Helical waves of an elastic cylindrical shell

Properties of helical waves of a cylindrical shell described by Kirchhoff-Love equations are considered. The problem is reduced to the case of the propagation of plane waves in an equivalent plate. On the basis of the corresponding dispersion equation and its solution, a conclusion is made about the anisotropy of the shell properties. Dispersion curves are plotted for different angles of propagation of helical waves with respect to the shell axis. Displacements of the shell along and across the direction of wave propagation are calculated.     

Helical normal waves near a cylindrical cavity in an elastic medium

The properties of helical waves arising near a cylindrical cavity in an elastic medium are described. These waves are a manifestation of aperiodic (in angle) solutions to the dynamic elasticity equations. The dispersion characteristics of the waves are determined, and the spatial structure of the waves is described.     

Effect of longitudinal space-charge waves of a helical relativisticelectron beam on the cyclotron maser instability

The influence of the longitudinal space-charge waves of a coherently gyrophased helical relativistic electron beam on the cyclotron maser instability is investigated in a cylindrical waveguide configuration using a three-dimensional kinetic theory. A dispersion relation that includes waveguide effects is derived. The stability properties of the cyclotron maser interaction are examined in detail. It is shown that, in general, the effects of space-charge waves on a coherently gyrophased beam are suppressed in a waveguide geometry, in comparison with an ideal one-dimensional cyclotron maser with similar beam parameters     

Diffraction of a convergent sound wave by an elastic cylindrical shell with a longitudinal fixation

The problem of the diffraction of a zero-order convergent cylindrical wave by a cylindrical shell with a longitudinal fixation along one of its generatrices is considered. The problem is solved on the basis of using the so-called helical waves, which are aperiodic eigensolutions to the equations of the shell motion. The diffraction field is represented in the form of a convergent series in cylindrical harmonics. The method of the solution allows for a generalization to several cases of longitudinal fixation with conditions of different forms. The calculation of the scattering amplitude of the diffraction field is carried out for various frequencies and shell parameters.     

充水圆柱壳声散射的环绕波分析

研究了内部充水圆柱壳散射声场的构成。采用弹性薄壳理论和Sommerfeld-Watson变换(SWT)方法导出散射声场的解析解。数值搜索环绕波的复波数极点,比较圆柱壳体内部真空和内部充水两种情况下表面环绕波的相速度、衰减等性质。用镜反射波和环绕波的叠加合成反向散射形态函数,与简正级数解符合良好。计算流体附加环绕波的回波时序并与实验数据对照。结果表明,流体附加环绕波的再辐射是内部充水圆柱壳的形态函数出现更加丰富的共振峰和回波结构形成的重要原因。      

Analysis of circumferential waves on a water-filled cylindrical shell

The formation of scattering field from a water-filled cylindrical shell was studied. The analytic solutions of scattering field are derived using elastic thin shell theory and Sommerfeld-Watson Transformation(SWT) method.Complex wave-number poles of circumferential waves are found numerically,the phase speed and attenuation of circumferential waves between the situation of a hollow cylindrical shell and a water-filled cylindrical shell are compared. The synthesis of backscattering form functions which are sum of specular reflection component and circumferential waves is consistent with normal mode result.The calculated echo sequences of additional fluid circumferential waves are compared with experimental results. The results show that richer resonance peaks appeared in the backscattering form functions of a water-filled cylindrical shell and the formation of echo’s structure are due to re-radiation effects of additional fluid circumferential waves.     

Nonlinear interactions of azimuthal surface waves in a magnetoactive plasma waveguide

Several possible three-wave and four-wave interactions, namely decay and modulational instabilities of a specific type of surface waves-azimuthal sufaces waves (ASW)-in a magnetoactive plasma waveguide are considered. The studied ASW propagate in the azimuthal direction at the cylindrical waveguide wall-plasma interface.     

Surface waves in cholesterics in a magnetic field

Propagating waves on the free surface of a cholesteric liquid crystal in a vertical magnetic field are considered for the case when the anisotropy of the magnetic susceptibility is negative. Surface fluctuations distort the helical structure and the dispersion relation and penetration depth are shown to depend on three possible restoring forces: the surface tension, the twist elastic forces associated with the helix, and the magnetic field.     

圆柱空腔上裂纹的爬波检测方法

通过牛顿迭代法求解了固体内部圆柱空腔上爬波的频散方程,分析了爬波的频散和衰减特性。利用动态光弹法显示了爬波的直观图像和圆柱空腔附近各散射波的空间关系。根据爬波具有的频散、衰减以及辐射横波特征,设计了斜入射脉冲回波实验装置,测量了特定位置处裂纹反射爬波辐射出的横波信号,其与柱面反射波的时差和理论预测一致。进一步实验研究发现,爬波回波幅度与特定位置的裂纹长度具有近似单调的对应关系,在裂纹长度较大时,回波幅度趋于稳定。以上工作为圆柱空腔上裂纹的爬波定量检测提供了物理基础和实现方法。      

Effect of anomalous transparency of a liquid-gas interface for sound waves

Problems of acoustic wave propagation near the interface between media are discussed. The processes that occur at a liquid-gas interface are considered, and their characteristic features related to the effect of inhomogeneous waves are pointed out. The transmission factors of spherical and cylindrical waves incident on the aforementioned interface are calculated with allowance for the contribution of the inhomogeneous component. Experimental dependences of the transmission factor on frequency and source depth measured with respect to the interface are presented. It is shown that the lower the frequency generated by the source and the closer the source to the water-air interface, the higher the acoustic transparency of the interface.     

