Dynamic stress from a circular hole in a functionally graded piezoelectric/piezomagnetic material subjected to shear waves

An analytical method is applied to investigate the scattering of magneto-electro-elastic waves and dynamic stress around a circular hole in a functionally graded piezoelectric/piezomagnetic material layer. Analytical solutions of the wave, electric and magnetic fields are expressed by employing a wave function expansion method. Analyses show that the piezoelectric and piezomagnetic properties greatly affect the dynamic stress in the region of the intermediate frequency, and the effect increases with increasing non-homogeneous parameter. The effects of the incident wave number and non-homogeneous parameter of the materials on the dynamic stress and electric field are also examined.     

Dynamic stress around a cylindrical nano-inhomogeneity with an interface in a half-plane under anti-plane shear waves

Taking into account the size of the nanostructure, the effect of surface/interface stiffness on the dynamic stress around a cylindrical nano-inhomogeneity embedded in an elastic half-plane subjected to anti-plane shear waves is investigated. The boundary condition at the straight edge of the half-plane is traction free, which is satisfied by the image method. The analytical solutions of displacement fields are expressed by employing a wave function expansion method. The addition theorem for a cylindrical wave function is applied to accomplish the superposition of wave fields in the two half-planes. Analyses show that the effect of the interface properties on the dynamic stress is significantly related to the nano-scale distance between the straight edge and the center of the cylindrical nano-inhomogeneity. The frequency and incident angle of incident waves and the shear modulus ratio of the nano-inhomogeneity to matrix also show different effect on the dynamic stress distribution when the inhomogeneity shrinks to nano-scale. Comparison with the existing results is also given.     

Dynamic effective elastic modulus of polymer matrix composites with dense piezoelectric nano-fibers considering surface/interface effect

Based on effective field method,the dynamic effective elastic modulus of polymer matrix composites embedded with dense piezoelectric nano-fibers is obtained,and the interacting effect of piezoelectric surfaces/interfaces around the nano-fibers is considered.The multiple scattering effects of harmonic anti-plane shear waves between the piezoelectric nano-fibers with surface/interface are averaged by effective field method.To analyze the interacting results among the random nano-fibers,the problem of two typical piezoelectric nano-fibers is introduced by employing the addition theorem of Bessel functions.Through numerical calculations,the influence of the distance between the randomly distributed piezoelectric nano-fibers under different surface/interface parameters is analyzed.The effect of piezoelectric property of surface/interface on the effective shear modulus under different volume fractions is also examined.Comparison with the simplified cases is given to validate this dynamic electro-elastic model.     

Elastic resonances of a periodic array of fluid-filled cylindrical cavities embedded in an elastic matrix

The resonant scattering by a periodic infinite array of fluid-filled cylindrical cavities in an elastic matrix is studied. The exact reflection and transmission coefficients of the array are calculated by means of a multiple scattering formalism taking into account all the interactions between the cavities. Numerical results are next given for low frequencies for which only the longitudinal and transverse zero modes propagate. A first study based on the analysis of the transmission coefficients clearly shows that the resonances of the array can be classified into two sets: those close to the resonances of a single cavity and those due to a resonant coupling between a cavity and its nearer neighbors. The resonant coupling is due to the interaction between the whispering-gallery surface waves propagating around each cavity. In the case of cavities with very close spacing, it is observed that the dispersion curves of the waves propagating along the array can also be classified into two sets: those with a positive group velocity have cut-off frequencies that correspond to the resonances of a single cavity, those with a negative group velocity have cut-off frequencies that correspond to the resonances resulting from the strong coupling. A new method for the analysis of the resonances is presented. It is based on the properties of the scattering matrix and consists in studying the resonant eigenvalues of the scattering matrix of the array once the background is removed. For the detection of very fine resonances, as well as in the separation of several resonances very close to each other, this method proves to be more efficient than one based on the analysis of the reflection and transmission coefficients.     

剪切波对时间反转调相的经颅聚焦超声的影响*

为研究颅骨中的剪切波对经颅聚焦超声的影响,该文利用Kelvin-Voigt固体声波方程并结合时间反转法,分别模拟了考虑剪切波和不考虑剪切波时,256-单元平面相控阵为实现超声经颅聚焦所需的相位调控,并将这两种相位调控都分别作用于考虑剪切波和不考虑剪切波时的聚焦情形。对这两种相位调控以及基于它们的经颅聚焦超声场的对比分析结果表明:聚焦深度较大时,剪切波对基于时间反转进行的相位调控影响较小;不过,剪切波对经颅聚焦超声场的强度分布影响较大,忽略剪切波会导致对焦域处声场聚焦强度的高估以及对颅骨附近声能量沉积的低估。     

Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber

In the framework of surface elasticity theory, the scattering of plane compressional and shear waves by a single nano-sized coated fiber embedded in an elastic matrix is studied using the method of eigenfunction expansion. The dynamic stress concentration factors along the interface between the coated fiber and the matrix induced by the plane elastic wave and scattering cross section are derived and numerically evaluated. The interface stress, inhomogeneous material constants and thickness of the coated layer on the scattering of the elastic wave become much more important when the radius of the coated-fiber is reduced to the nanometer scale. These were confirmed by the use of numerical results. Our results can aid in understanding the dynamic mechanical properties of nano-composites. The proposed method has potential applications in the characterization of the interfacial layer that links reinforced fibers to their matrix.     

