Propagation Of Transverse Waves Research Articles

Transverse wave propagation analysis in single-walled and double-walled carbon nanotubes via higher-order doublet mechanics theory

ABSTRACT In the present study, transverse wave propagation in single-walled and double-walled carbon nanotubes is investigated based on doublet mechanics theory. The Euler–Bernoulli and Timoshenko beam theories are considered to study the wave dispersion relations of single-walled and double-walled carbon nanotubes (CNTs) with the set of relevant governing equations are achieved by use of the variational Hamilton’s principle. Obtained governing equations are presented for zigzag and armchair CNT models. Using these models, scale dependent wave frequency, phase velocity and group velocity of CNTs are obtained. It has been observed that doublet mechanics results have so called van Hove singularity. This property is the first seen among the scale-dependent continuum theories. The effectiveness and validity of the present method are approved by comparing the predicted numerical results with molecular dynamics simulation and nonlocal Timoshenko beam theory. An excellent validation is obtained between the doublet mechanics based on Timoshenko beam theory and molecular dynamics simulation for phase velocities of (5,5) and (10,10) armchair single-walled CNTs. Also, this work clarifies the importance of the length scale effect on transverse wave dispersion in multi-walled CNTs.

CREEPING SURFACE LONGITUDINAL ACOUSTIC WAVE: MAIN PROPERTIES AND APPLICATION POSSIBILITIES

Creeping ultrasonic waves have long been successfully used for flaw detection of near-surface and near-bottom zones of metal products. However, due to the fact that the creeping wave generates a lateral transverse wave directed into the metal volume at the third critical angle, it is also possible to test internal defects in principle. At known velocities of propagation of longitudinal and transverse waves in the metal, the third critical angle is easily calculated. Therefore, the time of propagation of the ultrasonic signal along any trajectory between points on the surface and in the volume of the metal can be calculated. Usually, creeping waves are used to test products of plane-parallel shape. There are no cases of their application on curved surfaces in the literature. It is possible that the creeping wave can also propagate over a concave surface. The aim of the article is to test experimentally new ways of using creeping waves. The propagation trajectories of the creeping and lateral transverse waves were studied on a steel plate. The time of passage of the ultrasonic signal along such trajectories of different lengths was measured, and the measurement results were compared with the calculated time values. The measured and calculated values coincided with accuracy sufficient for the coherent accumulation of echo signals that passed through the metal part of the path by the creeping wave and another part of the path by the lateral transverse wave.The propagation of the creeping wave over a concave surface was studied on a steel sample with cylindrical faces of different radii. As a result, it turned out that on a concave surface, the creeping wave propagates at the same speed of longitudinal waves as on a flat surface, but it decays much more strongly with distance. Studies have shown that creeping waves can be used in ultrasonic tomography, where a preliminary calculation of the propagation trajectories of ultrasonic signals is required. The propagation of creeping waves over concave surfaces extends the capabilities of the TOFD method to the area of intube testing

Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses

Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak (BP). For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al 2019, Sci. Rep. 9 19514], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the BP scales only with that of the global shear modulus. This observation suggests that the spatial heterogeneity of the local shear modulus distribution is insensitive to changes in the bending rigidity. Here, we demonstrate the insensitivity of elastic heterogeneity by directly measuring the local shear modulus distribution. We also study transverse sound wave propagation, which is also shown to scale only with the global shear modulus. Through these analyses, we conclude that the bending rigidity does not alter the spatial heterogeneity of the local shear modulus distribution, which yields vibrational and acoustic properties that are controlled solely by the global shear modulus of a polymer glass.

