the material type, isotropic, transversely isotropic, or orthotropic, of the medium in which the wave propagates, shape of the waveguide, etc. Inability to model waveguides of arbitrary cross-section by existing matrix methods has led to development of Semi-Analytical Finite Element(SAFE) Method. In this study, rapid and accurate prediction of the propagation characteristics for guided waves in a wide range of structures has been performed by implementation of SAFE method. Damped and undamped waveguides of different shapes can be modelled. Wave propagation characteristics in both isotropic and anisotropic composite structures can also be studied. To benchmark the solution, a case study using Transfer Matrix Method (TMM) for composite plate has been evaluated. It was found that the element discretizaton plays an important role in accurate prediction of modes in SAFE method, neglecting which leads to loss of higher order modes.

Study of Abnormal Group Velocities in Flexural Metamaterials

Generally, it has been known that the optical branch of a simple one-dimensional periodic structure has a negative group velocity at the first Brillouin zone due to the band-folding effect. However, the optical branch of the flexural wave in one-dimensional periodic structure doesn’t always have negative group velocity. The problem is that the condition whether the group velocity of the flexural optical branch is negative, positive or positive-negative has not been studied yet. In consequence, who try to achieve negative group velocity has suffered from trial-error process without an analytic guideline. In this paper, the analytic investigation for this abnormal behavior is carried out. In particular, we discovered that the group velocity of the optical branch in flexural metamaterials is determined by a simple condition expressed in terms of a stiffness ratio and inertia ratio of the metamaterial. To derive the analytic condition, an extended mass-spring system is used to calculate the wave dispersion relationship in flexural metamaterials. For the validation, various numerical simulations are carried out, including a dispersion curve calculation and three-dimensional wave simulation. The results studied in this paper are expected to provide new guidelines in designing flexural metamaterials to have desired wave dispersion curves.

Селективное возбуждение упругих волн в композитах

This study analyzes the effect of various parameters of the piezoelectric transducer on the wave fields generated in the composite plate. A semi-analytical approach based on the application of the Fourier transform, integration by residues and the stationary phase method is used to calculate dispersion curves and wave fields in a wide frequency range. This model allowed us to calculate the displacement fields excited in the anisotropic plate, as well as to distinguish and analyze the contribution of each wave mode to the resulting wave field. The excited fields were calculated and analyzed over a wide frequency range. Another objective of the study was to obtain the information about the shapes and positioning of multiple piezoelectric elements, which facilitate the excitation of directed waves and individual Lamb wave modes. A technique for the selection of parameters and the positioning of piezoelectric actuators required for the wave excitation was developed. It was applied and successfully tested for a combination of several ring-shaped actuators. The relations between the stress amplitudes specified on the surfaces of all actuators from the combination were determined and allowed to suppress certain waves in a multi-layered composite host-structure. It was shown that by varying the voltage applied to the piezoelectric rings, it is possible to suppress or amplify individual waves without changing their size.

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.

Site characterization using passive seismic techniques: A case of Suez city, Egypt

