Transverse wave band gaps and longitudinal wave band gaps in solid phononic crystals

Based on the properties of transverse (divergenceless) waves and longitudinal (irrotational) waves, we divided the transverse wave modes and longitudinal wave modes from the mixed eigen modes in solid phononic crystals. By investigating the transverse wave and longitudinal wave band structures at low frequency, we found that transverse bands and longitudinal bands exhibit different behaviors in solid systems including spherical scatterers. Phononic crystal with a large density ratio of solid spheres to the background can guarantee both the large longitudinal and large transverse band gap, but solid spheres with a small ratio of longitudinal wave velocity to transverse wave velocity can only help to enlarge the longitudinal band gap, and do not help to enlarge the transverse band gap.     

Negative refraction imaging of solid acoustic waves by two-dimensional three-component phononic crystal

By using of the multiple scattering methods, we study the negative refraction imaging effect of solid acoustic waves by two-dimensional three-component phononic crystals composed of coated solid inclusions placed in solid matrix. We show that localized resonance mechanism brings on a group of flat single-mode bands in low-frequency region, which provides two equivalent frequency surfaces (EFS) close to circular. The two constant frequency surfaces correspond to two Bloch modes, a right-handed and a left-handed, whose leading mode are respectively transverse (T) and longitudinal (L) modes. The negative refraction behaviors of the two kinds of modes have been demonstrated by simulation of a Gaussian beam through a finite system. High-quality far-field imaging by a planar lens for transverse or longitudinal waves has been realized separately. This three-component phononic crystal may thus serve as a mode selector in negative refraction imaging of solid acoustic waves.     

The radiation Q factors obtained from the partial derivatives of the phase of the reflection coefficient of an elastic plate

The phase gradient method is applied to study the partial derivatives of the phase of the reflection coefficient of a fluid-loaded elastic plate. We consider the derivatives with respect to the frequency f, the incidence angle theta, the phase velocities of the longitudinal and transverse waves propagating in the plate, cL and cT, respectively, and the phase velocity in the fluid cF. The partial derivatives with respect to f, cL, cT, cF are linked by a relation involving products of one of these variables with the corresponding partial derivative. At a resonance frequency, the product of frequency with the frequency phase derivative can be identified as a radiation quality factor. By analogy, the other products correspond to quality factors. It can be shown that the product assigned to the fluid phase velocity corresponds to an angular radiation quality factor. The products assigned to the longitudinal and transverse phase velocities are identified as longitudinal and transverse radiation quality factors. These quality factors are shown to be related to stored energies associated with either standing waves across the plate, guided waves, longitudinal waves or transverse waves. A reactive power balance between the plate and the fluid is also established.     

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Plane waves in the bimetric gravitation theory

Field equations for plane waves are set up and some solutions are obtained. Transverse, longitudinal, and mixed waves are possible. In the purely transverse case the energy density is positive definite. In the purely longitudinal case it may be negative. However, in one example investigated it is positive if the Riemannian metric tensor satisfies a condition corresponding to space-time having satisfactory physical properties.     

Lattice Waves in Two-Dimensional Hexagonal Quantum Plasma Crystals

Lattice waves including a longitudinal wave and a transverse wave in two-dimensional hexagonal quantum plasma crystals are investigated by using the modified Debye-Hückel screening potential. It is shown that there exists an unstable region of lattice parameters, where the system will melt. The general dispersion relations are derived, and the waves propagating parallel to a primitive translation vector are discussed. We find that both the longitudinal and transverse waves are acoustic-like, and the longitudinal wave has a greater sound speed than that of the transverse wave in the long wavelength limit region.     

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System

Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.     

