Quasi-longitudinal Waves Research Articles

Initial Excited State and Divergence of Wave Beams as Factors Responsible for the Realization of the Wave Process that Controls the Growth of Transformation Twins

In the dynamic theory of martensitic transformations the wave mechanism of growth of martensite crystals is controlled by the overlap of wave beams of quasi-longitudinal (or longitudinal) waves that carry deformation of the “tension–compression” type in orthogonal directions. The appearance of wave beams is considered a consequence of the appearance of the initial excited (vibrational) states. The presence of the transformation twins is interpreted as the result of the matched propagation of relatively long-wave (𝓁 waves) and short-wave (s waves) displacements. With the aid of the Fourier transforms, an analysis was performed of the influence of the diffraction divergence of a pair of orthogonal wave beams on the formation of a region of their superposition, including the limiting case of narrow beams with one of the transverse dimensions of the front less than λ/2, where λ is the wavelength. The connection of the distribution of the amplitudes of spatial harmonics with the configuration of the initial excited state is discussed.

Laser Doppler vibrometer and bending wave based dynamic material characterization of organic aerogel panels

To what extent aerogels are useful in noise and vibration control applications remains an open question. With the advent of low cost, facile synthesis, ductile, and purely polymeric aerogels, the prospects are alluring. Within the polyurea family of aerogels, multiple nanomorphologies exist with some being amenable to rheological paradigms. An inverse problem approach is applied to tease out material parameters with the aid of viscoelastic models and a pair of dynamic characterization techniques. A specialized transfer function driven, quasi-longitudinal wave eliciting, material characterization setup is refined and augmented with laser Doppler vibrometry. This effort seeks to improve repeatability and increase frequency limits, two factors whose absences plague many schemas. Intriguing properties previously uncovered with this method, such as broadband negative dynamic mass, are reexamined. In tandem, a bending wave excitation arrangement and characterization method is introduced. Low bending and quasi-longitudinal phase speeds in addition to high static and low dynamic moduli shed light on the enhanced noise and vibration control performance reported in the literature. This paper discusses the dynamic measurement method and possible applications which may benefit from this unique combination of properties.

Reflection of plane waves in an anisotropic magnetothermoelastic diffusive medium with temperature dependent properties

In this article, a model of two dimensional problem of generalized thermoelasticity for an anisotropic magnetothermoelastic diffusive medium under the effect of temperature dependent properties is established. The enunciation is applied to generalized thermoelasticity theory based on Green-Lindsay model. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD), and quasi-transverse wave (qSV) in the medium. Amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programing. Effects of temperature dependent properties, magnetic and diffusion parameters on the amplitude and energy ratios are depicted graphically. Expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during the reflection phenomenon, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.

Strong nonlinearity, anisotropy, and solitons in a lattice with holonomic constraints

The nonlinear dynamics of a crystal lattice where the atoms are positioned along parallel rods is studied. They may move only in one direction and this constraint leads to the appearance of nonlinearity even the forces between the atoms obey the linear Hooke’s law. This nonlinearity turns out to be strong. The equations of motion of the individual lattice atoms are written, and. in the continuum limit when the lattice period is small in comparison with the wavelength, a new strongly nonlinear partial differential equation is derived. The waves traveling in the direction orthogonal to the rods are purely transverse slow waves, governed by an equation of the Heisenberg type. In the direction along the rods, a fast purely longitudinal wave can propagate. In general, when the wave travels at an arbitrary angle, it is neither purely longitudinal nor transverse and the periodic structure exhibits anisotropic properties. Their velocity depends strongly on the direction of propagation and the structure exhibits properties similar to a skeletal muscle with stretched fibers. Special attention is paid to the soliton solutions of this equation and their behavior is studied. For non-stationary quasi-longitudinal waves, a new evolution equation, rich in symmetries, is derived. One of the solutions with a fixed transverse structure is described by elliptic integrals and evolves in accordance with a cubic nonlinear equation of the Klein–Gordon type.

