Dispersion Characteristics Of Waves Research Articles

Analytical solutions for dispersions and waveforms of acoustic logging in a cased hole

Acoustic logging is one of the most promising methods for the quantitative evaluation of cement bond conditions in cased holes. However, inefficient use of full-wave information yields unsatisfactory interpretation accuracy. Fundamentally, this is because the wavefield characteristics have not been thoroughly investigated under various cement bonding conditions. Thus, this study derives analytical solutions of wavefields for a single-cased-hole model and emphasizes the dispersion calculation algorithm. To solve the dispersion equation when solving for the poles of the propagating modes with real wavenumbers, we renormalize the Bessel function related to the borehole fluid by multiplying it with an attenuation factor. For leaky modes with complex wavenumbers, we develop a novel method to find local peaks of the matrix condition number (LPMCN) in the frequency domain to determine dispersion poles, avoiding the local optimization issues resulting from the traditional Gauss-Newton iteration method. Combining these two methods, we establish a fast and accurate workflow for evaluating the dispersion of all modes in cased holes using a relatively fast bisection method to manage the dispersion of the propagating modes and using the LPMCN method to derive the dispersion curves of leaky modes. Furthermore, all propagating modes are individually investigated in the monopole measurement by evaluating the residues of the real poles in a casing-free model. The analysis demonstrates that the first-order pseudo-Rayleigh wave (PR1) and inner Stoneley wave (ST1) are the two strongest modes. Finally, we focus on the waveforms and dispersion characteristics of the outer Stoneley wave (ST2) related to the fluid channel in the cement annulus. The results reveal that as the fluid thickness increases, the phase velocity of the ST2 mode decreases, and its amplitude increases. Therefore, the ST2 mode can potentially evaluate the thickness of the fluid channel in a cement annulus if an effective weak-signal-extraction method is used.

Influence of the Schottky Junction on the Propagation Characteristics of Shear Horizontal Waves in a Piezoelectric Semiconductor Semi-Infinite Medium

In this paper, a theoretical model of the propagation of a shear horizontal wave in a piezoelectric semiconductor semi-infinite medium is established using the optimized spectral method. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are derived with the consideration of biased electric fields. Then, considering the propagation of a shear horizontal wave in the piezoelectric semiconductor semi-infinite medium, two equivalent mathematical models are established. In the first mathematical model, the Schottky junction is theoretically treated as an electrically imperfect interface, and an interface characteristic length is utilized to describe the interface effect of the Schottky junction. To legitimately confirm the interface characteristic length, a second mathematical model is established, in which the Schottky junction is theoretically treated as an electrical gradient layer. Finally, the dispersion and attenuation curves of shear horizontal waves are numerically calculated using these two mathematical models to discuss the influence of the Schottky junction on the dispersion and attenuation characteristics of shear horizontal waves. Utilizing the equivalence of these two mathematical models and the above numerical results, the numerical value of the interface characteristic length is reliably legitimately confirmed; this value is independent of the thickness of the upper metal layer, the doping concentration of the lower n-type piezoelectric semiconductor substrate, and biasing electric fields. Only the biasing electric field parallel to the Schottky junction can provide an evident influence on the attenuation characteristics of shear horizontal waves and enhance the interface effect of the Schottky junction. Since the second mathematical model is also a validation of our previous mathematical model established through the state transfer equation method, some numerical results calculated using these two mathematical models are compared with those obtained using the previous method to verify the correctness and superiority of the research work presented in this paper. Since these two mathematical models can better calculate the dispersion and attenuation curves of high-frequency waves in micro- and nano-scale piezoelectric semiconductor materials, the establishment of mathematical models and the revelation of physical mechanisms are fundamental to the analysis and optimization of micro-scale resonators, energy harvesters, and amplifications.

