Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.     

Flexural and transversal wave motion in homogeneous isotropic thermoelastic plates by using asymptotic method

The present investigation is concerned with the flexural and transversal wave motion in an infinite, transversely isotropic, thermoelastic plate by asymptotic method. The governing equations for the flexural and transversal motions have been derived from the system of three-dimensional dynamical equations of linear theory of coupled thermoelasticity. The asymptotic operator plate model for free vibrations; both flexural and transversal, in a homogenous thermoelastic plate leads to fifth degree and cubic polynomial secular equations, respectively, that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. All the coefficients of differential operator have been expressed as explicit functions of the material parameters. The velocity dispersion equations for the flexural and transversal wave motion have been deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity have also been derived. The thermoelastic Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established with that of asymptotic method. The dispersion curves for phase velocity, group velocity and attenuation coefficient of various flexural and transversal wave modes are shown graphically for aluminum-epoxy material elastic and thermoelastic plates.     

Ultrasonic waves in crystals with charged dislocations

A system of equations for charged dislocations, where the quadratic nonlinear terms are taken into account, is derived using the variational principle. This system describes the propagation of ultrasonic (US) waves in crystals with charged dislocations. From the linearized system of equations a linear dispersion equation is derived. Formulas for the phase linear velocity of the wave and the absorption coefficient are obtained, which show essential influence of charged dislocations and electrical properties of media on the mentioned quantities. For a nonlinear US wave an equation for the amplitude of the first harmonic is derived and, as a consequence, expressions are obtained for the nonlinear velocity of the US wave, for the attenuation of the first harmonic's amplitude, and for phase variation.     

Linear and nonlinear waves in crystals with charged dislocations

Based on the principle, a set of equations describing ultrasonic wave propagation in a dielectric crystal with charged dislocations has been derived. The linear dispersion relation has been derived, and the ultrasonic wave velocity and absorbance have been determined. In the case of the nonlinear ultrasonic wave, equations for its amplitude damping and phase variation have been obtained.     

黏弹介质包裹的充液管道中低频轴对称波传播特性

研究埋地充液管道中低频轴对称波传播特性.将土壤考虑为黏弹介质,结合Kennard薄壳方程和Kelvin-Voigt线性黏弹性模型,引入土壤载荷矩阵,推导出土-管滑移情形下流体主导波和管壁压缩波的相速度表达式.通过数值模拟计算得到流体主导波和管壁压缩波的频散和衰减曲线并进行可靠性验证,分析两种波引起的管壁径向位移之比,讨...     

Theoretical Study for Folded Waveguide Traveling Wave Tube

A wideband folded waveguide traveling-wave tube (TWT) amplifier has advantages of simpler coupling structures and robust structure over the conventional helix TWT. The phase velocity of waves in folded waveguide is slowed down to the velocity of electron beam. Slow-wave interaction with the electron beam in folded waveguide is studied in a linear fashion. For a cold beam, the linear theory predicts a gain of 2 dB/cm and a bandwidth of 37% at the center frequency of 14 GHz. A closed algebraic dispersion relation for the frequency and the axial phase shift per period is obtained using an equivalent circuit model. Numerical solution calculated from the dispersion relation and three-dimensional electromagnetic code, HFSS simulations predict a mode coalescing in the folded waveguide. And a theoretical phase velocity prediction of the electromagnetic wave in this circuit is verified by HFSS simulations.     

Investigation of Ion Drift Waves in the PSI‐2 Using Langmuir‐Probes

The properties of on drift waves observed in the rotating magnetized plasma column of the PSI‐2 are analysed. Their parallel wave numbers are found to be nearly zero, the measured azimuthal dispersion relation is approximately linear, and the azimuthal phase velocity is nearly equal to the azimuthal on drift velocity. Furthermore, the potential fluctuations always lag behind the density fluctuations with a phase shift slightly below π. A simple analytical model, describing the potential‐and density distribution of the ion drift wave, shows the underlying mechanism of the on drift instability. Finally, a classification of the observed on drift instability is given.     

Nonlinear theory of electrostatic baryonic waves in ambiplasma

A collisionless nonmagnetized ambiplasma consisting of Maxwellian gases of protons, antiprotons, electrons, and positrons is considered. The dispersion relation for electrostatic baryonic waves is derived and analyzed and exact expressions for the linear wave phase velocities are obtained. Two types of such waves are shown to be possible in ambiplasma: acoustic and plasma ones. Analysis of the dispersion relation has allowed the ranges of parameters in which nonlinear solutions should be sought in the form of solitons to be found. A nonlinear theory of baryonic waves is developed and used to obtain and analyze the exact solution to the basic equations. The analysis is performed by the method of a fictitious potential. The ranges of phase velocities of periodic baryonic waves and soliton velocities (Mach numbers) are determined. It is shown that in the plasma under consideration, these ranges do not overlap and that the soliton velocity cannot be lower than the linear velocity of the corresponding wave. The profiles of physical quantities in a periodic wave and a soliton (wave scores) are plotted.     

