Propagation Of Transverse Waves Research Articles

Transverse Electric Guided Wave Propagation in a Plane Waveguide with Kerr Nonlinearity and Perturbed Inhomogeneity in the Permittivity Function

The paper focuses on the problem of transverse electric wave propagation in a plane-shielded waveguide filled with a nonhomogeneous and nonlinear (Kerr) medium. The nonlinear part of the permittivity is characterized by the Kerr law in the focusing regime, while its linear part is a constant that is perturbed by a small continuous function. Such perturbation can be considered to be an attempt to take into account the inevitable presence of impurities in the medium, causing slight deviations in the dielectric permittivity. In the paper, the existence of solutions to the considered problem is proved, including solutions with and without linear counterparts. Some numerical results are presented as well.

Effect of Finite Ion Larmor Radius (FLR) Corrections on Thermal Instability of Rotating Radiative Porous Astrophysical Plasma in Interstellar Medium (ISM)

Infinite homogeneous plasma’s thermal instability has been studied in relation to finite ion Larmor radius (FLR) corrections, rotation, and porosity, as well as the impacts of radiative heat-loss function and thermal conductivity. With the aid of a normal mode analysis framework and the necessary difficulty-appropriate linearized perturbation equations, a universal dispersion relation is investigated. For the propagation of transverse waves, this dispersion relationship further condenses for rotation axes parallel to and at right angles to the magnetic field. It is proven that the presence of rotation, porosity, thermal conductivity, and radiative heat-loss function altered the thermal instability criterion. To show how different parameters affect the rate at which the thermal instability grows, numerical calculations have been carried out. We discover that rotation, FLR corrections, and medium porosity stabilised the growth rate of the thermal system in the transverse mode of propagation. The conclusion of this research states that the rotation, porosity, and FLR corrections have an impact on the configuration of dense molecular clouds and star formation.

Investigation of the Information Possibilities of the Parameters of Vibroacoustic Signals Accompanying the Processing of Materials by Concentrated Energy Flows

Creating systems for monitoring technology processes based on concentrated energy flows is an urgent and challenging task for automated production. Similar processes accompany such processing technologies: intensive thermal energy transfer to the substance, heating, development of the melting and evaporation or sublimation, ionization, and expansion of the released substance. It is accompanied by structural and phase rearrangements, local changes in volumes, chemical reactions that cause perturbations of the elastic medium, and the propagation of longitudinal and transverse waves in a wide frequency range. Vibrational energy propagates through the machine's elastic system, making it possible to register vibrations on surfaces remotely. Vibration parameters can be used in monitoring systems to prevent negative phenomena during processing and to be a tool for understanding the processes' kinetics. In some cases, it is the only source of information about the progress in the processing zone.

Unfolding the dynamics of free-falling folded chain: Experiments and simulations

Contrary to educated intuition, the tip of a free-falling U-folded chain accelerates faster than gravity without violating the Newtonian laws. In the current work, we study the dynamics of a free-falling U-folded chain experimentally as well as numerically. To this end, high-speed imaging (up to 10000 fps) is used to capture the chain’s falling tip by using different openings between the two tips of the chain. Thanks to high-speed digital imaging, the detailed geometry of the dynamic unfolding is captured. The post-processing of captured images has provided detailed quantitative temporal data for displacement, velocity, and acceleration of the falling tip of the chain. The experimental observations have revealed the various phases of dynamics of the falling U-folded chain, including unfolding, whipping, and rebounding phases for the first time. Furthermore, a Henky-type model is developed to capture the associated phenomena related to these phases, such as rebound effect, whip effect, local buckling, and transverse wave propagation. The model that includes nonlinear elastic, dissipative and bilateral gap-contact features, could successfully capture the experimentally observed phases and phenomena of the unfolding dynamics qualitatively.

Transient Propagation of Longitudinal and Transverse Waves in Cancellous Bone: Application of Biot Theory and Fractional Calculus

In this paper, the influence of the transverse wave on sound propagation in a porous medium with a flexible structure is considered. The study is carried out in the time domain using the modified Biot theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The viscous exchanges between the fluid and the structure are described by fractional calculus. When a sound pulse arrives at normal incidence on a porous material with a flexible structure, the transverse waves interfere with the longitudinal waves during propagation because of the viscous interactions that appear between the fluid and the structure. By performing a calculation in the Laplace domain, the reflection and transmission operators are derived. Their time domain expressions depend on the Green functions of the longitudinal and transverse waves. In order to study the effects of the transverse wave on the transmitted longitudinal waves, numerical simulations of the transmitted waves in the time domain by varying the characteristic parameters of the medium are realized whether the transverse wave is considered or not.