This article introduces a site investigation study using quick and low-cost passive seismic techniques at Suez city which located in the northeastern part of Egypt. The Spatial Auto Correlation (SPAC) method is applied, as well as the newly developed Centerless Circular Array (CCA) method for estimating the shear wave velocity (Vs) structures of the subsurface layers using microtremor array data. The Horizontal/Vertical Spectral Ratio (HVSR) approach is employed in determination of predominant frequency (f0) of a site and its equivalent peak amplitude of ground motion (A0) using a single station microtremor measurements.In this study, microtremor array measurements have been carried out at five sites distributed in Suez city. In order to cover a wide frequency band, different array sizes are carried out at each observation site. Measurements are made using high performance accelerometers with a sampling rate 100 sample per second. In both SPAC and CCA methods, only the vertical component of microtremor data is considered in the analysis. The analysis includes two main stages, i.e., calculation of surface wave dispersion curves and inversion process to infer the Vs structure of the ground. The obtained dispersion curves cover frequency band (2.0–21.0 Hz) and show a good fitting between the observed and the calculated ones at all measured sites, proving the reliability of the inversion process performed in this work. In HVSR analysis, the E-W, N-S, and vertical components of microtremors are considered, and the ratio between the horizontal and the vertical components spectra is calculated, then the spectral ratio curves are produced. The predominant frequency (f0) and the peak amplitude (A0) of HVSR curve are reported for each site of observation. The inferred Vs profiles are used for calculating the average velocity value of shear wave up to 30 m depth (AVS30) which in turn employed in site classification at the investigated area.The results demonstrate that the parameter AVS30 varies between 248 m/s and 310 m/s in Suez city. The created site classification incorporates only one class (Class D), appearing no significant variation in the characteristics of the superficial and shallow soils in Suez city. The site predominant frequency (f0) ranges between 0.35 Hz and 5.0 Hz with relevant amplification (A0) between 1.6 and 4.2.These outputs represent a crucial site response model for future seismic hazard assessment and risk decrease studies in Suez area which is currently witnesses large investments and rapid land use planning.

Near-surface Shear Velocity Structure Estimation using Ground-roll in Moran Area, Central Upper Assam Basin, India

Abstract The frequency dependent characteristics of Rayleigh-wave, which is considered to be noise during body-wave prospecting, can be utilized to infer near surface elastic properties. To generate the near surface VS profiles, initially spectral analysis of surface waves (SASW) was used, which has now been replaced by more sophisticated multi-channel analysis of surface waves (MASW). In the present study, MASW for impulsive source is applied to the seismic (impulsive source) datasets acquired in the Moran area of the central part of upper Assam basin to estimate the near-surface S-wave velocity (Vs) structure with the objective of its application to static correction during S-wave reflection data processing, and geotechnical and environmental studies in the area. Multichannel surface waves are extracted from conventional seismic record. The multichannel analysis includes construction of dispersion curves from observed Rayleigh-waves, and inversion of VS profile from calculated dispersion curves. The near surface 1D VS profiles, derived from the extracted ground roll vary from 200 m/sec (near the surface) to about 450 m/sec at 40m depth, and provides a good estimation of vertical shear velocity structure in the area. The 2D near surface shear velocity structure (VS) is generated by horizontal interpolation of individual vertical profiles. The results are in agreement with the available three component low velocity layer (3C-LVL) data.

Detection of a fracture zone using microtremor array measurement

We have conducted microtremor array measurements to estimate shallow S-wave velocity ([Formula: see text]) structures at two sites (the 921 Earthquake Museum of Taiwan and the Taiwan Provincial Consultative Council) located near surface ruptures of the Chelungpu Fault. Ten stations, consisting of three different-aperture triangles and a central station, are adopted for each array deployment. Using the array data, we calculate dispersion curves of Rayleigh waves using the frequency-wavenumber spectrum method and then estimate [Formula: see text] structures by the surface-wave inversion technique. The obtained 2D [Formula: see text] profiles could clearly show compressive and flexural deformation structures with the surface ruptures located at relatively weak (low [Formula: see text]) zones. This indicates compressive buckling as the most likely mechanism for surface rupturing along these low [Formula: see text] zones. Importantly, this study successfully depicts strata disturbances in a fault fracture zone using microtremor array measurements and forward numerical modeling of trishear fault-propagation folds.

Dispersion engineering of hyperbolic plasmons in bilayer 2D materials.

Recent progress on anisotropic 2D materials brings new technologies for directional guidance of hyperbolic plasmons. Here, we investigate the plasmonic modes in twisted bilayer 2D materials (e.g., black phosphorous). Calculated dispersion curves show that two hyperbolas split as the twisted angle increases. The topological transition from closed ellipses to open hyperbolas is achieved by varying the frequency, indicating switching between highly directional and omnidirectional plasmons. These findings will provide potential applications of anisotropic 2D materials in the design of tunable field effect transistors and waveguides.