Guided wave dispersion curves for a bar with an arbitrary cross-section,a rod and rail example

Theoretical and experimental issues of acquiring dispersion curves for bars of arbitrary cross-section are discussed. Since a guided wave can propagate over long distances in a structure, guided waves have great potential for being applied to the rapid non-destructive evaluation of large structures such as rails in the railroad industry. Such fundamental data as phase velocity, group velocity, and wave structure for each guided wave mode is presented for structures with complicated cross-sectional geometries as rail. Phase velocity and group velocity dispersion curves are obtained for bars with an arbitrary cross-section using a semi-analytical finite element method. Since a large number of propagating modes with close phase velocities exist, dispersion curves consisting of only dominant modes are obtained by calculating the displacement at a received point for each mode. These theoretical dispersion curves agree in characteristic parts with the experimental dispersion curves obtained by a two-dimensional Fourier transform technique.     

Study of Love-type wave propagation in an isotropic tri layers elastic medium overlying a semi-infinite elastic medium structure

This paper deals with the propagation of Love-type wave in a composite isotropic structure embraced of tri layers elastic medium overlying a semi-infinite elastic medium. The heterogeneity is caused due to the variation of linear, exponential, and quadratic with respect to the depth. Modified Bessel function with Debye Asymptotic Expansion approach is used to achieve closed form of dispersion equation analytically and found to be in well agreement to the classical Love wave equation. Numerical computation has been carried out to accomplish the graphical demonstration to unravel some important peculiarities of wave number associated in presence or absence of layers medium and effect of heterogeneities on phase velocity of Love-type wave.     

A guided wave technique for the characterization of highly attenuative viscoelastic materials

The measurement of the acoustic properties of highly attenuative materials such as bitumen is very difficult. One possibility is to use measurements of the extent to which filling a cylindrical waveguide with the material affects the dispersion relationship of the cylinder. Torsional modes have been excited using piezoelectric transducers placed at one end of the cylinder, while the phase velocity and attenuation spectra have been measured by means of laser scanning. At each frequency, under the hypothesis of linear viscoelasticity, the phase velocity and attenuation of the fundamental torsional mode have been calculated as a function of the bulk shear velocity and the bulk shear attenuation of the inner core at that frequency. The resulting phase velocity and guided wave attenuation contour plots have been employed for deriving the unknown shear properties from the measured velocity and attenuation of the guided wave. The monochromaticity of the approach has not required a particular frequency dependence of the material properties to be assumed. Results for bitumen are given.     

Evolution of a langmuir wave in a weakly inhomogeneous plasma with a positive concentration gradient

Spatial evolution of a Langmuir wave excited by external sources in a weakly inhomogeneous electron plasma without external sources is considered for a small positive gradient of the plasma concentration in the direction of propagation of the wave. At the first state of the evolution, the dispersion of the wave is close to linear. When the phase velocity is doubled, the second stage of the evolution begins. The wave loses its individuality and becomes a hybrid of two waves. Its profile acquires the shape of an alternating sequence of fragments of these waves. The wave dispersion is determined by the dispersion of each fragment. In the course of evolution, the spacing between the equilibrium values of the wave fragments increases; as a result, the wave decays into two waves, which are also loaded by trapped electrons. Prior to decay, the humps of the wave become steeper; as a result, at the instant of the decay, the wave is transformed into a sequence of solitons with different polarities.     

The group velocity variation of Lamb wave in fiber reinforced composite plate

Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics are not the same as the theoretical group velocities which is calculated with the Lamb wave dispersion equation. This discrepancy arises from the fact that the angle between the group velocity direction and the phase velocity direction in anisotropic materials exists. Wave propagation in a composite material with anisotropic characteristics should be considered with respect to magnitude correction in addition to direction correction. In this study, S0 mode phase velocity dispersion curves are depicted with the variation of degree with respect to the fiber direction using a Lamb wave dispersion relation in the unidirectional, bidirectional, and quasi-isotropic composite plates. Slowness surface is sketched by the reciprocal value of the phase velocity curves. The magnitude and direction of the group velocity could be calculated from the slowness surface. The recalculated group velocities with consideration of the magnitude and direction from the slowness surface are compared with experimentally measured group velocities. The proposed method shows good agreements with theoretical and experimental results.     

Effect of Polynomial Expressed Distribution Dust Particles for Unmagnetized Two-Ion-Temperature Dusty Plasma

Linear dispersion relation for linear wave and a Kadomtsev-Petviashvili (KP) equation for nonlinear wave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species. The numerical results of variationsof linear dispersion with respect to the different dust size distribution are given. Moreover, how the amplitude, width, and propagation velocity of solitary wave vary vs different dust size distribution is also studied numerically in this paper.     