Propagation of transverse waves in the solar chromosphere probed at different heights with ALMA sub-bands

The Atacama Large Millimeter/sub-millimeter Array (ALMA) has provided us with an excellent diagnostic tool for studies of the dynamics of the Solar chromosphere, albeit through a single receiver band at one time presently. Each ALMA band consists of four sub-bands that are comprised of several spectral channels. To date, however, the spectral domain has been neglected in favour of ensuring optimal imaging, so that time-series observations have been mostly limited to full-band data products, thereby limiting studies to a single chromospheric layer. Here, we report the first observations of a dynamical event (i.e., wave propagation) for which the ALMA Band 3 data (centred at 3 mm; 100 GHz) is split into a lower and an upper sideband. In principle, this approach is aimed at mapping slightly different layers in the Solar atmosphere. The side-band data were reduced together with the Solar ALMA Pipeline (SoAP), resulting in time series of brightness-temperature maps for each side-band. Through a phase analysis of a magnetically quiet region, where purely acoustic waves are expected to dominate, the average height difference between the two side-bands is estimated as 73 ± 16 km. Furthermore, we examined the propagation of transverse waves in small-scale bright structures by means of wavelet phase analysis between oscillations at the two atmospheric heights. We find 6% of the waves to be standing, while 54% and 46% of the remaining waves are propagating upwards and downwards, respectively, with absolute propagating speeds on the order of ≈96 km s−1, resulting in a mean energy flux of 3800 W m2.

New behavior of tsunami and tidal oscillations for Long- and short-wave interaction systems

The Jacobi elliptic function expansion method is one of the most powerful tools for exploring exact solutions of nonlinear partial differential models, which is used in this work to characterize the interaction between one long longitudinal wave and one short transverse wave propagation in a generalized elastic medium. First, we applied a wave transform to the proposed system of equations and obtained an ordinary differential equation. We obtain the values of involved free parameters after performing necessary operations, then substitute the obtained values to the ordinary differential equation by considering the constructed solutions to the ordinary and then to the partial differential equation. As a result, different structures of solutions are constructed such as solitary dark–bright, dark, bright, singular, trigonometric function, Jacobi elliptic function, and hyperbolic function solutions. In order to illustrate the tsunami and tidal oscillations, we draw 3D surfaces and 2D graphics for the obtained solutions by giving a specific value for the involved parameters under the given conditions.

Elastic Metagratings with Simultaneous Highly Efficient Control over Longitudinal and Transverse Waves for Multiple Functionalities

Elastic metagratings that can efficiently manipulate the propagation of bulk longitudinal and transverse waves are highly desired in various applications, such as geological exploration and nondestructive detection. Here, a class of elastic metagratings consisting of a one-dimensional array of elliptical hollow cylinders carved in a steel background is proposed and studied. With the help of elastic-wave-diffraction analysis and a genetic-algorithm-based optimization approach, these intelligently designed metagratings can reflect longitudinal and transverse waves in a highly efficient and spatially separated way. Various wave-front-manipulation functionalities, such as specular reflection for longitudinal waves and anomalous reflection for transverse waves, can be simultaneously achieved with an almost perfect efficiency. Interestingly, different functionalities over both longitudinal and transverse waves can be realized by using the same cylinders with different rotation angles. Due to the nonresonant characteristics, the exhibited functionality shows robustness over both working frequencies and unit-cell configurations, which are beneficial for practical applications.

Influences of defects on the propagation of transverse waves in periodic piezoelectric laminate structure with nanoscaled layers

By the stiffness matrix method based on the nonlocal elastic continuum theory, the transmission spectra of the transverse elastic waves propagating normally in nanoscaled periodic piezoelectric laminates with defects are investigated in detail in this paper. Defect is introduced by replacing a constituent layer or inserting another layer in a unit-cell. The thicknesses of all sub-layers and defect layer are at the nanoscale. Simultaneously, complex band structures and localization factors are calculated and employed to verify the band structures described by the transmission spectra. The influences of the defect type, the defect material, the volume fraction of the defect layer in the unit-cell, the piezoelectric constants of the defect layer, and the nanoscale size-effect on the transmission spectra are analyzed and discussed in detail. The present study provides a theoretical guide for the design and applications of the nanoscaled acoustic filters or transducers with defects.