Evaluation of Effective Elastic Properties of Nitride NWs/Polymer Composite Materials Using Laser-Generated Surface Acoustic Waves

In this paper we demonstrate a high potential of transient grating method to study the behavior of surface acoustic waves in nanowires-based composite structures. The investigation of dispersion curves is done by adjusting the calculated dispersion curves to the experimental results. The wave propagation is simulated using the explicit integral and asymptotic representations for laser-generated surface acoustic waves in layered anisotropic waveguides. The analysis of the behavior permits to determine all elastic constants and effective elastic moduli of constituent materials, which is important both for technological applications of these materials and for basic scientific studies of their physical properties.

Nuanced superconductivity in endohedral gallide Mo8Ga41

We report on synthesis and characterization of gallide cluster based Mo8Ga41 superconductor. Transport and magnetization measurements confirm the superconducting transition temperature to be 9.8 K. The upper critical field (Hc2), lower critical field (Hc1), Ginzburg–Landau coherence length ( ξGL) and penetration depth(λ) are estimated to be 11.8 T, 150 G, 5.28 nm, 148 nm respectively. The electronic band structure, density of states and phonon dispersion curve calculations are obtained by using Density Functional Theory. The core level x-ray Photoelectron Spectroscopy (XPS) reveals the binding energy information of the constituting elements Mo and Ga in Mo8Ga41. The valence band spectra from XPS are in good agreement with calculated density of states (DOS). The zero field critical current density (Jc) at T = 2 K is ∼3 × 105 A/cm2 which is indicative of efficient flux pinning in the as grown compound. About two fold enhancement in critical current density with application of external pressure (1.1 GPa) is observed with marginal decrease in transition temperature. The fitting of current density to double exponential model confirms possibility of two gap superconductivity in Mo8Ga41.

Model-based inversion of ultrasonic guided waves for cortical bone properties

Axial transmission ultrasonography, which uses a set of transmitting and receiving probes placed on the same waveguide’s surface, shows the potential clinical application for cortical bone quality assessment. In this work, a model-based parameter sweep inversion approach has been developed to estimate the thickness and elastic velocities of the cortex from the dispersive axially-transmitted snapshots. The inversion algorithm is formulated in the frequency-phase velocity (f-c) domain. To solve the inverse problem, i.e., to extract bone properties from ultrasound data, a forward modeling has been developed to simulate the f-c dispersion curves given a bone model. A semi-analytical finite element (SAFE) method is used to compute the dispersion curves for a complex structure of a cortical bone plate coupled with overlying soft tissues. A parameter sweep is used to seek within a range of values an optimized solution with the least misfit. The proposed method optimizes the mismatch between the measured and theoretically calculated dispersion curves with a least-square constraint. Numerical and in-vivo experimental data examples are presented to illustrate the technique’s performance.

High‐Frequency (>2 Hz) Ambient Seismic Noise on High‐Melt Glaciers: Green's Function Estimation and Source Characterization

Using ambient noise to characterize subsurface structures has revolutionized solid earth seismology. In glacial applications, this technique could provide valuable information about ice thickness and bed properties, which to date are deduced from laborious and/or expensive active source geophysics or deep drilling. Despite challenging conditions such as minimal scattering and changing sources, we show that stacks of cross‐correlation functions of several hours of ambient seismic noise can converge towards Green's functions under favorable conditions. These contain the sought‐after information about subsurface seismic velocities and ice thickness. Applying this technique to two Alpine glaciers in Switzerland, we calculate signal‐to‐noise ratios of noise correlation functions. Faster Green's functions convergence during elevated ambient noise levels suggests that increased surface melt promotes spatially homogeneous excitation of noise sources. With the help of Green's functions amplitude asymmetry as well as standard beamforming, we locate dominant noise sources. In combination with spectrograms, glacier surface velocities from GPS and proglacial water discharge measurements, we find glacier noise in the range from 2 to 8 Hz to be a combination of tremor induced by flowing water, icequakes, and anthropogenic sources. We finally calculate dispersion curves from the cross‐correlation functions to arrive at an estimate of the ice thickness. In combination with H/V spectral ratios, the method shown here allows sampling the depth and the properties of the glacier bed by deploying only two seismometers for several hours. Ambient noise correlations could therefore be a valuable ingredient for studies of glacier and ice sheet beds.

