Estimation of dynamic elastic constants from the amplitude and velocity of Rayleigh waves

In this paper a method is proposed to characterize the elasticity of isotropic linear materials from the generation and detection of an acoustic surface wave. For the calculation of the elastic constants, it is sufficient that only one of the faces of the sample be accessible. The methodology is based on both the measurement of the Rayleigh wave velocity and on the determination of the normal to longitudinal amplitude ratio calculated from the normal and longitudinal components of the displacement of a point. The detection of two consecutive surface wave pulses using a single experimental setup permits the determination of the elastic constants. The method is applied to calculate Young's modulus and Poisson's ratio of an aluminum sample as well as their systematic uncertainties. The results obtained give a relative uncertainty for Young's modulus on the order of the sixth part of that calculated for Poisson's ratio.     

Explicitly covariant light-front dynamics and relativistic few-body systems

The wave function of a composite system is defined in relativity on a space–time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane ω·x=0, where ω is an arbitrary four-vector with ω²=0. The standard non-covariant approach is recovered as a particular case for ω=(1, 0, 0,−1). Using the light-front plane is of crucial importance, while the explicit covariance gives strong advantages emphasized through all the review.The properties of the relativistic few-body wave functions are discussed in detail and are illustrated by examples in a solvable model. The three-dimensional graph technique for the calculation of amplitudes in the covariant light-front perturbation theory is presented.The structure of the electromagnetic amplitudes is studied. We investigate the ambiguities which arise in any approximate light-front calculations, and which lead to a non-physical dependence of the electromagnetic amplitude on the orientation of the light-front plane. The elastic and transition form factors free from these ambiguities are found for spin 0, and 1 systems.The formalism is applied to the calculation of the relativistic wave functions of two-nucleon systems (deuteron and scattering state), with particular attention to the role of their new components in the deuteron elastic and electrodisintegration form factors and to their connection with meson exchange currents. Straightforward applications to the pion and nucleon form factors and the ρ−π transition are also made.     

Diffraction of sound by an elastic cylinder near the surface of an elastic halfspace

Diffraction of an acoustic wave by an elastic cylinder near the surface of an elastic halfspace is considered. The solution relies on a Helmholtz-type integral equation and uses the Green function of an elastic halfspace. The latter function is represented in the form of an integral over the Sommerfeld contour on the plane of a complex variable that has the meaning of the angle of the wave incidence on the halfspace boundary. An integral equation for the sound pressure distribution over the cylinder surface is derived. This equation is reduced to an infinite system of equations for the Fourier-series expansion coefficients of this distribution. The results obtained are valid for the diffraction of a cylindrical wave and a plane wave. They also describe the diffraction of a spherical wave when the transmitter and receiver are far from the cylinder and lie in one plane that is orthogonal to the cylinder axis.     

纳米陶瓷粉末在爆炸压实过程中的破碎行为研究

 在爆炸压实过程中，纳米颗粒所受冲击载荷发生显著变化的时间远远大于应力波传过颗粒特征长度所用时间；同时，陶瓷颗粒在爆炸冲击过程中主要表现为脆性。基于以上两个事实提出了弹性假设，推导了颗粒在压实过程中的受力状态。回顾了判断脆性材料破坏的三个准则，即Hugonoit弹性极限、动态屈服强度和理论剪切强度，并从这三种判据的交集值出发来判断爆炸压实过程中陶瓷颗粒是否有发生破碎的可能。通过具体计算得出颗粒内存在两个最大剪应力的位置：一个位置发生在距颗粒接触面0.5 nm范围以内，此处剪应力最大；另一个位置发生在距接触面较远处。这一结果为解释陶瓷粉末颗粒在爆炸压实过程中存在塑性行为和破碎行为提供了理论依据。     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

Analysis of the space-time dynamics of acoustic fields on the surface of a solid

The space-time dynamics of an acoustic field produced by a piezoelectric transducer in a pulsed mode is studied. The detection of acoustic fields is achieved using a Doppler laser interferometer. It is shown that, for a pictorial representation of the dynamics of a pulsed process, it is convenient to use the patterns of instantaneous spatial field distributions within the scanning area, the observation of which at successive instants makes it possible to trace the acoustic field variations on a time scale considerably smaller than the period of the ultrasonic wave. Experimental data demonstrating the process of phase propagation along the sample boundary as a function of time are presented. They are in good agreement with theoretical results obtained by using various methods of acoustic field calculation and different scalar potential distributions over the transducer surface. It is shown that the velocity of phase propagation along the sample boundary, which is mainly determined by the wave front curvature of the elastic wave incident on the sample surface, can considerably exceed the wave velocity in the unbounded medium.     

The elastic and inelastic scattering of 30.5 MeV protons by24Mg

Measurements of the differential cross sections for the elastic scattering of 30.5 MeV protons by ²⁴Mg and for the inelastic scattering to the 1.37, sum of 4.12 and 4.23, 5.22 and 6.0 MeV states are reported. Optical model fits to the elastic data, a distorted wave calculation for the first excited state, and coupled channel calculations are also presented.     

