基于三维弹性理论的碳纤维板中Lamb波建模

基于主动Lamb波的结构健康监测是目前复合材料结构损伤监测技术研究的热点之一,了解Lamb波的传播特性对进行可靠的损伤监测非常重要.本文结合经典三维弹性理论与Lamb波的运动位移方程,对碳纤维复合材料板中传播的Lamb波传播特性进行了建模研究,在此基础上推导了碳纤维板的相速度频散曲线,并讨论了Lamb波传播方向与坐标轴之间的夹角及碳纤维铺层方向对频散曲线的影响,建模结果证明了这种建模方法的正确性.     

Simulation of acoustic wave propagation in dispersive media with relaxation losses by using FDTD method with PML absorbing boundary condition

We present a method to incorporate the relaxation dominated attenuation into the finite-difference time-domain (FDTD) simulation of acoustic wave propagation in complex media. A dispersive perfectly matched layer (DPML) boundary condition, which is suitable for boundary matching to such a dispersive media whole space, is also proposed to truncate the FDTD simulation domain. The numerical simulation of a Ricker wavelet propagating in a dispersive medium, described by second-order Debye model, shows that the Ricker wavelet is attenuated in amplitude and expanded in time in its course of propagation, as required by Kramers-Kronig relations. The numerical results also are compared to exact solution showing that the dispersive FDTD method is accurate and that the DPML boundary condition effectively dampens reflective waves. The method presented here is applicable to the simulation of ultrasonic instrumentation for medical imaging and other nondestructive testing problems with frequency dependent, attenuating media.     

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.     

Characteristic of Waves in A Multi-Walled Carbon Nanotube

A multi-walled carbon nanotube is modeled as a multiple-elastic cylindrical structure. The numerical-analytical method is adopted to analyze the characteristics of harmonic waves propagating along an anisotropic carbon nanotube. Each wall of the carbon nanotube is divided into three-nodal-line layer elements. The deflections of two adjacent tubes are coupled through the van der Waals. The governing equation of element is obtained from Hamilton's principle. A set of system equation of dynamics equilibrium for the entire structure is obtained by the assembling of all the elements. From solution of the eigenvalue equations, the dispersive characteristics, group velocities of multi-walled carbon nanotubes are achieved, and these properties of the six characteristic wave surfaces are also obtained.     

Vavilov-Cherenkov radiation in active biresonant media

The radiation of a charged particle moving in a dispersive medium with two resonance frequencies is theoretically studied. It is shown that such a medium can amplify the generated electromagnetic waves, provided that the low-frequency resonance is active, the high-frequency resonance is passive, and the particle velocity is within a certain interval. A method of calculation of the amplification effect is described and a particular example is presented.     

Propagation of inhomogeneous plane waves in anisotropic viscoelastic media

A new technique is explained to study the propagation of inhomogeneous waves in a general anisotropic medium. The harmonic plane waves are considered in a viscoelastic anisotropic medium. The complex slowness vector is decomposed into propagation vector and attenuation vector for the given directions of propagation and attenuation of waves in an unbounded medium. The attenuation is further separated into the contributions from homogeneous and inhomogeneous waves. A non-dimensional inhomogeneity parameter is defined to represent the deviation of an inhomogeneous wave from its homogeneous version. Such a partition of slowness vector of a plane wave is obtained with the help of an algebraic method for solving a cubic equation and a numerical method for solving a real transcendental equation. Derived specifications enable to study the 3D propagation of inhomogeneous plane waves in a viscoelastic medium of arbitrary anisotropy. The whole procedure is wave-specific and obtains the propagation characteristics for each of the three inhomogeneous waves in the anisotropic medium. Numerical examples analyze the variations in propagation characteristics of each of the three waves with propagation direction and inhomogeneity strength.     

基于TI介质模型的凸起地形对平面SH波的放大作用

在模拟地震波在介质中传播过程的研究中,正演模拟是一个重要的方面。该文采用间接边界元法（IBEM）对横观各向同性（TI）不同参数介质的凸起场地中入射SH波的散射问题进行了正演模拟,研究了TI凸起场地对SH波的放大效应。放大效应是通过地表位移与基岩露头位移幅值的比值来体现的。该间接边界元法结合了层状TI半空间精确动力刚度矩阵和均布斜线荷载动力格林函数,具有较高的精度。该文分别给出了TI介质凸起中SH波散射问题在频域和时域内的解答。频域内研究分析表明,土体TI介质参数的变化会对场地位移幅值的放大谱和空间分布产生显著的影响,即改变了凸起部分和土层的动力特性,使得两者动力相互作用发生改变。时域内研究表明,SH波在凸起周围的传播同时依赖于TI介质参数的具体取值和传播方向。时域位移幅值云图清晰地展示入射波、透射波、反射波和散射波的传播过程,凸起角点产生的散射波在TI介质中传播呈现"半椭圆"型,而在各向同性介质中呈现"半圆"型。     