A Helmholtz resonator buried in the ground as a source of seismic waves and low-frequency sound in the atmosphere

The procedure is given for calculating the total power of low-frequency sound and seismic waves produced by a Helmholtz resonator in the form of an air-filled spherical cavity buried in the ground and supplied with a hole through which it is connected with the atmosphere. The sound is generated by air oscillations in the resonator’s neck section that is open to the atmosphere, while the compression and shear elastic waves are generated in the bulk of the ground by cyclic pressure fluctuations that act on the spherical walls of the cavity. Calculations show that the coincidence of the resonance frequencies (within approximately ten to hundred hertz), at which both the sound radiation to the atmosphere and the elastic seismic radiation in the form of longitudinal and transverse bulk waves are maximum, can occur only when the resonator is placed in a loose ground characterized by reduced elastic characteristics. In these conditions, the power of transverse waves exceeds the sound power by a factor of two and the power of longitudinal waves is smaller than the sound power by a factor of several tens.     

用纵横波声时比法测螺栓轴力精度研究

用纵横波测量螺栓轴力的技术已取得较大发展,本文介绍了纵横波比值法原理,通过理论推导,获得比值法计算的简易公式。建立试验平台,用现场用螺栓进行标定和测量,得出比值法在工程实践状态下的测量误差为10%以内,基本能满足工程应用的要求。此外,针对试验结果,本文还初步探讨了误差出现的原因以及提高精度的方法。本文介绍的比值法,无需精确测量标定螺栓长度和纵横波声速,现场应用更加简洁,具有较大的工程应用价值。     

Relativistic nonlinear waves in a magnetised plasma

Relativistic propagation of a nonlinearly-coupled circularly-polarised electromagnetic wave and a Langmuir wave along the applied magnetic field is considered. Analytical solutions are given or are indicated for some special cases like purely transverse waves and purely longitudinal waves. In the presence of an applied magnetic field, the incident circularly polarised electromagnetic wave is found to propagate further into denser regions of the plasma — a result which is in accord with the so-called inverse Faraday effect. Finally, we shall consider general coupled transverse and longitudinal waves for which we give an approximate solution. We investigate whether this system of coupled waves exhibits any internal resonances and consequent energy exchange between them.     

A slow wave with the structure of an electromagnetic wave in piezoelectric and magnetostrictive media

The propagation of elastic waves in piezoelectric and magnetostrictive materials is considered theoretically. It is shown that an elastic wave in a piezoelectric can create not only a longitudinal electric field parallel to the wave normal (longitudinal piezoactivity) but also a transverse field of electric induction (transverse piezoactivity). The presence of a transverse induction field leads to the appearance of a magnetic field perpendicular to the direction of the wave normal and to the induction vector; therefore, the transverse-piezoactive wave is accompanied by a transverse wave having the structure of an electromagnetic wave and propagating with the speed of sound. Transverse-magnetostrictive elastic waves in magnetostrictive dielectrics are accompanied by a similar wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 32–36, October, 1976.     

Kinetic study of instability growth rate in a helicon plasma discharge source

In this work, a kinetic model is developed to study the effects of the radio frequency antenna wavenumber, helicon plasma electron density, as well as their drift velocity and temperature on the instability increment rate of the helicon wave in both longitudinal and transverse directions. The ion acoustic (IA) wave frequencies and wavenumbers of the helicon waves are obtained when the maximum wave energy is deposited on the plasma ions. Moreover, it is shown that, at the IA wavenumber and frequencies, while the longitudinal instability increment rates for both the helicon and IA waves are ignorable, the transverse instability increment rate for both the helicon and IA wave increases. Besides, the longitudinal instability increment rate for the helicon or IA wave has non‐zero resonant frequencies. On the other hand, the transverse instability increment rate of helicon or IA wave can be neglected. Furthermore, it is observed that, while both the imaginary part of longitudinal permittivity and longitudinal instability increment rate are not influenced by the electron temperature, their transverse component increases linearly with the electron temperature. In addition, the imaginary part of transverse permittivity increases almost linearly with the drift velocity of the plasma electrons.     

Transverse rod vibrations under a short-term longitudinal impact

Transverse vibrations of a thin rod caused by a short-term longitudinal impact are considered. After the impact, a system of compression-tension waves, which causes transverse vibrations, appears in the rod. Parametric resonance, which leads to an unbounded rise in the amplitude of transverse vibrations, is investigated in the linear approximation. With a nonlinear approach, beats appear in the resonance vicinity, in which the mutual exchange of the energy of longitudinal and transverse vibrations occurs. The influence of viscoelastic resistance forces is investigated.     