Acoustic scattering from complex elastic shells: visualization of S0, A0 and A waves

Acoustic scattering phenomena from complex immersed elastic shells are studied by high-speed Schlieren visualization for spark-generated spherical quasi-Dirac excitations. The situations considered are air-filled cylindrical shells under normal insonification and air-filled cylindrical shells soldered at one end with a hemispherical endcap under axial and non-axial incidences. The results are compared with those provided by the Methode d'Isolement et d'Identification des Resonances (MIIR) method and corresponding analytical theoretical solutions. The combination of these complementary approaches better highlights some of the behaviors of the symmetric S0- and antisymmetric A0-Lamb waves, as well was the Scholte-Stoneley A-wave, on the considered targets. In particular, the influence of the internal solder inhomogeneities on the creation and/or the conversion of these modes is demonstrated.     

Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation

In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves.     

Nonlinear waves in a plasma cylinder

Nonlinear electron plasma waves in a cold plasma bounded by a cylindrical dielectric are investigated using the exact electron fluid equations. After the spatial wave structure is determined, a set of nonlinear equations governing the temporal behavior of the field quantities is solved. It is shown that finite amplitude waves and explosively unstable behavior can occur     

Gravitational collapse of dissipative fluid as a source of gravitational waves

Gravitational collapse of cylindrical anisotropic fluid has been considered in analogy with the work of Misner and Sharp. Using Darmois matching conditions, the interior cylindrical dissipative fluid (in the form of shear viscosity and heat flux) is matched to an exterior vacuum Einstein–Rosen space–time. It is found that on the bounding 3-surface the radial pressure of the anisotropic perfect fluid is linearly related to the shear viscosity and the heat flux of the dissipative fluid on the boundary. This non-zero radial pressure on the bounding surface may be considered as the source of gravitational waves outside the collapsing matter distribution.     

Generation and amplification of terahertz electromagnetic waves in a plasma waveguide with a dielectric rod and an annular degenerate plasma

The theoretical investigation of terahertz waves and their excitation by electron beam injection in a cylindrical metallic plasma waveguide is investigated. This metallic waveguide includes a cold collisionless unmagnetized annular degenerate plasma and a dielectric rod. The dispersion characteristics of these waves, the frequency spectra of fast and slow E-modes waves (transverse magnetic field), are studied. Also, the effects of the dielectric permittivity, the radius of the dielectric rod and the radius of the plasma on the frequency spectra and the time growth rate of waves are simulated. In addition, the electric field profiles in this waveguide are plotted.     

Revolving superposed standing waves in a spinning Timoshenko Beam

The aim of the present paper is to study the revolving superposed standing waves in a spinning Timoshenko beam based on the results obtained by the first author with others in two recently published papers. The concept of superposed standing wave as normal mode and the knowledge about the helical feature of propagating wave will be used to depict a physical picture about the vibration of the spinning beam, from describing the basic constituent waves to showing the orthogonality property of the revolving normal modes. The wave-mechanics approach will be invoked throughout the study with an algebraic procedure used to reveal the two eigenvalues of the gyroscopic-coupling phase factor. A table for tabulating the phases of the centroidal positions of the beam in time and space due to the passing of a wave is invented, through which one could show the helical structure of the wave without ambiguity. From the present result, two types of revolving standing waves are identified, each manifesting as a gyroscopic precession in association with a frequency-splitting phenomenon, in either the clockwise or the anticlockwise direction. It is shown that the revolving waves should be represented by wavefunctions in a form of four-component column matrix vectors.     

The effect of curvature on Stoneley waves

The effect of curvature is investigated for plane waves propagating in the circumferential direction along concave and convex cylindrical surfaces, and at the interface of a circular cylindrical inclusion in smooth or bonded contact with an unlike infinite medium. The waves propagate with an arbitrary, but generally large number of circumferential modes. These problems reduce to Rayleigh and Stoneley waves in the limit as the curvature vanishes. Dispersion relationships are presented for each case.     

Cylindrical and spherical dust ion-acoustic solitary waves in quantum plasmas

Dust ion-acoustic solitary waves in unmagnetized quantum plasmas are studied in spherical and cylindrical geometries. Using quantum hydrodynamic model, the electrostatic waves are investigated in the weakly nonlinear limit. A deformed Korteweg-de Vries (dKdV) equation is derived by using the reductive perturbation method and its numerical solutions are also presented. The quantum diffraction and quantum statistical effects incorporated in the system modifies the characteristics of dust ion-acoustic waves in cylindrical and spherical geometries. The role of stationary dust particles in quantum plasmas are also discussed. It is shown that the cylindrical and spherical dust ion-acoustic solitary waves behave quite differently from one-dimensional planar solitary waves in quantum plasmas.