Effect of rotation and FLR corrections with radiative heat-loss functions on transverse thermal instability of astrophysical porous plasma in interstellar medium (ISM)

The effect of rotation, finite ion Larmor radius (FLR) corrections and porosity on the thermal instability of infinite homogeneous plasma has been explored taking the effects of radiative heat-loss function and thermal conductivity. The general dispersion relation is derived by means of the normal mode analysis scheme with the help of appropriate linearized perturbation equations of the problem. This dispersion relations is further reduces for rotation axis parallel and perpendicular to the magnetic field for transverse wave propagation. It is found that the presence of rotation, FLR corrections and porosity amend the fundamental thermal criterion of instability. Numerical computations have been executed. Our result demonstrates that the rotation, porosity and FLR corrections affect the dens molecular clouds configuration and star formation.

Robust large-area elastic transverse wave transport in active acoustic metamaterials

We investigate robust large-area elastic transverse wave propagation in an actively tunable membrane-type acoustic metamaterial. The waveguide with multiple degrees of freedom to control the width of the interface mode is realized by designing a heterostructure including three domains. One central domain is constructed by periodic unit cells in an ordinary state, where a Dirac cone can be observed in the band structure. The other two domains consist of periodic unit cells possessing opposite valley Chern numbers, respectively. By employing a finite element model, the topologically protected interface states with tunable degrees of freedom are exhibited. The energy of interface states distributes equally in the large-central region. Although a larger degree of freedom leads to lower amplitudes of interface states, larger total energy is demonstrated by defining a quality factor. Moreover, we design several waveguides with straight lines and sharp corners with different angles and denote three different notations to show clearly that the large-area transverse wave can propagate robustly through sharp corners. Finally, it is found that the large-area transverse wave transport shows immunity to disorders and defects in the propagation path.

Selection of size dependency theory effects on the wave's dispersions of magneto-electro-thermo-elastic nano-beam resting on visco-elastic foundation

Current research develops a comprehensive wave propagation analysis of a magneto-electro-thermo-elastic (METE) nano-beam (NB) resting on the visco-elastic medium. To model the size dependency effects, modified couple stress (MCS) and Eringen's nonlocal (ENL) theories are employed to analyze and describe the wave propagation behaviors for those nano-beams. These theories were the most used in the literature due to the inclusion of one additional size-dependent length scale parameter. Those theories are compared side by side in this investigation and their impacts/differences on the wave propagation of specific materials are explored. Sinusoidal shear deformation beam model with Hamilton's principle is adopted to develop the governing equations of motion. Then, an analytical solution is executed to extract numerical results for transverse wave propagation in both elastic and METE configurations of the nano-beam. The effects of size-dependent length scale of both theories, thickness of NB, Winkler-Pasternak coefficients, thermal gradient, and magnetic potential and external electric voltage are illustrated and discussed in details. It is concluded that wave frequency decreases with increment of nonlocal parameter for ENL model. On the other hand, a stiffening effect takes place for the wave frequency when the MCS model is considered. Hence, the results indicate that there is a significant difference between ENL and MCS theories in the estimation of the behavior of wave propagation in small-scale structures. One of the main results of this investigation indicates that the MCS theory has similar nonlocal effects as the Eringen's theory for specific conditions.

Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance

This paper is concerned with the time-dependent Maxwell’s equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we have constructed a generalized Fourier transform which diagonalizes the Hamiltonian that represents the propagation of transverse electric waves. In this second paper, we use this transform to prove the limiting absorption and limiting amplitude principles, which concern, respectively, the behavior of the resolvent near the continuous spectrum and the long time response of the medium to a time-harmonic source of prescribed frequency. This paper also underlines the existence of an interface resonance which occurs when there exists a particular frequency characterized by a ratio of permittivities and permeabilities equal to −1 across the interface. At this frequency, the response of the system to a harmonic forcing term blows up linearly in time. Such a resonance is unusual for wave problem in unbounded domains and corresponds to a non-zero embedded eigenvalue of infinite multiplicity of the underlying operator. This is the time counterpart of the ill-posdness of the corresponding harmonic problem.