On wave propagation in nanobeams

Wave propagation in Rayleigh nanobeams resting on nonlocal media is investigated in this paper. Small-scale structure-foundation problems are formulated according to a novel consistent nonlocal approach extending the special elastostatic analysis in Barretta et al. (2022). Nonlocal effects of the nanostructure are modelled according to a stress-driven integral law. External elasticity of the nano-foundation is instead described by a displacement-driven spatial convolution. The developed methodology leads to well-posed continuum problems, thus circumventing issues and applicative difficulties of the Eringen–Wieghardt nonlocal approach. Wave propagation in Rayleigh nanobeams interacting with nano-foundations is then analysed and dispersive features are analytically detected exploiting the novel consistent strategy. Closed form expressions of size-dependent dispersion relations are established and connection with outcomes available in literature is contributed. A general and well-posed methodology is thus provided to address wave propagation nanomechanical problems. Parametric studies are finally accomplished and discussed to show effects of length scale parameters on wave dispersion characteristics of small-scale systems of current interest in Nano-Engineering.

Node-based wave analysis method for the dynamic response and stiffness of long-span cable-stayed bridges

For dynamic analysis of long-span cable-stayed bridges (LCB) with high flexibility and long force transmission paths, wave analysis method offers unique advantages over modal analysis. However, conducting wave analysis for the entire LCB poses challenges due to the modeling complexity and the substantial computational cost associated with solving numerous wave equations. Therefore, a simple analytical approach for wave analysis of LCB is proposed, which entails the discretization of the entire bridge into waveguides and the subsequent recombination of the regularized local wave propagation models. The feasibility and strategy of solving the global propagation function using local double coordinate systems and specific node-based local wave propagation models are demonstrated. Additionally, based on the geometric and mechanical configuration of nodes in the LCB, local wave scattering and propagation models corresponding to the four standardized nodes types are proposed. A unified Node-Based Wave Analysis (NWA) method for LCB is developed, considering the viscoelastic behavior of cable-stayed beams according to the Kelvin-Voigt model to enhance structural realism. The reasonable damping coefficient in bridge is determined by means of theory and dynamic in situ test of three bridges. Finally, an extended case study is conducted on a typical two-pylon cable-stayed bridge, focusing on the impact of moving loads and material properties on wave characteristics. The results demonstrate the reliability of the proposed NWA method in predicting wave energy distribution, highlighting the suitability of wave analysis for dynamic analysis of LCB. In comparison to undamped structures, it has been found that the presence of damping results in a pair of additional flexural waves with a new dispersion relation in cable-stayed bridges. Furthermore, the study reveals the stiffness enhancement mechanism associated with wave dispersion characteristics in cable-stayed bridges.

Seismic wave dispersion and attenuation resulting from multiscale wave-induced fluid flow in partially saturated porous media

SUMMARY Sedimentary rocks are typical heterogeneous porous media induced by fluid patches and pore fabric. It is well acknowledged that the wave-induced fluid flow (WIFF) at different scales will cause seismic wave dispersion and attenuation in a wide frequency range. Consequently, modelling wave dispersion and attenuation due to multiscale WIFF is of significance for reservoir characterization from multiscale geophysical measurement and interpretation. In this study, the multiscale WIFF in partially saturated porous media, including global, 3-D mesoscopic and squirt flows, are investigated. And we derive the wave equations by introducing the Rayleigh's spherical bubble oscillation and the porous grain models into Santos poroelasticity theory. Numerical simulations demonstrate that the multiscale model can interpret the transition of rock states as frequency increases and capture the broad-band seismic wave dispersion and attenuation characteristics, which are directly associated with the heterogeneity scale. Besides, the multiscale model can be degraded to a single- or dual-scale model under specific parameters. We validate the proposed model with board-band experimental data of partially saturated sandstones, confirming its comprehensive characterization of velocity dispersion and attenuation over a wider range of frequencies. Moreover, the model successfully interprets the unrelaxed state of partially saturated rock at ultrasound frequencies.

Dispersion Characteristics of Low-Frequency Electron Waves in a Magnetoactive Plasma of Arbitrary Density

The article studies waves in a collisionless magnetoactive plasma with frequencies much lower than the electron cyclotron frequency at an arbitrary ratio between the electron plasma and cyclotron frequencies. A general dispersion relation is obtained for the wave frequency as a function of the wave vector and the ratio of the plasma frequency to the cyclotron frequency. This relation is a bicubic equation with respect to frequency. Based on this equation, the existence domains of various wave modes depending on the specified parameter, their group velocity, polarization, and energy density are studied. Special attention is paid to low-frequency whistler waves in a low-density plasma, since, among the propagating wave modes existing in the specified range of parameters, whistler waves have the highest refractive index and play an important role in theresonant interaction of waves and particles.

