Dispersion Characteristics Of Waves Research Articles

Enhanced probabilistic damage localization for composite plate based on joint recurrence plots

Localizing damage is a key aspect of monitoring composite laminate structural health. To address the problem of generating the damage index (DI) of composite laminates using Lamb waves, a reconstruction approach for probabilistic damage inspection (RAPID) based on joint recurrence plots (JRP) was proposed. First, the dynamics of the Lamb wave signals are analyzed using phase space reconstruction. Second, the damage information in each sensing path is represented using JRP, and the DI based on the JRP is built with variational auto-encoder (VAE). Finally, the relative magnitude of the DI was employed to modify RAPID’s weight distribution function, allowing for composite plate damage localization detection. The findings of finite element modeling and experiment data reveal that the approach can achieve accurate localization imaging of the composite plate’s interior damage while also properly identifying the damage under 20 dB and 10 dB noise interference. The approach does not require an understanding of Lamb wave dispersion characteristics and involve the extraction of complicated wave packet signals, making it promising for structural health monitoring based on damage index.

Lamb Wave TDTE Super-Resolution Imaging Assisted by Deep Learning

Abstract Ultrasonic Lamb waves undergo complex mode conversion and diffraction at non-penetrating defects, such as plate corrosion and cracks. Lamb wave imaging has a resolution limit due to the guided wave dispersion characteristics and Rayleigh criterion limitations. In this paper, a full convolutional network is designed to segment and reconstruct the received signals, enabling the automatic identification of target modalities. This approach eliminates clutter and mode conversion interference when calculating direct and accompanying acoustic fields in time-domain topological energy imaging. Subsequently, the measured accompanying acoustic field is reversed for adaptive focusing on defects and enhance the imaging quality. To circumvent the limitations of the Rayleigh criterion, the direct acoustic field and the accompanying acoustic field were fused to characterize the pixel distribution in the imaging region, achieving Lamb wave super-resolution imaging. Experimental results indicate that compared to the sign coherence factor-total focusing method (SCF-TFM), the proposed method achieves a 31.41% improvement in lateral resolution and a 29.53% increase in signal-to-noise ratio for single-blind-hole defects. In the case of multiple-blind-hole defects with spacings greater than the Rayleigh criterion resolution limit, it exhibits a 27.23% enhancement in signal-to-noise ratio. On the contrary, when the defect spacings are relatively smaller than the limit, this method has a higher resolution limit than SCF-TFM in super-resolution imaging.

Identification and Application of Wave Field Characteristics of Channel Waves in Extra-Thick Coal Seams

Channel wave seismic activity often occurs with thin and medium-thick coal seams being the main target layer. To address the problem of channel wave applicability detection in extremely thick coal seams, the propagation and identification characteristics of channel waves remain the focus of research. Therefore, this paper takes the in-seam wave exploration of a 27 m extremely thick coal seam as an example and uses the staggered mesh finite difference method to construct a three-dimensional medium model for numerical simulation. An analysis of the physical parameters of coal and rock, along with the dispersion characteristics of channel waves in extra-thick coal seams, is utilized, through the Zoeppritz equation and the total reflection propagation method, to calculate the imaging. We found the following: (1) The dispersion areas and weak dispersion areas along the detection direction are extremely thick coal seams. (2) There are apparent channel waves in extra-thick coal seams, with a waveform similar to body waves; the length of the wave train is shorter than that of the conventional channel wave, and the arrival time can be estimated accurately. The amplitude of the apparent channel wave is affected by the degree of dispersion, with lower attenuation and higher resolution. The characteristic of total reflection in extremely thick coal seams is that the incident angle is equal to the critical angle, and the dispersion characteristics are weak. (3) The channel waves with weak dispersion characteristics in extra-thick coal seams are mainly Love-type waves.

Complex Dispersion Analysis of Flexural Wave Propagation in Periodic Track Structure

The periodic characteristics of the track structure have filtering characteristics for the propagation of vibration waves within it, and the dispersion analysis is of great significance to understand the vibration transmission characteristics of the track structure. The accuracy of the traditional virtual spring method depends on the value of spring stiffness, which leads to poor stability. Therefore, this paper adopts a null space method with both stability, accuracy and efficiency, and takes the CRTSIII ballastless track structure as the research object. Based on the null space method and energy functional variational principle, the damping factor and the material frequency variation effect are considered in detail, and the complex frequency dispersion of the CRTSIII ballastless track structure is analyzed. The accuracy of the proposed method is verified by comparing it with the results of the existing literature, and the influence of fastener stiffness frequency variation, fastener damping and concrete support layer damping on the complex dispersion characteristics of vibration waves of track structures is analyzed by using this method. The results show that the stiffness frequency effect, fastener damping and concrete support layer damping have a great influence on the attenuation domain and attenuation rate of vibration, which must be considered in the vibration transmission analysis of track structures.