Attenuation of acoustic waves and Grüneisen tensor in lithium fluoride crystals

The anisotropy of acoustic attenuation in lithium fluoride crystals in the range of 0.4–1.6 GHz was studied by the method of Bragg light diffraction on acoustic waves. The obtained values of the velocity and attenuation coefficient of acoustic waves were used to determine all independent real and imaginary elastic constants. Based on the Akhiezer attenuation mechanism, the anisotropy of acoustic attenuation was determined for the propagation of longitudinal and transverse waves in the (001) and (110) planes. All directions along which pure longitudinal and transverse acoustic waves propagate are found. To describe the anisotropy of acoustic attenuation, the Grüneisen acoustic tensor is used for the first time, the components of which have been determined from the values of the attenuation coefficient of acoustic waves along the crystallographic axes [100], [110], and [111]. It is shown that the orientational dependence of the effective Grüneisen constant, defined in terms of the components of this tensor, describes well the anisotropy of the attenuation of acoustic waves in the studied frequency range. The proposed approach can be used to all cubic crystals in which the main attenuation mechanism is the phonon–phonon Akhiezer mechanism.

Experimental observation of transverse and longitudinal wave propagation in a metamaterial periodically arrayed with nonlinear resonators

Elastic wave propagation in solids composed of elastic metamaterials always exists as both transverse and longitudinal waves simultaneously. By using the Hamilton principle, Bloch theorem, and finite-element method, an approach is proposed to explore the band energy structures of the metamaterial, this is observed in an experiment on an ultralow frequency metamaterial periodically positioned nonlinear resonators and this means the broadband isolation of both longitudinal and transverse waves was verified. Comparison of the propagation of transverse and longitudinal waves in the ultralow frequency metamaterials, the Bragg band-gaps (BBGs) and local resonance band-gaps (LRBGs) differ with both the frequency of the bandwidth and the depth of the band-gap.

Numerical investigation of fibre failure mechanisms of one single Kevlar yarn under ballistic impact

This paper presents a microscopic numerical investigation of the fibre failure mechanisms of one single crimped Kevlar® KM2 yarn subjected to ballistic impact. Generally, one yarn consists of about 400 fibres, which poses many challenges for modelling. Also, a high computation time is required due to the vast number of elements. Therefore, the concept of an equivalent fibre representing one set of fibres is introduced. Then, two sub-yarn level numerical models in which 400 fibres are represented by 42 and 98 equivalent ones are conducted. These models are evaluated by comparing with the mesoscopic model and qualitatively validated by results from the literature. Fibre failure mechanisms are analysed. The evolution of yarn energies, transverse wave propagation, and projectile velocity versus time are investigated. The tension force of each fibre is also obtained. It is highlighted that both models can predict the global behaviour of the yarn. However, fibre failure mechanism and fibre–fibre interaction are only accurately captured by the 98-fibres model. Therefore, this sub-yarn level model can be used to develop a micro-mesoscopic multi-scale model of Kevlar fabric in further works.

Numerical study on stress in a solid wall caused by the collapse of a cavitation bubble cloud in hydraulic fluid

The stress in a solid due to the collapse of a bubble cloud in hydraulic fluid is investigated by the numerical simulation, which considers the fluid-structure coupling and employs the bubbly flow model with Euler-Lagrange method. The dynamics of the bubble at the subgrid scale is described by the Keller-Miksis equation. Heat transfer at the bubble interface is considered to reproduce thermal damping effect. As the result of the fluid-structure coupling simulation, the high von Mises stress region is observed in the solid due to the collapse of the bubble cloud attached on the solid surface, and the propagation of longitudinal and transverse waves in the solid is reproduced. As the standoff distance YC from the solid surface to the center of the bubble cloud decreases, the peak von Mises stress in the solid increases, taking a maximum at YC=0.4RC, and then decreases. Thus, the peak von Mises stress is highest under the condition that the bottom quarter of the bubble cloud is on the wall. Due to the increase of the initial void fraction and the decrease of the initial bubble radius in the bubble cloud, the collapse pressure of the bubble cloud increases. Under certain conditions, the peak von Mises stress can be higher than the 0.2% yield stress value of 250MPa for a cast iron. This is expected to induce cavitation erosion of the solid surface.