Noninvasive ultrasound image guided surface wave method for measuring the wave speed and estimating the elasticity of lungs: A feasibility study

Lung diseases, such as acute respiratory distress syndrome (ARDS) and idiopathic pulmonary fibrosis (IPF), are closely associated with altered lung elastic properties. Pulmonary function testing and imaging are routinely performed for evaluating lung diseases. However, lung compliance, a measure of lung elastic properties, is rarely used in clinic, because it is invasive and provides only a global and arguably biased estimate of lung elastic properties. Current ultrasound methods also cannot be used for imaging lungs because ultrasound cannot penetrate the lung tissue. In this paper, an ultrasound image guided and surface wave based method is proposed to measure regional lung surface wave speed and estimate lung elasticity noninvasively. The method described here was not explored before to the best knowledge of the authors. Experiments in an ex vivo pig lung and an in vivo human lung pilot study are reported. The surface wave speed is measured to be 1.83 ± 0.02 m/s at 100 Hz by ultrasound for the ex vivo pig lung at 3 mmHg pressure, which is validated by an optical measurement. An in vivo human lung pilot experiment measures the surface wave speed to be 2.41 ± 0.33 m/s for the 100 Hz sinusoidal wave at total lung capacity (TLC) and 0.99 ± 0.09 m/s at functional residual capacity (FRC). These values of wave speed fall well within the range of available literature.     

Estimation of tissue's elasticity with surface wave speed

The mechanical response of tissues to external forces has gained considerable interest in medical diagnosis. One approach to imaging tissue elastic properties is to apply an external force on the surface of the body. Another approach is to generate a localized force inside the tissue with the radiation force of ultrasound. In this paper, a new method is developed to estimate tissue's elasticity based on surface wave speed measurement. The theory of surface wave speed is developed for estimating tissue's elasticity. Experiments are carried out on a tissue-mimicking ultrasound phantom. An amplitude modulated ultrasound signal of a few hundred hertz is used to generate a localized force in the phantom. The surface wave fields are measured with a laser vibrometer. It shows that the surface wave speed can be used for inversely estimating tissue's elastic properties based on tissue's surface measurement.     

海底沉积物声速与物理性质的理论关系

为建立海底沉积物声速与物理性质的关系,引入密度变化比和弹性模量变化比为参数描述海底沉积物声速。密度变化比是描述声速的一个复合参数,由孔隙率、固相密度和海水密度三个物理参数表示;弹性模量变化比是描述声速的另一个复合参数,由孔隙率、固相体积模量和海水体积模量三个物理参数表示;声速公式可展开为这两个复合参数的泰勒多项式。两个复合参数的变化构成声速曲面,声速曲面包含了声速特性与沉积物性质的完整信息;而单参数声速公式是声速曲面上的一条曲线。数值计算与测试结果对比表明:把孔隙率-声速经验公式变换为参考声速乘以一个调制函数的标准形式,各个海区的孔隙率-声速经验公式的调制函数是相当接近的。论文导出的声速公式与Wood声速公式的区别在于弹性模量的模型不同。      

The use of OPW's in the Lindgren approximation of conduction-core exchange and the lattice dynamical properties of rubidium

This paper reports a first principles nonlocal pseudopotential calculation for the lattice dynamical properties of rubidium metal. In these calculations, an orthogonalized plane wave (OPW) has been used for the first time to represent the conduction state in the Lindgren approximation of conduction-core exchange. A comparison is made of phonon spectra and elastic shear constants using both plane wave (PW) and OPW conduction states. It is found that the OPW results are in excellent agreement with experiment and consistently better than the PW results for both phonon spectra and elastic constant. Similar results are found for other simple alkali metals.     

Field of a point source in a semi-infinite elastic medium

An exact solution for the tensor Green's function of a harmonic field for a semi-infinite elastic medium is presented in an easy-to-use form in the theory of wave scattering. The solution is derived in the form of a sum of the Green's functions for an infinite medium and the term satisfying the homogeneous wave equation for a semi-infinite elastic medium. The results reproduce the known far-field asymptotics containing longitudinal, transversal and surface Rayleigh-type wave modes. The near-field asymptotic is essentially different for the regions far and near the boundary.     

Elastic plate as floating wave breaker in a beach zone

Wave propagation and damping mechanism due to elastic coating of the sea surface is considered. The hydrodynamic performance of an elastic plate is analyzed for various conditions in terms of wave reflection and transmission, plate deflection, and surface strain. Rigidity and geometrical scales of the coating plate essentially affect the wave transmission characteristics. The model of wave propagation and scattering is constructed in the long-wave approximation. The case of elastic plate with fixed edges is considered. It is shown that optimally designed horizontal flexible membrane can be a very effective wave barrier in a beach zone.     