Propagation of plane waves in an orthotropic magneto-thermodiffusive rotating half-space

The present article is aimed at studying the reflection phenomena of plane waves in a homogeneous, orthotropic, initially stressed magneto-thermoelastic rotating medium with diffusion. The enuciation is applied to generalized thermoelasticity based on Lord-Shulman theory. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD) and quasi-transverse wave (qSV) in the medium. The amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The effects of rotation, initial stress, magnetic and diffusion parameters on the amplitude ratios are depicted graphically. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.

Вырожденная структура двойников превращения и оценка плотности дислокаций мартенситных кристаллов

Abstract In the dynamic theory of martensitic transformations, the wave mechanism of controlling martensite crystal growth is determined by the superposition of wave beams of quasi-longitudinal (or longitudinal) waves carrying the “tensile–compression” deformation in the orthogonal directions. The wave beam formation is considered to be a result of the formation of excited (vibrational) states. The existence of transformation twins is interpreted as a result of a matched propagation with respect to long-wave ( l waves) and short-wave ( s waves) shifts. The matching condition is analyzed for the γ–α martensitic transformation in iron-base alloys. It is shown for the first time that the transition to a degenerate twin structure with the allowance for the medium discreteness enables one to estimate the dislocation density in crystals with habit {557}, which agrees with that observed experimentally.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

Abstract The present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

Reflection and refraction of plane waves at the loosely bonded common interface of piezoelectric fibre-reinforced and fibre-reinforced composite media

The rapid development of the modern age has increased the urge of using composite structures having applications in the realm of various engineering fields. Specifically, fibre-reinforced piezoelectric composites are in the forefront of the present era because of its light weight, great strength and hence improved performance over the piezoelectric materials alone. Therefore, the present paper delves with the problem of reflection and refraction of plane waves when it is incident at the interface of a Piezoelectric Fibre-reinforced Composite (PFRC) medium and Fibre-reinforced Composite (FRC) medium. It is assumed that the media are loosely bonded to each other and are under horizontal initial stresses. It is established that the boundary conditions are satisfied by the set of three coupled waves associated with the PFRC medium (namely quasi-longitudinal wave (qP), quasi-transverse wave (qSV), electrostatic wave (EA)) and two coupled waves associated with the FRC medium (namely quasi-longitudinal wave (qP), quasi-transverse wave (qSV)). The amplitude ratio of reflected and refracted waves are obtained with the aid of suitable boundary conditions at the common interface of the two media. The effect of anisotropy, initial stresses and loose bonding on the amplitude ratio are studied numerically and demonstrated by means of graphs. The effect of anisotropy is also studied on the slowness curves, plotted in slowness surface. Moreover, the relation for energy partition is also derived and it is established that the total normal energy flux balance at the interface is unity.

GENERAL SCALARIZATION METHOD OF DYNAMIC ELASTIC FIELDS IN TRANSVERSALLY ISOTROPIC MEDIA AND ITS NEW APPLICATIONS

Introduction. An efficient technique of tensor field scalarization is successfully used while investigating tensor elastic fields of displacements, stresses and deformations in the layered structures of different materials, including transversally isotropic composites. These fields can be expressed through the scalar potentials corresponding to the quasi-longitudinal, quasi-transverse, and transverse-only waves. Such scalarization is possible if the objects under consideration are tensors relating to the subgroup of general coordinate conversions, when the local affine basis has one invariant vector that coincides with the material symmetry axis of the material. At this, the known papers consider structures where this vector coincides with the normal to the boundary between layers. However, other cases of the mutual arrangement of the material symmetry axis of the material and the boundaries between layers are of interest on the practical side.Materials and Methods. The work objective is further development of the scalarization method application in the boundary value problems of the dynamic elasticity theory for the cases of an arbitrary arrangement of the material symmetry axis relative to the boundary between layers. The present research and methodological apparatus are developed through the general technique of scalarization of the dynamic elastic fields of displacements, stresses and strains in the transversally isotropic media.Research Results. New design ratios for the determination of the displacement fields, stresses and deformations in the transversally isotropic media are obtained for the cases of an arbitrary arrangement of the material symmetry axes of the layer materials with respect to the boundaries between layers. Discussion and Conclusions. The present research and methodological apparatus are successfully used in determining the stress-strain state in the layered structures of transversally isotropic materials, and in analyzing the diagnosis results of the state of the plane-layered and layered cylindrical structures under operation.