Using the Partial Wave Method for Wave Structure Calculation and the Conceptual Interpretation of Elastodynamic Guided Waves

The partial-wave method takes advantage of the Christoffel equation’s generality to represent waves within a waveguide. More specifically, the partial-wave method is well known for its usefulness when calculating dispersion curves for multilayered and/or anisotropic plates. That is, it is a vital component of the transfer-matrix method and the global-matrix method, which are used for dispersion curve calculation. The literature suggests that the method is also exceptionally useful for conceptual interpretation, but gives very few examples or instruction on how this can be done. In this paper, we expand on this topic of conceptual interpretation by addressing Rayleigh waves, Stoneley waves, shear horizontal waves, and Lamb waves. We demonstrate that all of these guided waves can be described using the partial-wave method, which establishes a common foundation on which many elastodynamic guided waves can be compared, translated, and interpreted. For Lamb waves specifically, we identify the characteristics of guided wave modes that have not been formally discussed in the literature. Additionally, we use what is demonstrated in the body of the paper to investigate the leaky characteristics of Lamb waves, which eventually leads to finding a correlation between oblique bulk wave propagation in the waveguide and the transmission amplitude ratios found in the literature.

Dispersion Analysis of Deep-Subwavelength-Decorated Metallic Surface Using Field-Network Joint Solution

Due to the abilities of remarkable field confinements and enhancements, plasmonic surfaces supporting spoof surface plasmon polaritons (SPPs) are important artificial structures with many potential applications. In this paper, we propose analytical derivation to the dispersion formulation of metallic surface with complicated subwavelength decorations using a field-network joint solution, which offers a new scheme to obtain the dispersion relations of plasmonic surfaces. Based on the proposed method, we could predict not only the dispersion relationship between the frequency and wavenumber but also the approximate near-field distribution on the plasmonic surface rapidly and accurately. As an example, we analyze a series of complex-decorated metallic plasmonic surfaces, with comparisons to the full-wave simulation and experiment. The analytical, numerical, and experimental results show that these plasmonic surfaces support electromagnetic surface modes that are similar to the SPPs at the optical frequency. Meanwhile, the calculated dispersion curve and field form have great matching to the simulation and measured results.

Dispersion Properties of Magnetostatic Surface Waves in a Ferrite Plate with Dissipation

Dispersion of forward and backward (dissipative) magnetostatic surface waves is analyzed in the geometry of a plane-parallel in-plane magnetized ferrite plate with dissipation. The results of calculation of dispersion curves and characteristics of the group velocity as a function of the real and imaginary parts of the wave number are presented. A limitation on the dispersion curves and the group velocity with respect to the maximum value of the wave number has been revealed and interpreted on the basis of the aperiodic propagation mode. Practical recommendations for lowering of this limitation are given.

A comparative study of different exchange-correlation functionals in understanding structural, electronic and thermoelectric properties of Fe2VAl and Fe2TiSn compounds

Fe2VAl and Fe2TiSn are full Heusler compounds with non-magnetic ground state. The two compounds are good thermoelectric materials. PBE and LDA (PW92) are the two most commonly used density functionals to study the Heusler compounds. Along with these two well studied exchange-correlation functionals, recently developed PBEsol, mBJ and SCAN functionals are employed to study the two compounds. Using the five functionals equilibrium lattice parameter and bulk modulus are calculated. Obtained values are compared with experimental reports wherever available. Electronic structure properties are studied by calculating dispersion curves, total and partial density of states. For Fe2VAl, band gap of 0.22 eV is obtained from the mBJ potential which is in reasonable agreement with experimental value while, for Fe2TiSn band gap of 0.68 eV is obtained. Fe2VAl is predicted to be semimetallic with different values of negative gaps from LDA, PBEsol, PBE and SCAN functionals. Whereas, Fe2TiSn is found to be semimetallic (semiconducting) from LDA, PBEsol (PBE,SCAN) functionals employed calculations. From the dispersion curve effective mass values are also computed to see the contribution to the Seebeck coefficient. In Fe2TiSn, a flat band is present along the Γ-X direction with calculated value of effective mass ∼36 more than the mass of electron. The improvements or inadequacies among the functionals in explaining the properties of full Heusler alloys for thermoelectric application are thus observed through this study.