Flexure mechanics of nonlocal modified gradient nano-beams

Abstract Two frameworks of the nonlocal integral elasticity and the modified strain gradient theory are consistently merged to conceive the nonlocal modified gradient theory. The established augmented continuum theory is applied to a Timoshenko–Ehrenfest beam model. Nanoscopic effects of the dilatation, the deviatoric stretch, and the symmetric rotation gradients together with the nonlocality are suitably accommodated. The integral convolutions of the constitutive law are restored with the equivalent differential model subject to the nonclassical boundary conditions. Both the elastostatic and elastodynamic flexural responses of the nano-sized beam are rigorously investigated and the well posedness of the nonlocal modified gradient problems on bounded structural domains is confirmed. The analytical solution of the phase velocity of flexural waves and the deflection and the rotation fields of the nano-beam is detected and numerically illustrated. The transverse wave propagation in carbon nanotubes is furthermore reconstructed and validated by the molecular dynamics simulation data. Being accomplished in revealing both the stiffening and softening structural responses at nano-scale, the proposed nonlocal modified gradient theory can be beneficially implemented for nanoscopic examination of the static and dynamic behaviors of stubby nano-sized elastic beams.

A solver based on pseudo-spectral analytical time-domain method for the two-fluid plasma model

A number of physical processes in laser-plasma interaction can be described with the two-fluid plasma model. We report on a solver for the three-dimensional two-fluid plasma model equations. This solver is particularly suited for simulating the interaction between short laser pulses with plasmas. The fluid solver relies on two-step Lax–Wendroff split with a fourth-order Runge–Kutta scheme, and we use the Pseudo-Spectral Analytical Time-Domain (PSATD) method to solve Maxwell’s curl equations. Overall, this method is only based on finite difference schemes and fast Fourier transforms and does not require any grid staggering. The Pseudo-Spectral Analytical Time-Domain method removes the numerical dispersion for transverse electromagnetic wave propagation in the absence of current that is conventionally observed for other Maxwell solvers. The full algorithm is validated by conservation of energy and momentum when an electromagnetic pulse is launched onto a plasma ramp and by quantitative agreement with wave conversion of p-polarized electromagnetic wave onto a plasma ramp.

Transverse wave propagation in viscoelastic single-walled carbon nanotubes with surface effect based on nonlocal second-order strain gradient elasticity theory

Nowadays, the viscoelastic carbon nanotubes (CNTs) have been used as one of the most promising candidates for nanodevices (or nanoelectronics) and super-strong reinforcement fibers in polymer nanocomposites. In recent years there have been many papers that considered the effects of material length scales in the investigations of the material constants related on the structural parameters on the wave propagation in the viscoelastic CNTs. By using different approaches, for examples, Eringen’s differential nonlocal model, modified couple stress theory, and strain gradient theories, the stiffness softening or strengthening effect can be well predicted. However, the influence of the rapid stiffness enhancing effect on the wave characteristics of the viscoelastic CNTs is still not reported. To deal with such problem, this work aims to investigate the transverse wave propagation in viscoelastic single-walled carbon nanotubes (SWCNTs) adhered by surface material based on the nonlocal second-order strain gradient elasticity theory. The characteristic equation of wave motion of the viscoelastic SWCNTs with surface effect is systematically formulated to achieve the analytical dispersion relation between the wave frequency (or phase velocity) and the wave number. In the end, some most important conclusions are concluded.

Преобразование Дарбу для т-симметричной нелокальной комплексной модифицированной системы уравнений Кортевега-де Фриза

onlinear partial differential equations are widely used as models to describe physical phenomena in various fields of sciences such as fluid mechanics, solid-state physics, plasma physics, chemical physics, condensed matter physics, optical fibers, biology, and geochemistry. One of the nonlinear partial differential equations is the complex modified Korteweg-de Vries equation. This equation has been proposed as a model for the nonlinear evolution of plasma waves and is the physical model that incorporates the propagation of transverse waves in a molecular chain model, and in a generalized elastic solid. In this paper, we study the T-symmetry nonlocal complex modified Korteweg-de Vries system of equations. This nonlocal system is obtained by Ablowitz-Musslimani type of reduction and is respectively T-symmetric nonlocal cmKdV system of equations. The Ablowitz - Musslimani type of reductions arises from remarkably simple symmetry reductions of general AKNS scattering problems. The method of the Darboux transformation is applied to obtain exact solutions.