The dispersion and attenuation of the multi-physical fields coupled waves in a piezoelectric semiconductor

The dispersion and attenuation features of the multi-physical fields coupled waves propagating in an infinite piezoelectric semiconductor and the reflection problem at a boundary which is mechanically free, electrically insulation and the dielectrically open circuit are studied in this paper. Different from the classic dielectric piezoelectric medium, there are four kinds of coupled elastic waves, i.e. the quasi-longitudinal wave (QP), the quasi-traverse wave (QSV), the electric–acoustic wave (EA) and the electron or hole carriers wave (CP), in a piezoelectric semiconductor. The influences of the steady carrier density and biasing electric field upon the dispersion and attenuation features of these coupled elastic waves and the reflection amplitude ratios are studied numerically. The energy flux of each wave and the interaction energy fluxes among all waves are also calculated, and the energy flux balance is checked. It is found that the piezoelectric semiconductor behaves like the viscoelastic solid to carry a decaying wave. The steady carrier density and biasing electric field have significant influences on the dispersion and attenuation features and can be used to regulate the propagation of the coupled elastic waves.

Axisymmetric Waves in Prestressed Incompressible Laminated Composite Materials with Sliding Layers

A statement and solving technique for the problem of axisymmetric wave propagation in an incompressible laminated composite material with initial stresses are considered in the framework of the three-dimensional linearized theory of elasticity for prestressed solids. The case of wave propagation along the layers is considered. The dispersion equation for quasi-longitudinal waves as well as the long-wave approximation for it are derived for both perfectly bonded and sliding contact of the layers. Numerical analysis is carried out for dispersion equations of elastic material that are described by a Treloar-type potential. The effect of initial stresses is studied for axisymmetric harmonic waves.

Anisotropy of acousto–optic figure of merit in lithium tetraborate crystals

We analyse anisotropy of acousto–optic figure of merit (AOFM) for Li2B4O7 crystals in order to estimate the prospects of these crystals in acousto–optics. We find that the maximal AOFM, 3.44 × 10−15 s3/kg, is peculiar for the isotropic acousto–optic interaction of the incident ordinary optical wave with the quasi-longitudinal acoustic wave. For the case of anisotropic diffraction in Li2B4O7, the maximum 1.87 × 10−15 s3/kg can be reached using the interaction of the extraordinary optical wave with the quasi-longitudinal acoustic wave. The case of collinear diffraction is characterized by small AOFMs, with the largest value 0.26 × 10−15 s3/kg.

Scattering phenomenon of qP wave at the interface of FGPM and piezoelectric medium

ABSTRACTThe present paper aims to investigate the reflection and refraction of quasi-longitudinal (qP) waves at the welded interface between rotating piezoelectric and FGPM half-spaces. The equation of motion and constitutive relations for both the media have been used to derive the expressions for reflection and refraction coefficients for various reflected and transmitted waves. Also, the energy ratios (dependent on incident angle) are calculated. Moreover, the sum of all energy ratios is approximately unity at each value of incident angle which ensures that the law of energy conservation at the interface. Moreover, it is observed that the reflection and refraction coefficients of various reflected and transmitted waves depend not only on the incident angle but also on the material constants of the medium, parameters of the electric potential, initial stress as well as rotation parameters of the two media. A particular case has been deduced to validate the present study. This investigation may have possible applications in the areas of signal processing, transduction, frequency shifting (a change in the velocity of surface waves and controlling the selectivity of a filter compensation) of individual devices.