Dispersion Characteristics of Low-Frequency Electron Waves in a Magnetoactive Plasma of Arbitrary Density

Dispersion Characteristics of Low-Frequency Electron Waves in a Magnetoactive Plasma of Arbitrary Density

Dispersion Properties of Surface Waves Decaying in Red-Shifted and Blue-Shifted Gaps in Photonic Hypercrystals

The dispersion characteristics of surface waves for transverse electric and magnetic polarization modes of photonic hypercrystals (PHC) are theoretically explored. PHC are composed of a dielectric and hyperbolic metamaterial (HMM) with thin layers of both metal and dielectric surface waves that decay inside red-shifted gaps have a negative group velocity, whereas surface waves that decay inside traditional blue-shifted gaps have more typical characteristics. Curve plotting is used to elucidate on how these surface waves depend on several other structural properties such as filling factor, widths of HMM and dielectric, frequency range and angle of incidence etc.

Anisotropy and dispersion of elastic waves in periodically multilayered anisotropic media

The propagation characteristics of elastic waves in general periodically multilayered media formed by alternate arrangement of two or more arbitrarily-anisotropic materials are comprehensively studied. Combining with the state-space formalism for obtaining the wave solutions to the constituent layers, the Floquet-Bloch theorem for providing the periodic relations between neighboring unit cells, the method of reverberation-ray matrix (MRRM) is employed to derive the general dispersion equations of the periodically multilayered anisotropic media. By solving the dispersion equations in cases of all possible sorts of wavenumber components, the complete anisotropic and dispersion characteristics of elastic waves can be provided. By numerical examples, the slowness and the phase velocity curves are provided to summarize the innovative anisotropic characteristics of elastic waves in three coordinate planes. The effects of the anisotropic parameters on the slowness/phase velocity curves have also been discussed. Moreover, all kinds of dispersion curves including the frequency-related and phase velocity-related curves along the directions perpendicular, parallel, and oblique to the layering are provided to reflect the general dispersion characteristics of elastic waves from various viewpoints. It is found that the innovative anisotropy characteristics of elastic waves in the periodically multilayered anisotropic media include that the slowness curves have periodicity in the thickness direction and the least positive period decreases with the increasing of frequency. As the frequency becomes big enough, the slowness/phase velocity curves show interactions between the modes within the overlapping neighboring periods. The common dispersion characteristics of elastic waves along various directions include the symmetry of wavenumber, the asymptotic of the wavelength and the phase velocity curves to the frequency lines corresponding to zero wavenumber, as well as the cutoff property of the phase velocities of the lowest three basis modes. The waves in oblique directions are special in that the mode transition and repulsion due to the zone folding effect of periodicity along thickness as well as the cutoff property of higher-than-third-order overtones along layering are simultaneously in effective.

Seismic wavefield characteristics in translational and rotational components for isolated velocity-anomaly bodies in two-dimensional shallow media

With the increasing utilization of underground space, detecting shallow isolated velocity-anomaly bodies such as karst and boulder has become a critical challenge in engineering seismic exploration. This study employs the finite-difference algorithm to investigate two-dimensional seismic wavefields in translational (X and Z) and rotational (Y) components for homogeneous half-space and layered medium models that incorporate low-velocity and high-velocity spheres. The dispersion characteristics analyses of Rayleigh wave for these models are conducted to compare the wavefield differences caused by shallow velocity-anomaly bodies using the methods including Multichannel Analysis of Surface Wave, Horizontal-to-Vertical Spectral Ratio (HVSR), and Rotational to Vertical-and-Horizontal Spectral Ratio (RVHSR). Results demonstrate that the velocity-anomaly bodies cause noticeable influences on kinematics and dynamics dispersion characteristics of Rayleigh waves, which can be visually depicted on the rotational Y component. It can be more effective to accurately delineate the property and spatial distribution of underground velocity-anomaly bodies by combining the seismic response of translational and rotational components.