ТОЧНЫЕ РЕШЕНИЯ УРАВНЕНИЯ ХИРОТА С ПОМОЩЬЮ МЕТОДА СИНУС–КОСИНУС

Nonlinear partial differential equations of mathematical physics are considered to be major subjects in physics. The study of exact solutions for nonlinear partial differential equations plays an important role in many phenomena in physics. Many effective and viable methods for finding accurate solutions have been established. In this work, the Hirota equation is examined. This equation is a nonlinear partial differential equation and is a combination of the nonlinear Schrödinger equation and the complex modified Korteweg–de Vries equation. The nonlinear Schrödinger equation is the physical model and occurs in various areas of physics, including nonlinear optics, plasma physics, superconductivity, and quantum mechanics. The complex modified Korteweg–de Vries equation has been applied as a model for the nonlinear evolution of plasma waves and represents the physical model that incorporates the propagation of transverse waves in a molecular chain model and in a generalized elastic solid. To find exact solutions of the Hirota equation, the sine-cosine method is applied. This method is an effective tool for searching exact solutions of nonlinear partial differential equations in mathematical physics. The obtained solutions can be applied when explaining some of the practical problems of physics.

A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals

In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM.

Propagation of transverse waves in a pre-stressed dissipative plate under influence of thermal stress, electromagnetic field and couple stress

Abstract The effects of thermal stress, electric field, magnetic field with couple stress on the propagation of shear waves in an anisotropic incompressible dissipative plate is studied. The frequency equation for the problem that determines the phase velocity of the shear waves using linear inhomogeneties has been obtained. Several particular cases are also examined. The numerical calculations are carried out for distinct values of anisotropic factor, initial stress parameter, electric field parameter, magnetic field parameter, couple stress parameter as well as wave number and the results are shown graphically using MATLAB. It is observed that the variation in parameters associated with anisotropy of the medium directly affects the propagation of transverse waves in the medium. Also, the velocity of transverse waves can be obviously tuned by the thermal effects, couple stress and electromagnetic field.

Estimation of parameters of the space tethered system for stable load transportation along the tether

In this work the problem of stability of the space tethered system for load transportation along the tether is considered. The whole system is designed to “clean” orbits of space debris. The system consists of a «big » satellite moving along a circular or slightly elliptical orbit (orbital station or some satellite for orbital missions where fragments of space debris can be captured), two endmasses (counterweights, space debris hubs) and tethers between them. Containers (loads) with space debris can be transported along the tethers. One of the main problems of stable working of the whole system and load transportation is longitudinal and transverse wave propagation and vibrations of the tethers. The conditions on the system parameters (initial speed, masses of system's parts) are obtained for stable movement of the containers and the tethers. Analytical research for conditions of the system for stable load transportation along the tether was made using non-linear partial differential equations for tether movement.

Effect of coronal loop structure on wave heating through phase mixing

Context. The mechanism(s) behind coronal heating still elude(s) direct observation and modelling of viable theoretical processes and the subsequent effect on coronal structures is one of the key tools available to assess possible heating mechanisms. Wave heating via the phase mixing of magnetohydrodynamic (MHD) transverse waves has been proposed as a possible way to convert magnetic energy into thermal energy, but MHD models increasingly suggest this is not an efficient enough mechanism. Aims. We modelled heating by phase mixing transverse MHD waves in various configurations in order to investigate whether certain circumstances can enhance the heating sufficiently to sustain the million degree solar corona and to assess the impact of the propagation and phase mixing of transverse MHD waves on the structure of the boundary shell of coronal loops. Methods. We used 3D MHD simulations of a pre-existing density enhancement in a magnetised medium and a boundary driver to trigger the propagation of transverse waves with the same power spectrum as measured by the Coronal Multi-Channel Polarimeter. We consider different density structures, boundary conditions at the non-drive footpoint, characteristics of the driver, and different forms of magnetic resistivity. Results. We find that different initial density structures significantly affect the evolution of the boundary shell and that some driver configurations can enhance the heating generated from the dissipation of the MHD waves. In particular, drivers coherent on a larger spatial scale and higher dissipation coefficients can generate significant heating, although it is still insufficient to balance the radiative losses in this setup. Conclusions. We conclude that while phase mixing of transverse MHD waves is unlikely to sustain the thermal structure of the corona, there are configurations that allow for an enhanced efficiency of this mechanism. We provide possible signatures to identify the presence of such configurations, such as the location of where the heating is deposited along the coronal loop.