Elastic wave scattering around cavities in inhomogeneous continua by the BEM

This work examines elastic wave scattering around cavities embedded in a continuum with depth-dependent shear modulus and under conditions of plane strain. A restricted case of inhomogeneity is considered, where the Poisson ratio is fixed at 0.25 and where the density profile also varies, but proportionally to the shear modulus. For this specific case, the wave speeds remain macroscopically constant and it becomes possible to recover the exact Green functions by using an algebraic transformation method. These functions are subsequently used as kernels in a standard 2D boundary element formulation defined in the Laplace transform domain. The final step involves an inverse Laplace transformation, whereby the transient behavior of cavities in the aforementioned inhomogeneous continuum can be recovered. Two basic examples are solved, namely the circular cylindrical cavity under sudden internal explosion and under a pressure wave sweep. In the latter case, it is possible to investigate the effect that the angle of wave incidence has on the displacement and stress that develop along the cavity's perimeter, given the fact that the shear modulus is changing along the vertical direction. These examples serve to illustrate the present approach and to reveal some interesting differences that are observed in transient wave scattering phenomena between homogeneous and continuously inhomogeneous models, where the latter models yield a more realistic representation of geological formations.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

ELASTIC WAVE SCATTERING AND DYNAMIC STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH A CIRCULAR CUTOUT

In this paper, based on the theory of elastic wave motion for open cylindrical shell, wave scattering and dynamic stress concentrations in open cylindrical shells with a hole are studied by making use of small parameter perturbation methods and boundary-integral equation techniques. The boundary-integral equations and iterative imminent series of scattered waves around the cavity of the cylindrical shell are derived. By employing this method, the approximately analytical solutions of scattered waves on the edge of cutout are gained. The computational formula for getting the dynamic stress concentration factors on the contour of cavity is developed. As an example, the numerical results of these dynamic stress concentration factors are graphically presented and discussed. The analytical methods put forward in the present work have practical significances for solving the problem of elastic wave scattering and dynamic stress concentrations in cylindrical shells with a circular cutout.     

表面裂纹对掠入射垂直偏振横波散射的动态光弹实验分析

利用动态光弹法研究掠入射垂直偏振横波(SV波)在表面裂纹处的散射声场,给出不同倾斜角度的表面裂纹引起的散射声场分布和简化波前示意图。以垂直表面裂纹为例,有限元仿真和电法测量分别直接地和间接地证明了光弹实验结果的可靠性。表面裂纹引起的各类散射波与裂纹参量密切相关且容易区分,可使用一阶散射声波到达时间反演表面裂纹的长度和倾角,实验测量值与真实值的相对误差在6%以下。     

Seismic scattering from a spherical inclusion eccentrically located within a homogeneous, spherical host: theoretical derivation

The scattered fields from a spherical body eccentrically located within an otherwise homogeneous host sphere are derived by satisfying the boundary conditions at both interfaces simultaneously. The source, which may be composed of any linear combination of S and P waves, is also located arbitrarily within the host sphere. The scattering system may have applications in seismic scattering, by cavities or dense bodies located near the Earth surface or to the Slichter mode.     

Bolt axial stress measurement based on a mode-converted ultrasound method using an electromagnetic acoustic transducer

A method is proposed to measure the stress on a tightened bolt using an electromagnetic acoustic transducer (EMAT). A shear wave is generated by the EMAT, and a longitudinal wave is obtained from the reflection of the shear wave due to the mode conversion. The ray paths of the longitudinal and the shear wave are analyzed, and the relationship between the bolt axial stress and the ratio of time of flight between two mode waves is then formulated. Based on the above outcomes, an EMAT is developed to measure the bolt axial stress without loosening the bolt, which is required in the conventional EMAT test method. The experimental results from the measurement of the bolt tension show that the shear and the mode-converted longitudinal waves can be received successfully, and the ratio of the times of flight of the shear and the mode-converted longitudinal waves is linearly proportional to the bolt axial tension. The non-contact characteristic of EMAT eliminates the effect of the couplant and also makes the measurement more convenient than the measurement performed using the piezoelectric transducer. This method provides a promising way to measure the stress on tightened bolts.     