Experimental investigation on interfacial defect detection for SCCS with conventional and novel contact NDT techniques

In order to ensure the mechanical performance and structural safety of steel–concrete composite structures (SCCS), advanced nondestructive testing (NDT) technique for bonding status at steel–concrete interfaces needs to be developed. In this study, the feasibility of multichannel analysis of surface waves (MASW)-based interfacial debonding detection is validated using the contact sensors array. Herein, the multichannel sensor arrays are composed of piezoceramic lead zirconate titanate patches and high-frequency acceleration meters, respectively. For comparison, the impact-response (IR) method and impact-transmission (IT) method are performed utilizing a force hammer and high-frequency acceleration meters, and corresponding damage imaging algorithms are developed. The applicability of ultrasonic computed tomography (CT) scanning test, scanning impact echo (IE) method, ultrasonic tomography (UT) technique on interfacial debonding detection is further discussed in depth. Research findings indicate that the developed contact MASW measurement can fully capture the variation of dispersion characteristics of surface waves induced by debonding defects in SCCS. The developed IR and IT methods are suitable for detecting interfacial debondings in different dimensions. Besides, the damage nephogram resolution of IR is higher than that of the IT method. In addition, the practicability of traditional ultrasonic CT scanning tests, scanning IE method, and UT techniques using commercial equipment is investigated. Experimental observations show that classical NDT testing techniques are incapable of effectively identifying the existence of interfacial damage and are unsuitable for NDT tests on SCCS. The research findings in this study clearly exhibit the precision and limitation of various contact NDT techniques and lay a solid foundation for interfacial debonding detection in practical SCCS.

Effects of surface topography and subsurface structural irregularities of river embankments on Rayleigh wave propagation

A numerical investigation of surface wave propagation in the surface wave exploration of river embankments is implemented using 3D shallow soil models with different subsurface shapes and S-wave velocities. The focus is on the effects of surface and subsurface irregularities on the propagation and dispersion characteristics of Rayleigh waves generated by a surface source and observed at points along the crest of the embankment. Rayleigh wave dispersion curves observed along the embankment crest are found to be contaminated by reflected waves, with the amount of contamination affected more by the position of the velocity boundary at the bottom edge of the embankment than the surface topography. When the velocity boundary is close to the ground surface, especially at the toe of the slope, the effect of reflected waves is sufficiently large to generate biases in the phase velocity estimates.Graphical

Observations of Love Wave Dispersion Properties Using Seismometers and Component Strainmeters

With amplitude ratio of two different types of ground motion, the information of phase velocity could be reflected in the frequency-dependent in the assumption of plane-wave propagation. In this paper, we test the possibility of determining local Love waves dispersion properties using transverse velocity and strain measurement. With the strain seismic wave recording of the four-component borehole strainmeters built at the Balun seismic station in Xinjiang, China., we estimated the Love wave phase velocities using amplitude ratios between transverse velocity and shear strain components. The results show the possibility that we could recover general Love wave dispersion characteristics that conformed to the realistic local structure at periods ranging from 20-120 s.

An inversion method for evaluating ballastless track degradation based on multi-channel analysis of surface wave

Due to the heterogeneous properties of constituent materials, traditional Multi-channel analysis of surface wave (MASW) method is unsuitable for evaluating ballastless track as surface waves exhibit different dispersion patterns. To overcome this limitation, firstly, the implementation process of MASW was introduced, and the phase shift method was employed to perform dispersion analysis of multi-channel surface wave signals. Secondly, a wave field solution model of ballastless track was established using the time-domain finite-difference method. Subsequently, the stiffness matrix method was improved to account for the heterogeneous properties of the constituent materials and to calculate the theoretical surface wave dispersion curve of ballastless track, followed by the analysis of surface wave dispersion characteristics in ballastless track and the proposal of an inversion method. Finally, the optimal excitation central frequency and receivers’ deployment were analyzed in the MASW method, and the inversion analysis of ballastless track degradation were conducted. Results shown that the surface wave dispersion curve is more sensitive to CA mortar degradation at low frequencies and concrete slab degradation at high frequencies. Appropriate excitation central frequency and receivers’ deployment are essential for accurately extracting the surface wave dispersion curve from the dispersion energy of ballastless tracks. The inversion method proposed in this study provides a more accurate evaluation of ballastless track degradation compared to assuming ballastless track as a homogeneous structure during inversion analysis.