Dispersion relation for transverse waves in pre-stressed irregular single-walled carbon nanotubes

This article studies the dispersion relation of transverse waves in an initially stresses single-walled carbon nanotube (SWCNT) with surface irregularity using Flügge shell theory. Taking into account the effects of surface irregularity and initial stresses, propagation of transverse waves is studied and dispersion curves are plotted for optical transverse waves in several figures. The effects of surface irregularity and initial stresses are confirmed by comparing obtained numerical results with those in cases of uniform and initial stress–free SWCNT. Obtained results turn out that, the increase of irregularity parameter increases the phase velocity of transverse waves, while the increase of the initial stress parameter decreases the phase velocity of transverse waves propagating in SWCNTs. To the author best knowledge, effects of surface irregularity and initial stresses on transverse waves propagation, especially propagation in single-walled carbon nanotubes, have not been done before. The previous studies were devoted to the uniform and initial stresses-free carbon nanotubes. It should be emphasized that the transverse waves propagation in pre-stressed and irregular single-walled carbon nanotubes is novel, workable, and at the beginning of the path. İn this manner, understanding the influences of surface irregularity as well as initial stresses on the phase velocity of transverse waves may serve as useful references for the applications and designs of nano oscillators and nanodevices, in which single-walled carbon nanotubes act as the most prevalent nanocomposite structural element.

Damage Severity Estimation of Timber Poles Using Stress Wave Propagation and Wavelet Entropy Evolution

AbstractTimber poles are widely used in electricity transmission and telecommunication sectors throughout the world. The stress wave propagation for the condition assessment of timber poles is identified as a promising non-destructive testing (NDT) technique due to its simplicity and cost-effectiveness compared to other traditional methods. In this paper, a novel damage severity evaluation criterion for timber poles is proposed on the basis of short-time wavelet entropy of the reflected stress waves. The stress waves are generated by transverse impacts close to the ground level of the pole. The reflected stress waves are recorded and processed in the time frequency domain using the discrete wavelet transform. The decomposed signal components using discrete wavelet analysis are used to determine the wavelet entropy. The wavelet entropies of intact and damaged poles are compared to obtain the relative wavelet entropy (RWE) for damage severity estimation. Further, a numerical model for an in situ pole system is developed to simulate the transverse stress wave propagation and to evaluate the capability of the proposed defect severity estimation method. The developed numerical model is validated with experimental data from controlled testing and the data from field tests. The validated numerical model is then used to simulate different defect scenarios. The wavelet entropy is sensitive to the damage severity in timber poles and can be used as an effective tool to evaluate the severity of damages.

Modelling Propagating Bloch Waves in Magnetoelectroelastic Phononic Structures with Kagomé Lattice Using the Improved Plane Wave Expansion

We studied the dispersion diagram of a 2D magnetoelectroelastic phononic crystal (MPnC) with Kagomé lattice. The MPnC is composed of BaTiO3–CoFe2O4 circular scatterers embedded in a polymeric matrix. The improved plane wave expansion (IPWE) approach was used to calculate the dispersion diagram (only propagating modes) of the MPnC considering the classical elasticity theory, solid with transverse isotropy and wave propagation in the xy plane. Complete Bragg-type forbidden bands were observed for XY and Z modes. The piezoelectric and the piezomagnetic effects significantly influenced the forbidden band widths and localizations. This investigation can be valuable for elastic wave manipulation using smart phononic crystals with piezoelectric and piezomagnetic effects.

Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics

An eigenvalue problem for Maxwell’s equations with anisotropic cubic nonlinearity is studied. The problem describes propagation of transverse magnetic waves in a dielectric layer filled with (nonlinear) anisotropic Kerr medium. The nonlinearity involves two non-negative parameters a, b that are usually small. In the case a = b = 0 one arrives at a linear problem that has a finite number of solutions (eigenvalues and eigenwaves). If a > 0, b ⩾ 0, then the nonlinear problem has infinitely many solutions; only a finite number of these solutions have linear counterparts. This shows that perturbation theory methods are inapplicable to study the problem in this case. For a = 0, b > 0 the nonlinear problem has a finite number of solutions; in this case each solution has a linear counterpart. Asymptotic distribution of the eigenvalues is found, periodicity of the eigenfunctions is proved and exact formula for the period is found, zeros of the eigenfunctions are determined, and a (nonlinear) eigenvalue comparison theorem is proved. Numerical experiments are presented.