Modeling of phase velocity and frequency spectrum of guided Lamb waves in piezoelectric-semiconductor multilayered structures made of AlAs and GaAs

Modeling of guided Lamb waves propagation in piezoelectric-semiconductor multilayered structures made of AlAs and GaAs is evaluated in this paper. Here, the Legendre polynomial method is used to calculate dispersion curves, frequency spectrum and field distributions of guided Lamb waves propagation modes in AlAs, GaAs, AlAs/GaAs and AlAs/GaAs/AlAs-1/2/1 structures. In fact, formulations are given for open-circuit surface. Consequently, the polynomial method is numerically stable according to the total number of layers and the frequency range. This analysis is meaningful for the applications of the piezoelectric-semiconductor multilayered structures made of AlAs and GaAs such as in novel acoustic devices.

Study of the first-principles correlation functional in the calculation of silicon phonon dispersion curves

In this study, the latest published first-principles Chachiyo correlation functional has been implemented to obtain the phonon dispersion relation of silicon. The calculations are based on local-density approximation (LDA) within the plane-wave pseudopotential method. We obtain good agreement and sufficient accuracy results compared with the experimental data and phonon dispersion curves from the typical Perdew–Zunger functional. As such, the Chachiyo formula used in phonon dispersion calculation has proven to be valid and therefore extends the use of LDA from relying on fitting to the first-principles correlation functional that provides a higher predictive power.

Global search for low-lying crystal structures using the artificial force induced reaction method: A case study on carbon

We propose an approach to perform the global search for low-lying crystal structures from first principles, by combining the artificial force induced reaction (AFIR) method and the periodic boundary conditions (PBCs). The AFIR method has been applied extensively to molecular systems to elucidate the mechanism of chemical reactions such as homogeneous catalysis. The present PBC/AFIR approach found 274 local minima for carbon crystals in the ${\mathrm{C}}_{8}$ unit cell described by the generalized gradient approximation--Perdew-Burke-Ernzerhof functional. Among many newly predicted structures, three low-lying structures, which exhibit somewhat higher energy compared with those previously predicted, such as $\mathrm{Cco}\ensuremath{-}{\mathrm{C}}_{8}$ ($Z$-carbon) and $M$-carbon, are further discussed with calculations of phonon and band dispersion curves. Furthermore, approaches to systematically explore two- or one-dimensional periodic structures are proposed and applied to the ${\mathrm{C}}_{8}$ unit cell with the slab model. These results suggest that the present approach is highly promising for predicting crystal structures.

Estimation of dispersion curves by combining Effective Elastic Constants and SAFE Method: A case study in a plate under stress

This paper presents an approach to calculate dispersion curves for homogeneous and isotropic plates subject to stress, via Semi-Analytical Finite Element and the Effective Elastic Constants, since stresses in the waveguide modify the phase and group velocities of the lamb waves. In the proposed methodology an isotropic specimen subjected to anisotropic loading is emulated by proposing an equivalent stress-free anisotropic specimen. This approximation facilitates determining the dispersion curves by using the well-studied numerical solution for the stress-free cases. The lamb wave in anisotropic materials can be studied by means of the Effective Elastic Constants, which reduces the complexity of the numerical implementation. Finally, numerical data available in literature were used to validate the proposed methodology, where it could be demonstrated its effectiveness as approximated method.