Joint inversion of formation radial shear-velocity profiles by dipole acoustic logging while drilling

Formation properties near a borehole are frequently altered by mechanical damage from drilling, leading to variations of formation elastic velocities in the radial direction. Inversions of radial shear profiles are necessary for a real-time evaluation of the drilling conditions. In this study, we investigate acoustic wave propagation in a logging-while-drilling (LWD) model excited by a dipole transducer in cylindrically layered media. It is revealed that the dispersion characteristics of the dipole waves of the LWD are sensitive to the radial formation velocity variation. Accordingly, we develop a joint inversion method that evaluates radial shear-velocity profiles using the dipole modes of the first and second orders. The propagation of these two modes is strongly influenced by formation alterations, but the inversion results obtained using a single dipole mode indicate ambiguity caused by the nonuniqueness problem. Through our joint inversion, the additional second-order dipole wave can effectively help address the nonuniqueness issue in dipole acoustic logging, although its dispersion features differ in fast and slow formations. It is validated that the joint inversion has considerably improved convergence and accuracy in evaluating the thickness and shear velocity of the altered zone, compared with the estimation by a single acoustic mode. Furthermore, we develop numerical results based on synthetic logging data to demonstrate the feasibility of this inversion in a continuously varying profile, regardless of whether the formation surrounding the borehole is fast or slow. Even when strong drilling noises of low frequencies are added to the receiver signal arrays, the means of joint inversion can remain stable, and the shear-velocity profiles can be evaluated with good precision.

Oblique Bernstein wave propagation in electron‐ion plasma with electron quantization effects

AbstractWe have studied the role of electron quantization effects on the dispersion characteristics of the oblique electron Bernstein wave (EBW) in an electron‐ion plasma using Vlasov‐Poisson model. Our analysis shows that large thermal effects (as compared to quantization effects) give rise to the usual classical results while in the limit of strong magnetic field, the dispersion characteristics changes. The existence of a quantum Bernstein mode has been proposed which appears purely due to the electron quantization effects. The damping of the oblique EBW has also been analyzed in detail and we found that the magnitude of the damping of the wave decreases as we decrease the obliqueness parameter (parallel to perpendicular wavenumber ratio) which agrees with the earlier theoretical and experimental findings. Moreover, the strong quantization effects () also tend to suppress the damping of EBW which contributes to the stabilization of the waves. The present findings are relevant to the laboratory laser‐produced plasmas where strong external magnetic fields exist, and also to the dense astrophysical plasma environments.

Band gap characteristics of multi-functional lattice metamaterials with adjustable thermal expansion and Poisson's ratio

The current development of science and technology has put increased demands on the versatility of metamaterials. In this paper, the band gap characteristics of a lattice metamaterial that can simultaneously modulate thermal expansion and Poisson’s ratio are studied, the dispersion characteristics of elastic waves propagating in periodic lattice metamaterials are analyzed, and the effects of different structures and parameters on the band gap are discussed. The results indicate that the configuration has excellent band gap properties while satisfying the tunable coefficient thermal expansion (CTE)and Poisson’s ratio functions. Through reasonable material selection and shape design, it is expected to achieve a multi-objective win-win for specific thermal expansion properties, Poisson’s ratio, and band gap design, resulting in better tunability and versatility of the metamaterial.