Wave propagation in a micro-isotropic,micro-elastic solid

This is an extension of Koh's work[1] on micro-elastic solids. Restrictions on the elastic moduli have been obtained from the positive definiteness of the strain energy function. These restrictions are applied to the dispersion relations of plane harmonic waves propagating in the medium. It is found that all the velocities of propagation have real values above certain cut-off frequencies. The medium theoretically allows the propagation of twelve waves, eleven dispersive and one non-dispersive, with six distinct velocities of propagation and three cut-off frequencies.     

Harmonic wave propagation in viscoelastic heterogeneous materials Part I: Dispersion and damping relations

An analytico-numerical method is presented to study the propagation of plane harmonic waves in infinite periodic linear viscoelastic media. Part I considers only the dispersion and attenuation of acoustical longitudinal and shear waves. To show the accuracy of the method, examples of plane harmonic wave propagation in an infinite homogeneous medium and in a periodic layered viscoelastic medium are presented. The method is then used to calculate the damping and dispersion relations for a fibre-reinforced viscoelastic composite material. The results show clearly the influence of materials' viscoelastic properties and heterogeneities on the propagation of plane harmonic waves through the media.     

Interface waves in functionally graded piezoelectric materials

We analyze the propagation of antiplane or shear-horizontal waves near the interface between two half-spaces of piezoelectric ceramics. The material properties vary in the direction perpendicular to the interface. Both electroded and unelectroded interfaces are considered. Transcendental equations that determine the dispersion relations of the waves are obtained. They reduce to a few known results in the literature as special cases. Different from similar waves in homogeneous materials, the waves obtained are dispersive. The equations for the dispersion relations are solved numerically. It is found that the wave speeds are sensitive to the variation of material properties. This suggests the possibility of manipulating the wave propagation behavior through proper design of materials.     

Propagation of shear waves generated by a modulated finite amplitude radiation force in a viscoelastic medium

An effective way to generate localized narrow-band low-frequency shear waves within tissue noninvasively, is by the modulated radiation force, resulting from the interference of two confocal quasi-CW ultrasound beams of slightly different frequencies. By using approximate viscoelastic Green's functions, investigations of the properties of the propagated shear-field component at the fundamental modulation frequency were previously reported by our group. However, high-amplitude source excitations may be needed to increase the signal-to-noise-ratio for shear-wave detection in tissue. This paper reports a study of the generation and propagation of dynamic radiation force components at harmonics of the modulation frequency for conditions that generally correspond to diagnostic safety standards. We describe the propagation characteristics of the resulting harmonic shear waves and discuss how they depend on the parameters of nonlinearity, focusing gain, and absorption. For conditions of high viscosity (believed to be characteristic of soft tissue) and higher modulation frequencies, the approximate shear wave Green's function is inappropriate. A more exact viscoelastic Green's function is derived in k-space, and using this, it is shown that the lowpass and dispersive effects, associated with a Voigt model of tissue, are more accurately represented. Finally, it is shown how the viscoelastic properties of the propagating medium can be estimated, based on several spectral components of the shear wave spectrum.     

复合材料薄壁管中的波传播

本文以波传播的特征理论为工具, 对正交各向异性复合材料板斜绕的薄壁管在拉扭联合作用下的平面应力波进行了分析, 给出了特征波速、特征关系和通解表达式。文中还通过对一个算例和简单波解的讨论指出了复合材料波所具有的一系列不同于各向同性材料中波的性质和物理现象。      

On the application of Biot's theory to acoustic wave propagation in snow

A fluid-saturated, elastic, porous media model is used to describe acoustic wave propagation in snow. This model predicts the existence of two dilatational waves and a shear wave. In homogeneous, isotropic snow the two dilatational waves are uncoupled from one another but involve coupled motion between the interstitial air and ice skeleton. Dilatational waves of the first kind and shear waves are slightly dispersive and attenuated with distance. Dilatational waves of the second kind are strongly dispersive and highly attenuated. The model also predicts that the wave impedance for snow is close to that of air and that snow strongly absorbs acoustic wave energy.Available experimental phase velocity, impedance and attenuation data support the calculated results. Phase velocity measurements indicate three identifiable categories: fast dilatational waves (phase velocity ? 500 m/s), slow dilatational waves (phase velocity < 500 m/s) and shear waves. Wave impedance and attenuation measurements illustrate the low impedance, highly absorbing characteristics of snow. Additional impedance, attenuation and phase velocity data are required to further test and improve the model.     