Dispersion Analysis of Plane Wave Propagation in Lattice-Based Mechanical Metamaterial for Vibration Suppression

Phononic crystals based on lattice structures provide important wave dispersion characteristics as band structures, showing excellent compatibility with additive manufacturing. Although the lattice structures have shown the potential for vibration suppression, a design guideline to control the frequency range of the bandgap has not been well established. This paper studies the dispersion characteristics of plane wave propagation in lattice-based mechanical metamaterials to realize effective vibration suppression for potential aerospace applications. Triangular and hexagonal periodic lattice structures are mainly studied in this paper. The influence of different geometric parameters on the bandgap characteristics is investigated. A finite element approach with Floquet–Bloch’s principles is implemented to effectively evaluate the dispersion characteristics of waves in lattice structures, which is validated numerically and experimentally with a 3D-printed lattice plate. Based on numerical studies with the developed analysis framework, the influences of the geometric parameters of lattice plate structures on dispersion characteristics can mainly be categorized into three patterns: change in specific branches related to in-plane or out-of-plane vibrations, upward/downward shift in frequency range, and drastic change in dispersion characteristics. The results obtained from the study provide insight into the design of band structures to realize vibration suppression at specific frequencies for engineering applications.

The collisional study of EIC waves in a magnetized dusty plasma with the inclusion of a DC electric field

This study investigates Electrostatic Ion Cyclotron (EIC) waves and their behaviour in weakly collisional plasmas, utilizing a proposed kinetic analytical model. The findings include alterations in EIC wave dispersion characteristics due to collisions, with parameters such as dust density, collision frequency, gyro-radius, magnetic field, density ratio, and electric field influencing wave growth rate and frequency. Temperature analysis reveals that higher electron-to-ion temperature ratios lead to increased frequency and critical drift velocity, while decreasing the growth rate. In addition, the critical drift velocity is studied for the unstable mode and it is observed that the relative density ratio increases with a reduction in critical drift velocity. Electron collisions destabilize EIC waves, while ion collisions stabilize them. Furthermore, the presence of dust particles decreases the growth rate of EIC waves as dust grain density increases. These results align with observations reported in previous literature.

Computation and analysis of surface wave dispersion and attenuation in layered viscoelastic-vertical transversely isotropic media by the generalized R/T coefficient method

SUMMARY In this study, we propose a systematic and effective method, that is, an extended version of the generalized reflection/transmission (R/T) coefficient method, for computing the phase-velocity (${c}_r$) dispersion curves, attenuation coefficient ($\alpha $) curves, and eigenfunctions of both Rayleigh and Love waves as well as the ellipticity of Rayleigh waves in layered viscoelastic-vertical transversely isotropic (VTI) media. The numerical scheme of combining the root-searching method with the local optimization method is designed for determining the complex-valued modal solutions (i.e. complex wavenumber $k = {\omega {/ {\vphantom {\omega {{c}_r - i\alpha }}}} {{c}_r - i\alpha }}$) of surface waves. The near-surface sedimentary geological environment is taken as the model example because it is typical viscoelastic-VTI media. Besides the anisotropic-viscoelastic (AV) media, our algorithm can also compute surface waves in isotropic-elastic (IE), isotropic-viscoelastic (IV) and anisotropic-elastic (AE) media by resetting the corresponding parameters. Using the six-layer half-space models and in these four media, we verify the correctness of our algorithm by benchmarking the modal solutions against those from other methods. In the four-layer half-space model, by comparing the results of IE, IV, AE and AV media, we analyse the effects of velocity anisotropy, viscoelasticity and attenuation anisotropy on the dispersion and attenuation characteristics of both Rayleigh and Love waves in detail. Our study can provide a theoretical basis and useful tool for surface wave imaging considering the anisotropy and/or viscoelasticity of the medium, which has the potential to better investigate the solid Earth's internal structure.

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.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ПОВЕДЕНИЯ СЛОИСТОЙ МУЛЬТИФЕРРОИДНОЙ СТРУКТУРЫ В НЕОДНОРОДНЫХ ЭЛЕКТРИЧЕСКИХ ПОЛЯХ В ОБЛАСТИ СВЕРХВЫСОКИХ ЧАСТОТ

In this work, based on the dispersion characteristics of spin waves and the theory of the magnetoelectric effect, a mathematical model of a multiferroic structure behavior in a non-uniform electric field is constructed. The nature of the exchange interaction is taken into account, and the Rado-Wirtman exchange boundary conditions are also considered based on their representation in terms of free energy density. Based on the constructed mathematical model, the contribution to the dispersion pattern of spin waves of an external electric field of different polarities is estimated. In conclusion, a number of cases of application of the constructed mathematical model in the design of electronically controlled devices for the directional propagation of spin waves, as well as basic devices for neuromorphic computing, are given.

Formirovanie polos nepropuskaniyaspin-volnovogo signala v meandrovykh strukturakh iz ZhIG

A meander waveguide made of an yttrium iron garnet (YIG) film with variation of the profile is studied with a view to the possible control of band bands for surface spin waves (SSWs). The finite element method is used to determine the control mechanism of forbidden band gaps in thin YIG films. The electromagnetic problem is solved, and the dispersion characteristics of spin waves are plotted for various geometrical parameters of the meander. The nature of the change in the frequency ranges of Bragg forbidden band gaps is studied in detail depending on the profile of the meander. It is demonstrated that a three-dimensional spin-wave structure with broken translational symmetry that uses vertical spin-wave transport provides an information signal transmission in a three-dimensional configuration of magnonic networks.

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.