Features of modeling of stress and strain waves in an anisotropic medium on the example of a wooden element

This article describes the hypotheses of the occurrence, propagation, and modification of stress and strain waves caused by external loads in isotropic and anisotropic infinite and finite elastic media. A model of an infinite elastic medium experiencing a point external impulse is presented. The model demonstrates the propagation of a longitudinal plane wave. Compaction and rarefaction of the medium are observed in the plane with wave propagation. A graph of changes in the amplitude of a longitudinal plane wave is presented in the same coordinate system. The problem is posed of expanding the numerical model of a finite elastic medium in the form of an anisotropic wooden rod experiencing a plane external impulse. The model should demonstrate the propagation of longitudinal and transverse waves and describe the volumetric deformation of an anisotropic material. Compaction and rarefaction of the medium are shown in the plane, coinciding with the direction of wave propagation. A graph of the change in the shear wave amplitude is presented in the same coordinate system. The combination of these two graphsreveals the difference in wave propagation velocities and the combination of amplitudes. The model will make it possible to identify the presence of Rayleigh waves and to describe the reflection of waves from the boundary of the medium.

Comparative study of destructive, nondestructive, and numerical procedures for the determination of moisture dependent shear moduli in Scots pine wood

Abstract In this study, moisture dependent shear moduli in Scots pine (Pinus sylvestris L.) wood were determined by a 45° off-axis (longitudinal, radial, and tangential) compression test and ultrasonic transverse wave propagation. Finite element modeling was performed to ascertain how the results agree with the numerical method. Ultrasonic transverse wave velocities on the LR, LT, and RT planes were decreased from 1347, 1323, and 589 m × s-1 to 1286, 1269, and 561 m × s-1 when relative humidity increased from 45 % to 85 % at a constant temperature of 20 ± 1 °C, respectively. The dynamic and static shear modulus on the LR, LT, and RT planes were decreased from 988, 953, and 189, and 966, 914, and 182 MPa to 927, 903, and 176, and 845, 784, and 154 MPa when relative humidity increased from 45 % to 85 % at a constant temperature of 20 ± 1 °C, respectively. Therefore, both velocity and modulus values at all principal axes and planes were decreased with an increase in moisture. Maximum (15.2 %) and minimum (2.3 %) differences between dynamic and the static shear modulus were observed for GLT at 85 % and GLR at 45 % relative humidity, respectively. Coefficients of determinations between the dynamic and static shear moduli were ranged from 0.68 (GLR at 65 % RH) to 0.97 (GLR at 85 % RH). Finite element analysis, only for 65 % RH values, was performed using Solid 45 element, and, according to results, load-deformation curves created by linear orthotropic material properties, are well-matched with the static curves.

A Wideband Millimeter-Wave Rotman Lens Multibeam Array Using Substrate Integrated Coaxial Line (SICL) Technology

This article presents a wideband Rotman lens multibeam array implemented with substrate integrated coaxial lines (SICLs) for millimeter-wave (mmW) applications. Unlike other dispersive transmission lines commonly used with printed circuit boards, SICL is a nondispersive planar coaxial line that supports the propagation of transverse electromagnetic waves, thus enabling broadband designs of mmW Rotman lenses. Two types of wideband, compact transition structures consisting of small strips and blind vias were designed to transfer energy between the input–output SICLs and parallel-plate lens cavity. Wideband tapered slot antennas excited by SICLs, with a compact lateral size and wide beamwidths, were introduced as the radiating elements to realize a wide scanning range over a large bandwidth. For a proof-of-concept demonstration, a multibeam array prototype that includes seven beam ports and ten array ports connected to ten antenna elements was designed and fabricated. Experimental results agree well with simulation results and show that the proposed multibeam array has an overall bandwidth of 57% (25–45 GHz) with nearly frequency-invariant beam steering performance within ±45°. The desirable wideband operation in conjunction with the ease of integration with planar circuits and low-cost fabrication make the proposed multibeam array design a promising solution for various mmW applications.