Effect of surface stresses on surface waves in elastic solids

This paper deals with the propagation of surface waves in homogeneous, elastic solid media whose free surfaces or interfaces of separation are capable of supporting their own stress fields. The general theory for the propagation of surface waves in a medium which supports surface stresses is first deduced, and then this theory is employed to investigate the particular cases of surface waves, viz. (a) Rayleigh waves, (b) Love waves and (c) Stoneley waves. It is seen that the Rayleigh waves become dispersive in nature; and, in case of low frequency with residual surface tension, a critical wavelength exists, below which the propagation of Rayleigh waves is not possible. This critical wave length is directly proportional to the surface tension. Some numerical calculations have been made in the case of Love waves and conclusions have been drawn.     

A scattering problem by means of the spectral representation of Green's function for a layered acoustic half-space

 The problem in this paper is for scattering waves caused by an object and a plane wave in a layered acoustic half space. The boundary integral equation method as well as the spectral representation of Green's function for a layered acoustic half space are introduced to the present analyses. The spectral form of Green's function developed here is expressed in terms of the eigenfunctions for the point and the continuous spectra, that is the extension form of Green's function expressed by Ewing, Jardetsky and Press (1957). The advantage of the spectral representation of Green's function is that it enables us to decompose the scattering waves into eigenfunctions for the layered medium. Several numerical calculations are carried out to examine the efficiency of the present method as well as the properties of the scattering waves. According to the numerical results, the spectral form of Green's function provides accurate values and is applicable to the boundary element analysis for a layered medium. The spectral structures of the scattering waves are also found to be able to explain their properties. Received 2 November 1999     

Band gaps of elastic waves in 1-D phononic crystal with dipolar gradient elasticity

The dispersive relations of Bloch waves in the periodic laminated structure formed by periodically repeating of two different gradient elastic solids are studied in this paper. First, the various wave modes in the gradient elastic solid, which are different from those in the classical elastic solid, are formulated. Apart from the dispersive P wave and SV wave, there are two evanescent waves, which become the P type and S type surface waves at the interface of two different gradient elastic solids. Next, the continuity conditions of displacement vector, the normal derivative of the displacement vector and the monopolar and dipolar tractions across the interface between two different gradient elastic solids are used to derive the transfer matrix of the state vector in a typical single cell. At last, the Bloch theorem of Bloch waves in the periodical structure is used to give the dispersive equation. The in-plane Bloch waves and the anti-plane Bloch waves are both considered in the present work. The oblique propagation situation and the normal propagation situation are also considered, respectively. The numerical results are obtained by solving the dispersive equation. The influences of two microstructure parameters of the gradient elastic solid and the microstructure parameter ratio of two different gradient elastic solids on the dispersive relation are discussed based on the numerical results.     

复合管内径壁厚比对导波速度的影响

文章分析了复合管材中超声纵向较低阶导波模式的频散特性，在一般的弹性动力学运动方程的基础上，讨论了内径-壁厚比对导波传播速度的影响。结果表明：当材料和频厚积一定时，复合管材中导波的速度只与内径-壁厚比有关；当内径-壁厚比和频厚积较小时，内径-壁厚比的变化对低阶导波模式的传播速度有较大的影响，但随内径-壁厚比和频厚积的增加，这种影响将减小。     

Uniformly Valid Multiple Spatial-Temporal Scale Modeling for Wave Propagation in Heterogeneous Media

A novel dispersive model for wave propagation in heterogeneous media is developed. The method is based on a higher-order mathematical homogenization theory with multiple spatial and temporal scales. By this approach a fast spatial scale and a series of slow temporal scales are introduced to account for rapid spatial fluctuations of material properties as well as for the long-term behavior of the homogenized solution. The problem of secularity arising from the classical multiple-spatial-scale homogenization theory for wave propagation problems is resolved, giving rise to a uniformly valid dispersive model. The proposed dispersive model is solved analytically and its solution is found to be in good agreement with the numerical solution of the source problem in a heterogeneous medium.     

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocities and attenuation of ultrasonic waves in two-component media are determined. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results for effective moduli, velocity and/or attenuation as functions of concentration of spherical inclusion material, or porosity, are graphically displayed.