Numerical analysis and experimental observation of ultrasonic wave propagation in CFRP with curved fibers

The relationship between the propagation directions of ultrasonic wave and the direction of the principal axis of anisotropy in uni-directional CFRP with straight fiber is well known. However, the behavior of ultrasonic wave in CFRP with curved fibers is not clarified in details. In this paper, numerical analyses using the finite difference method were conducted to visualize the behavior of ultrasonic waves in CFRP with concentrically curved fibers. Numerical simulation results showed the energy of quasi-longitudinal ultrasonic wave curved along the fiber direction. In order to confirm the analytical result, CFRP specimen with curved fibers were prepared by utilizing 3D-printer and the behavior of ultrasonic propagation was observed by using Laser ultrasonic system. The observed results confirmed the analytical results that the ultrasonic wave curved along carbon fibers.

Piezo-optic and elasto-optic properties of monoclinic triglycine sulfate crystals.

For the first time, to the best of our knowledge, we have experimentally determined all of the components of the piezo-optic tensor for monoclinic crystals. This has been implemented on a specific example of triglycine sulfate crystals. Based on the results obtained, the complete elasto-optic tensor has been calculated. Acousto-optic figures of merit (AOFMs) have been estimated for the case of acousto-optic interaction occurring in the principal planes of the optical indicatrix ellipsoid and for geometries in which the highest elasto-optic coefficients are involved as effective parameters. It has been found that the highest AOFM value is equal to 6.8×10-15 s3/kg for the case of isotropic acousto-optic interaction with quasi-longitudinal acoustic waves in the principal planes. This AOFM is higher than the corresponding values typical for canonic acousto-optic materials, which are transparent in the deep ultraviolet spectral range.

S-wave singularities in tilted orthorhombic media

Quasi S-wave propagation in low-symmetry anisotropic media is complicated due to the existence of point singularities (conical points) — points in the phase space at which slowness sheets of the split S-waves touch each other. At these points, two eigenvalues of the Christoffel tensor (associated with the quasi S-waves) degenerate into one and polarization directions of the S-waves, which lay in the plane orthogonal to the polarization of the quasi longitudinal wave, are not uniquely defined. In the vicinity of these points, slowness sheets of the S-waves have complicated shapes, leading to rapid variations in polarization directions, multipathing, and cusps and discontinuities of the shear wavefronts. In a tilted orthorhombic medium, the point singularities can occur close to the vertical, distorting the traveltime parameters that are defined at the zero offset. We have analyzed the influence of the singularities on these parameters by examining the derivatives of the slowness surface up to the fourth order. Using two orthorhombic numerical models of different shear anisotropy strength and with different number of singularity points, we evaluate the complexity of the slowness sheets in the vicinity of the conical points and analyze how the traveltime parameters are affected by the singularities. In particular, we observe that the hyperbolic region associated with the singularity points in a model with moderate to strong shear anisotropy spans over a big portion of the slowness surfaces and the traveltime parameters are strongly affected outside the hyperbolic region. In general, the fast shear mode is less affected by the singularities; however, the effect is still very pronounced. Moreover, the hyperbolic region associated with the singularity points on the slow S-wave affects the slowness surface of the fast mode extensively. In addition, we evaluate a relation between the slowness surface Gaussian curvature and the relative geometric spreading, which has anomalous behavior due to the singularities.