REFLECTION OF PLANE WAVES BY THE FREE BOUNDARY OF A POROUS ELASTIC HALF-SPACE

In the present paper, we study reflection of inclined incident plane waves from a free boundary of the half-space in which the material is described by constitutive equations valid for elastic solids with voids. Both the cases of the transverse and longitudinal incident waves are considered, and it is shown that only the transverse one can propagate in the solid without attenuation, after having been reflected from the free boundary surface. The reflection coefficient and the amplitude of the surface oscillations are expressed in explicit form. The general results are demonstrated for several hypothetical porous materials, and it is shown that the reflection coefficient and the vibration amplitude are typically less than in classical media without voids. However, for relatively large transverse wave speed and high porosity, free boundary oscillation can exceed the classical one.     

On the effect of the correlation in phonon motion on the viscosity of impure dielectrics

The effect of the correlation in phonon motion on the viscosity of impure dielectrics is studied. It is shown that for perfect dielectrics the relaxation times entering the expressions for the absorption of longitudinal and transverse acoustic waves are different due to phonon correlations. The influence of impurities on the viscosity of dielectrics is discussed. Special emphasis is given to the problem of longitudinal-acoustic-wave absorption in impure dielectrics. It is shown that the effect of impurities on phonon correlations can lead to a substantial change in absorption of longitudinal waves.     

Oscillations of a three-component assembly with or without magnetic field

The plasma is taken to be composed of singly ionized molecules, free electrons and neutral molecules, each of the component being described by the hydromagnetic equations, modified to take into account the displacement current, existence of free charge in the medium, and the modified current equation without involving the scalar conductivity. The basic equations are linearized and only small amplitude waves are considered. In the absence of any external magnetic field, the transverse and longitudinal modes of oscillation separate out. In the transverse part a coupled plasma oscillation occurs which could be propagated only above a certain critical frequency and in the longitudinal part one extraordinary mode of propagation occurs having a forbidden range of frequencies. When there is an external applied magnetic field, ordinary and extraordinary waves are propagated along the direction of the magnetic field, whereas only ordinary waves are propagated transverse to the magnetic field. The critical frequencies above which these waves are propagated are evaluated and, the possible explanation of this medium like behaviour could be the implicit assumption of conductivity being not a scalar.     

固-固界面退化特性的超声反射评价方法

提出了一种基于有限宽超声束反射的固-固界面退化特性评价方法,从理论和数值仿真角度进行了分析和计算。将两固体界面间的薄层简化为界面弹簧模型,以界面法向和切向劲度系数表征界面的退化程度。通过数值计算求得有限宽超声纵波束在不同入射角和界面不同退化程度下的反射横波、反射纵波的镜面反射系数。进一步地,通过建立二维有限元模型,仿真研究了有限宽超声纵波束在给定入射角及界面不同退化程度下镜面反射系数的变化规律。结果表明,反射纵波和反射横波的镜面反射系数随有限宽超声纵波束的入射角及界面劲度系数的改变而变化,且存在镜面反射系数随界面劲度系数单调且敏感变化的入射角,据此可准确评价界面的退化程度。     

Transverse waves and the liquid and gaseous states

The distinction between liquid and gas, in a computer simulated Lennard-Jones fluid, persists above the critical temperature, the liquid supporting both transverse and longitudinal waves while the gas displays only longitudinal waves.     

Dispersion relations of lattice waves in three-dimensional strongly coupled complex plasma crystals

Dispersion relation matrices, with the screened Coulomb interaction between a charged dust particle and all other particles taken into account, are derived for waves in body centred cubic (bcc) and face centred cubic (fcc) lattices in three-dimensional strongly coupled complex plasma crystals separately. The matrices are then calculated in characteristic directions to obtain the longitudinal and transverse eigenmodes. The longitudinal and transverse waves for these cases are discussed separately.