Equations and fundamental characteristics of transverse waves propagating in fluid-saturated porous materials

The main purpose of the paper is to present an extended analysis of the coupled system of linear equations describing wave propagation in fluid-saturated porous materials used for the determination of their fundamental characteristics. The present paper is the first part, mainly devoted to the analysis of the system of equations describing transverse wave propagation. The analysis of equations for compressional waves will be presented in a separate paper. The starting point of considerations are nonlinear equations describing the dynamic behavior of the medium formulated in the spirit of the theory of interacting continua in which parameters of isotropic pore space structure are explicitly present in the model, and constitutive equations are formulated for each physical component separately. They contain all fundamental mechanical couplings between components of this medium in the general nonlinear form and of clear physical meaning. Linear equations of this theory for barotropic fluid and hyperelastic skeleton are the subject of the analysis performed in the paper. They are equivalent to Biot's model, widely used in the description and analysis of wave propagation in saturated porous materials and wave interaction with the boundary of such media. A new method of analysis is proposed in the paper, based on spectral decomposition of the system of equations in the two-dimensional vector space of rotations of solid and fluid particles. It is shown that each choice of the base in this vector space defines the division of the medium into two new components and transforms the system of equation to the form describing the dynamic behavior of these components, and the requirement of the basic dynamic properties of the medium to be invariant in each chosen base uniquely determines the mass densities and bulk modules of the new components. Such an approach enabled decomposition of the system of equations for particle rotations to two uncoupled scalar equations, the only one of which describes propagation of the transverse wave. This also allowed obtaining expressions characterizing transverse wave propagation in fluid-saturated porous materials: velocity, effective mass densities and wave impedance of the medium associated with this wave and its frequency characteristics: phase velocity and attenuation coefficient. It is shown that both frequency characteristics are fully defined by the effective mass densities of both components associated with the transverse wave, the tortuosity of the pore space, and the coefficient characterizing the viscous interaction of the fluid with the skeleton.

Elastoplastic deformation processes in materials with cubic symmetry of properties

Some results of studies of the processes of elastoplastic deformation in a material with a cubic symmetry of elastic and plastic properties are presented. Cases of shock loading of a cylinder from a single crystal alloy on a rigid target (Taylor test) along three different directions ([111], [001] and [011]) are considered. These directions are characterized by the fact that along them propagation of longitudinal and transverse waves with different speeds is possible. Using the example of solving the Taylor test problem, it is shown that the differences in elastic properties along the [011] directions in cubic crystals determine elastoplastic deformations.

On the Calculation of the Spectral Bands of One-Dimensional Photonic Crystals

In this work we consider the propagation of transverse electromagnetic waves in one-dimensional photonic crystals consisting of periodic arrays of slabs. On the basis of the Floquet theory we obtain the characteristic function of the periodic medium, which defines the photonic bands of the crystal. The characteristic function is constructed from the monodromy matrices of the slabs. Entries of monodromy matrices are explicitly given as power series of the spectral parameter. The present analysis can be applied not only to homogeneous slabs, but also to slabs with varying refractive indexes. The power series representation of the entries of monodromy matrices leads to an effective numerical method for the calculation of the spectral bands of one-dimensional photonic crystals.

A Study on Transverse Magnetic Wave Propagation Characteristics of Dielectric Wrapped Wire

The transverse magnetic wave propagation characteristics of the dielectric wrapped wires are studied. The transverse magnetic wave transmission model of a dielectric wrapped wire is revised based on the variable seperation method. The spatial relationship between electromagnetic wave emission and reflection is obtained. An experiment is developed using the new actuator and coupler. The results show that the surface wave guide formed by a single wire wrapped in a low loss medium can ben used as a high speed data transmission channel.