On research of dispersion characteristics of multi-component surface waves from traffic-induced seismic ambient noise

As one of the commonly used sources in passive surface wave exploration, traffic-induced seismic ambient noise is widely used in urban underground velocity structure detection at present. However, characteristics of the dispersion curve extracted from such kind of ambient noise lack systematical research, especially for the multi-component surface wave. Due to the complex character of the real-world underneath structures, dispersion characteristics concluded from real-world traffic-induced seismic ambient noise that is hard to verify. The numerical simulation technique is a good choice for systematical research of characteristics of dispersion curves extracted from multi-component traffic-induced seismic ambient noise. Most of the numerical examples that appeared in the present literature, however, are based on the dispersion-curve-based numerical simulation technique. Hence, most of these can only simulate the vertical component. In this paper, the two-dimensional finite difference method is used to simulate multi-component traffic seismic ambient noise. The characteristics of original traffic noise are analyzed, and the effect of trace intervals on surface wave imaging of different types of traffic-induced noise is studied. Rayleigh wave dispersion energy image is extracted by the passive surface-wave frequency wavenumber transformed method. The differences in Rayleigh-wave dispersion images in traffic noise with different components are analyzed and compared. The results show that Rayleigh wave dispersion energy images appearing different characteristics in different components. The surface wave dispersion information presented by different types of traffic noise is frequency-dependent. The trace spacing also strongly affect the surface-wave dispersion energy images extracted from different types of traffic-induced noise. The numerical results are significant for guiding the traffic-induced seismic noise data acquisition and processing.

A refined spectral element model for wave propagation in multiscale hybrid epoxy/carbon fiber/graphene platelet composite shells

The propagation of elastic waves in heterogeneous media is of interest for impact dynamics and non-destructive detection. This work presents a refined spectral element model (RSEM) to study the wave propagation in multiscale hybrid composite (MHC) shells subjected to impulsive loadings. The doubly-curved MHC shell consists of epoxy, carbon fibers, and graphene platelets (GPLs). The GPLs are functionally distributed along the thickness of the shell. For the three-phase MHC, the Halpin-Tsai micromechanical model in conjunction with the Mori-Tanaka approach is exploited to determine the effective material properties. In the framework of four-variable shear deformation theory, the governing equations along with the natural boundary conditions are derived using Hamilton's principle. A two-node spectral shell element is developed according to the closed-from solutions. The accuracy of the RSEM is verified by comparison with published results in aspects of the natural frequency and transient responses. The wave dispersion characteristics, including the wave number, phase velocity, and group velocity are examined. In the context of high frequency and short wavelength, the proposed RSEM achieves high computational efficiency benefiting from its independence of mesh structure. The time domain responses clearly indicate the wave-boundary interactions, e.g., wave reflection, dispersion, and interference. It is revealed that the present model can well capture the fundamental wave modes of the MHC shell. Moreover, the inclusion of GPLs plays a significant role in improving transverse moduli and mitigating the discontinuities of inter-laminar shear stress.

Dispersion characteristics of surface wave in SCCS: theoretical analysis, numerical simulation and MASW-based NDT

To fully validate the feasibility of multichannel analysis of surface waves (MASW)-based interfacial debonding detection for steel–concrete composite structures (SCCS), dispersion characteristics of surface waves in SCCS are systematically investigated using theoretical analysis and elaborate 3D numerical simulations. First, the influences of material strength and thickness of concrete core, steel plate thickness on the dispersion figures are analyzed based on the theoretical dispersion characteristic of Rayleigh wave. Scientific layering strategy, including single steel plate, double-layer, and three-layer medium assumptions, is investigated using the theoretical dispersion analysis of Lamb wave. Besides, the dispersion characteristics of surface wave in circular steel pipes are calculated to determine the appropriate theoretical dispersion curves for MASW measurement. Finally, the stress wave propagation processes in SCCSs with various internal structures, including stiffeners, studs, and diaphragms, as well as the debonding width, are simulated using 3D numerical simulation to validate the research finding of theoretical analysis and detectability of MASW-based non-destructive testing on interfacial debonding defects in rectangular and circular concrete-filled steel tubulars. Finally, the dispersion characteristics corresponding to displacement, velocity, and acceleration of surface waves are comparatively discussed. The research findings of this study are the cornerstone of experimental study and essential theoretical support for identifying interfacial debonding and bond-slip damage of SCCS components utilizing MASW method.