FREQUENCY DISPERSION CHARACTERISTICS OF PHASE VELOCITIES IN SURFACE WAVE FOR ROTATIONAL COMPONENTS OF SEISMIC MOTION

When rotational components of ground motion produced by seismic surface waves are computed, the phase velocities must always be dealt with in earthquake engineering. In this paper, appropriate methods are presented to obtain the calculation formulas for the phase velocities of surface waves by applying the theory of elastic wave propagation. Frequency dispersion characteristics of phase velocities are discussed. The rocking component around a horizontal axis and the torsional component around a vertical axis, which are generated, respectively, by the Rayleigh and Love waves, are reasonably given. A procedure is developed to calculate the time histories of these rotational components.     

磁流变液构成的类梯度结构振动传递特性

提出了一种磁流变液构成的类梯度结构,并通过理论建模、数值计算和实验研究了该结构的振动传递特性.磁流变液在磁场作用下具有液固转换的特殊理化性质,而液固转换过程就是磁流变液的振动传递阻抗变化过程.因此,基于磁流变液的这一特性,通过控制磁场,构建了类梯度结构.基于弹性波传递的一维波动方程,建立了垂直入射的弹性波在类梯度结构中传递的波动方程.然后,使用连续介质的离散化方法和传递矩阵法进行求解,得到振级落差的表达式,对其进行数值计算,分析类梯度结构的振级落差随弹性波频率和磁场强度的变化趋势.最后,对类梯度结构的振动传递特性进行了实验研究,分析了磁场强度对类梯度结构振动传递特性的影响.研究结果表明,与均匀场作用的磁流变液相比,类梯度结构对弹性波的衰减效果更好,且该结构具备良好的可调控特性.     

Surface waves and mode conversion at a surface coated with an elastic heavy layer

A surface wave of frequency lying within bulk band of transverse waves is found in an elastic medium coated with a thin layer endowed with a surface mass density, surface Young's modulus and surface bending modulus. The wave is a particular case of surface resonance with infinite lifetime. In materials with negative Poisson's ratio (auxetics) the wave exists even for coating material with zero bending modulus, whereas with positive Poisson's ratio it requires the surface bending modulus to be larger than the surface Young's modulus. The manifestation of this wave in the reflection coefficient seems promising for fabrication of devices showing monochromator properties.     

The radiation impedance and the energy partition among wave fields generated by a normal force strip radiator on isotropic solid surface

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Nematic liquid crystals at rough and fluctuating interfaces

Nematic liquid crystals at rough and fluctuating interfaces are analyzed within the Frank elastic theory and the Landau–de Gennes theory. We study specifically interfaces that locally favor planar anchoring. In the first part we reconsider the phenomenon of Berreman anchoring on fixed rough surfaces, and derive new simple expressions for the corresponding azimuthal anchoring energy. Surprisingly, we find that for strongly aligning surfaces, it depends only on the geometrical surface anisotropy and the bulk elastic constants, and not on the precise values of the chemical surface parameters. In the second part, we calculate the capillary waves at nematic-isotropic interfaces. If one neglects elastic interactions, the capillary wave spectrum is characterized by an anisotropic interfacial tension. With elastic interactions, the interfacial tension, i.e., the coefficient of the leading q² term of the capillary wave spectrum, becomes isotropic. However, the elastic interactions introduce a strongly anisotropic cubic q³ term. The amplitudes of capillary waves are largest in the direction perpendicular to the director. These results are in agreement with previous molecular dynamics simulations.     

Characteristics of Biot waves produced by a vibration exciter in a fluid-saturated medium

Results of a theoretical calculation of the directional characteristics of elastic waves excited by an oscillating point force in a fluid-saturated porous medium are presented. Based on Boit’s theory and the theory of elementary acoustic sources, the wave amplitude and radiation power are calculated for two kinds of longitudinal waves and the transverse wave. An analysis of the spatial angular characteristics of elastic waves is performed for two types of rock, namely, water-and gas-saturated sandstones. The angular distributions of vibrations in the solid and liquid (gaseous) phases of the medium and the frequency dependences of the radiation power associated with each of the three types of acoustic waves are presented in graphical form.     

The existence of pure surface modes in elastic materials with orthorhombic symmetry

A pure surface mode in a semi-infinite elastic body with a traction-free boundary is a progressive harmonic surface wave in which the displacement is everywhere co-planar with the wave and surface normals. When the elastic material has orthorhombic symmetry, with one of the 2-fold symmetry axes normal to the bounding plane, there are generally only two directions in which a pure surface mode may propagate, but additional directions appear when the transmitting material has higher symmetry. It is shown that for all the possibilities arising in this way the positive definiteness of the strain energy is a sufficient condition for the existence of a unique pure surface mode. The properties of pure modes in elastic materials belonging to the orthorhombic, tetragonal, hexagonal and cubic systems are discussed with particular reference to conditions under which the motion has the same features as a Rayleigh wave.