The analysis and interpretation of some special properties of higher order symmetric lamb waves: the case for plates

Results derived from exact linear homogeneous elastodynamic theory are used for two-dimensional unloaded plates in order to understand certain features generated by proper symmetric Lamb modes. It is shown that S1 modes for all elastic materials have a phase velocity defined below the usual critical frequency and which initially exhibits anomalous dispersion (has a negative slope with respect to frequency). Over a certain range, it has a phase velocity that is double valued. In addition, there are an infinite number of proper symmetric Lamb modes that have this characteristic for materials with a Poisson ratio equal to 1/3. It also appears that all A3n modes are anomalous when V(L) < or = 2 V(T). The cause and implication of these effects are examined, including an associated negative group velocity over a small frequency zone for these modes. Further, it is noted that all proper symmetric Lamb modes have a plateau region in phase velocity with respect to wave number. It is shown that this always occurs for a phase velocity corresponding to the longitudinal bulk velocity of the elastic material. These issues are examined along with how one may obtain material parameters and possibly plate thickness from their dispersion curves.     

Generalized thermoelastic extensional and flexural wave motions in homogenous isotropic plate by using asymptotic method

In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.     

Effect of initial stress on Love waves in a piezoelectric structure carrying a functionally graded material layer

The effect of initial stress on the propagation behavior of Love waves in a piezoelectric half-space of polarized ceramics carrying a functionally graded material (FGM) layer is analytically investigated in this paper from the three-dimensional equations of linear piezoelectricity. The analytical solutions are obtained for the dispersion relations of Love wave propagating in this kind of structure with initial stress for both electrical open case and electrical short case, respectively. One numerical example is given to graphically illustrate the effect of initial stress on dispersive curve, phase velocity and electromechanical coupling factor of the Love wave propagation. The results reported here are meaningful for the design of surface acoustic wave (SAW) devices with high performance.     

Electron exchange-correlation effects on dispersion properties of electrostatic waves in degenerate quantum plasmas

Based on the quantum Magnetohydrodynamic (QMHD) model, the obliquely propagation of electrostatic waves in degenerate magnetized quantum plasmas with electron exchange-correlation effects are theoretically investigated. The modified linear dispersion relations of electrostatic waves are obtained and discussed in some specific cases. The analytical results clearly show that the dispersion properties of the high frequency electron waves (including the Langmuir wave and upper-hybrid wave) and the low frequency ion acoustic wave are modified by the quantum effects together with the electron exchange-correlation effects. The numerical results depict that the Langmuir wave and upper-hybrid wave can be unstable in the presence of the electron exchange-correlation effects, and it is also evidently indicated that the electron exchange-correlation effects can reduce the phase velocity of the waves, especially in the high wave number region. The corresponding results should be of relevance for identifying electrostatic fluctuations which transport in an inhomogeneous and magnetized quantum plasmas.     

Excitation of microwave by an annular electron beam in a plasma-filled dielectric lined waveguide

An axial relativistic electron beam passing through a slow wave structure is unstable to an electromagnetic perturbation whose phase velocity equals the velocity of the beam. This phenomenon of Cherenkov emission is the basis of all traveling wave tubes. In this paper an excitation of Cherenkov radiation by a thin annular relativistic electron beam in a plasma-filled dielectric-lined waveguide is analysed by use of the self-consistent linear theory. The effect of the thin annular electron beam on the beam-wave interaction is completely described by a jump condition. The dispersion equation and the simultaneous condition of the beam-wave interaction are derived. Finally, the growth rate of the wave is obtained, and the effect of the background plasma density and the electron beam radius on the growth rate of the wave are presented.This work is supported by National Natural Science Foundation of China.     

Flexural edge waves in semi-infinite elastic plates

This paper presents a detailed analysis of the dispersion for flexural edge waves in semi-infinite isotropic elastic plates. A solution to the dynamic equations of motion is constructed by the superposition of two partial solutions, each providing zero shear stresses at the plate faces. A dispersion equation is expressed via the determinant of an infinite system of linear algebraic equations. The system is reduced to a finite one by taking into account the asymptotic behaviour of unknown coefficients. The accuracy of the solution is confirmed by a good agreement with the available experimental data and by a proper satisfaction of the prescribed boundary conditions.A detailed analysis of dispersion properties for the edge wave and corresponding displacements at various frequencies is carried out. In addition to the well-known results it is shown that the plate height does not influence the existence of the edge wave at high frequencies and, as the frequency increases, the phase velocity of the edge wave in a semi-infinite plate asymptotically approaches the velocity of an edge wave in a right-angled wedge. The performed analysis allows evaluating the plate theories such as the Kirchhoff theory or other refined plate theories developed for modeling edge waves in semi-infinite elastic plates at low frequencies.