Surfatron accelerator in the local interstellar cloud

Taking into account results of numerous experiments, the variability of the energy spectra of cosmic rays (protons and helium nuclei) in the energy range of 10 GeV to ~107 GeV is explained on the basis of a hypothesis of the existence of two variable sources close to the Sun. The first (soft) surfatron source (with a size of ~100 AU) is located at the periphery of the heliosphere. The second (hard) surfatron source (with a size of ~1 pc) is situated in the Local Interstellar Cloud (LIC) at a distance of <1 pc. The constant background is described by a power-law spectrum with a slope of ~2.75. The variable heliospheric surfatron source is described by a power-law spectrum with a variable amplitude, slope, and cutoff energy, the maximum cutoff energy being in the range of E СН/Z < 1000 GeV. The variable surfatron source in the LIC is described by a power-law spectrum with a variable amplitude, slope, and cut-off energy, the maximum cut-off energy being E СL/Z ≤ 3 × 106 GeV. The proposed model is used to approximate data from several experiments performed at close times. The energy of each cosmic-ray component is calculated. The possibility of surfatron acceleration of Fe nuclei (Z = 26) in the LIC up to an energy of E CL ~ 1017 eV and electron and positrons to the “knee” in the energy spectrum is predicted. By numerically solving a system of nonlinear equations describing the interaction between an electromagnetic wave and a charged particle with an energy of up to E/Z ~ 3 × 106 GeV, the possibility of trapping, confinement, and acceleration of charged cosmic-ray particles by a quasi-longitudinal plasma wave is demonstrated.

P-wave ray velocities and the inverse acoustic problem for anisotropic media

The specific features of the calculation of ray velocities of quasi-longitudinal waves in anisotropic media have been considered. A technique for calculating elastic constants using P-wave ray velocities measured in an ultrasonic experiment on spherical samples is presented. It is shown by an example of tabular data that elastic constants С 11, С 22, and С 33 and combinations of constants (С 12 + 2С 66), (С 13 + 2С 55), (С 23 + 2С 44), (С 14 + 2С 56), (С 25 + 2С 46), and (С 36 + 2С 45) can be calculated most accurately for the general case of anisotropic media with elastic properties of arbitrary symmetry. Since the determining system of equations is illconditioned, the values of elastic constants entering these combinations depend on the choosed initial approximation.

Analysis of plane waves in anisotropic piezothermoelastic diffusive medium

Purpose – The purpose of this paper is to study the propagation of harmonic plane waves in a homogeneous anisotropic piezothermoelastic diffusive medium. Design/methodology/approach – After developing the mathematical model and theoretical analysis of the problem, computational work has been performed to study the different characteristics of the plane harmonic waves. Findings – The existence of waves namely, quasi-longitudinal wave (QP), quasi-thermal wave and quasi-mass diffusion wave have been found which propagates in an anisotropic piezothermoelastic diffusive medium. The different characteristics of waves like phase velocity and attenuation quality factor are computed numerically and presented graphically to show the piezoelectric effect. Originality/value – A significant piezoelectric effects have been observed on the different characteristics of the waves in an anisotropic piezothermoelastic diffusive medium.

In-Situ Characterization of Isotropic and Transversely Isotropic Elastic Properties Using Ultrasonic Wave Velocities

Abstract In this paper, a one-sided, in situ method based on the time of flight measurement of ultrasonic waves was described. The primary application of this technique was to non-destructively measure the stiffness properties of isotropic and transversely isotropic materials. The method consists of generating and receiving quasi-longitudinal and quasi-shear waves at different through-thickness propagation angles. First, analytical equations were provided to calculate the ultrasonic wave velocities. Then, an inverse method based on non-linear least square technique was used to calculate the stiffness constants using the ultrasonic wave velocities. Sensitivity analysis was performed by randomly perturbing the velocity data, thus observing the effects of perturbations on the calculated stiffness constants. An improved algorithm was proposed and tested to reduce the effects of random errors. Based on the sensitivity analysis, minimum number of angles required to inversely calculate the stiffness constants were suggested for isotropic and transversely isotropic material. The method was experimentally verified on an isotropic 7050-T7451 aluminum with two different thicknesses and a transversely isotropic composite laminate fabricated using 24 plies of CYCOM 977-2 12 k HTA unidirectional carbon fiber reinforced polymer (CFRP) prepregs. The results demonstrated that this technique is able to accurately measure the material properties of isotropic material. As for the transversely isotropic material, this method was able to accurately measure the material properties if the experimental errors can be reduced to less than 1 %.