The quantum acousto-optic effect in Bose-Einstein condensate

We investigate the interaction between a single mode light field and an elongated cigar shaped Bose-Einstein condensate (BEC), subject to a temporal modulation of the trap frequency in the tight confinement direction. Under appropriate conditions, the longitudinal sound like waves (Faraday waves) in the direction of weak confinement acts as a dynamic diffraction grating for the incident light field analogous to the acousto-optic effect in classical optics. The change in the refractive index due to the periodic modulation of the BEC density is responsible for the acousto-optic effect. The dynamics is characterised by Bragg scattering of light from the matter wave Faraday grating and simultaneous Bragg scattering of the condensate atoms from the optical grating formed due to the interference between the incident light and the diffracted light fields. Varying the intensity of the incident laser beam we observe the transition from the acousto-optic effect regime to the atomic Bragg scattering regime, where Rabi oscillations between two momentum levels of the atoms are observed. We show that the acousto-optic effect is reduced as the atomic interaction is increased.     

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。     

Seismic scattering from a spherical inclusion eccentrically located within a homogeneous,spherical host: theoretical derivation

Abstract

The scattered fields from a spherical body eccentrically located within an otherwise homogeneous host sphere are derived by satisfying the boundary conditions at both interfaces simultaneously. The source, which may be composed of any linear combination of S and P waves, is also located arbitrarily within the host sphere. The scattering system may have applications in seismic scattering, by cavities or dense bodies located near the Earth surface or to the Slichter mode.     

利用Taylor展开法研究Lamb波在功能梯度材料中的传播特性

超声技术可用于对功能梯度材料(FGMs)的性质进行评估. 由于FGMs性质的非均匀性,采用分布函数来描述FGMs弹性常数和密度沿厚度方向的变化趋势,并提出利用Taylor展开的方法来解决分布函数为任意函数时的FGMs中Lamb波的传播问题. 利用本征函数展开法得到了铁基氧化铝FGMs中Lamb波的相速度色散曲线,讨论了材料性质分布对铁基氧化铝FGMs中Lamb波传播特性的影响. 为FGMs性质(沿板厚方向变化)的反演提供了理论依据. 关键词： 功能梯度材料 Lamb波 Legendre多项式 分布函数     

The scattering of steady-state SH waves in a bi-material half space with multiple cylindrical elastic inclusions

The scattering of steady-state SH waves in a bi-material half space with multiple cylindrical elastic inclusions is presented analytically. Mirror method and multi-polar coordinate systems are developed to solve the complex boundary value problem. Considering the displacement and stress continuity conditions, a series of integral equations for unknown coefficients are obtained and solved by truncation. The solution is used to calculate the dynamic stress concentration factor around the edge of the inclusion, and the analysis and numerical results are discussed. The results show that degree of dynamic stress concentration around the circular inclusion is influenced by the incident angle, the incident wave number, and the parameters of medium.     

Elastic model for simulating ultrasonic inspection of smooth and rough defects

A model is presented for the scattering of ultrasonic waves from smooth and randomly rough defects. The model uses Kirchhoff theory and is elastic, such that mode-conversion between compressional and shear waves is included in the formulation. The model is designed to simulate ultrasonic non-destructive testing situations, by specifying the location and orientation of a defect within an isotropic material, together with transmitter and receiver locations on an inspection surface. Results are presented for the scattering of both monochromatic waves and of pulses. It is shown how small levels of roughness can affect echodynamic curves and how diffracted signals may become lost due to scatter from the rough faces of defects. It is also shown that the usual rules for coupling between waves of all three modes no longer hold when roughness is present. In particular, roughness leads to coupling between horizontally polarized shear (SH) waves and the other two wave modes. The model predictions are also compared with an earlier acoustic model, indicating the importance of mode-conversion effects when considering rough defects embedded within solids.     

Nonlinear Effect and Atomic Entanglement in a Coupled-Cavity Array

By introducing the nonlinear effects that arise from Kerr medium, we theoretically study the nonlinear effect and the entanglement between two atoms in two coupled cavities. We give out the process of dynamic stability and solve the eigen problem of the system under high-intensive fields. The dynamics of the two coupled cavity with high-intensity fields inside is also studied numerically, the effects of atom-field coupling on the self-trapping as well as on the entanglement are also analyzed and discussed. In vacuum and high-intensity fields we calculate the concurrence of the two atoms in both theoretical and realistic situation, and discuss the nonlinear effect on the atomic entanglement. The result shows that the nonlinear interaction can play a controlling role in entangling two atoms.     

Dynamic stress concentration in a ribbed plate using the acoustical wave propagator technique

This paper presents an explicit acoustical wave propagator technique to investigate the flexural wave scattering and dynamic stress concentration in a ribbed plate based on Mindlin plate theory. A scheme combining Chebyshev polynomial expansion and fast Fourier transformation is introduced to implement the operation of the acoustical wave propagator. The exact analytical solutions are also presented to demonstrate the validity of the present technique. The wave propagation patterns are used to investigate the effect of rib on the flexural wave scattering and distribution of dynamic stress concentration. Dynamic stress concentration factors around the discontinuities are examined in detail.