Strain energy density of a circular cavity buried in semi-infinite functionally graded materials subjected to shear waves

In this paper, based on the theory of multiple scattering of elastic waves, employing wave functions expansion method, multiple scattering and strain energy density in semi-infinite functional graded materials with a circular cavity are investigated, the analytical solution of the problem is derived, and the numerical solution of the strain energy density factors around the cavity is also presented. The effects of the distance between the cavity and the edge of the materials, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. From analysis, it can be seen that when the non-homogeneous parameter of materials is less than zero, it has less influence on the maximum strain energy density factor around the cavity; however, it has greater influence on the distribution of strain energy density factors around the cavity. When the non-homogeneous parameter of materials is greater than zero, it has greater influence on both the maximum strain energy density factor and the distribution of strain energy density factor around the cavity, especially in the case that the distance between the cavity and the edge is comparatively little.     

Strain energy density of a circular cavity buried in a semi-infinite slab of functionally graded materials subjected to anti-plane shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and strain energy density in a semi-infinite slab of functionally graded materials with a circular cavity. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. The analytical solution of the problem is derived, and the numerical solutions of the strain energy density factors around the cavity are also graphically presented. The effects of the distances between the cavity and the boundaries of the semi-infinite slab, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. Analyses show that the strain energy density around the cavity increases with increasing non-homogeneous parameter of materials and incident wave number. The boundaries of the semi-infinite slab have great effect on both the maximum strain energy density and the distribution around the circular cavity, and the effect increases with increasing incident wave number. When the distance between the semi-infinite boundary and the cavity varies, the effect of the upper and lower boundaries on the distribution of the strain energy density factors around the cavity is also examined.     

Theory of scattering from a nearly transparent anomaly

Summary Recent advances in the design of uhf and microwave communication equipment, coupled with the increasing need for expanding the usable frequency spectrum, have generated considerable interest in making use of scattered signals which are propagated beyond the radio horizon. Although a large number of experimental measurements have been reported in the literature, much theoretical work in interpreting the basic scattering phenomena remains to be done. In order to gain a more detailed insight into the scattering mechanism, an approximate equation of propagation of electromagnetic energy in a nearly transparent medium is applied to the case in which the medium contains a dielectric inhomogeneity in the form of an isolated gaussian-shaped perturbation in the refractive index. Equations for the scattering caused by the perturbing blob are illustrated graphically. The energy extracted from the incident wave by the blob is illustrated graphically by a plot of the total scattering cross-section as a function of blob size.     

论岩体软弱结构面对应力波传播的影响

本文引入岩体软弱结构面上的边界条件,给出应力波斜入射到能滑移、有摩擦的软弱结构面时,波势、应力和能流的透反射关系和一些计算结果。在此基础上,提出了判断岩体是否沿结构面产生相对滑移的准则,给出计算结构面能量耗损的关系式和一些计算结果,并就与工程爆破有关的一些问题进行了讨论。     

The scattered energy around a circular hole by SH wave in anisotropic media

A new approach based on complex function for solving the SH-wave scattering problem around a circular hole in an anisotropic media is desribed in this paper. It is found that the scattered energy depends on the incident wave number and the hole radius. Finally, some numerical results of scattered energy of a circular hole in an anisotropic media are given.The project has been supported by National Natural Science Foundation of China.     

波形控制器对杀伤战斗部破片飞散特性影响研究

为提升杀伤战斗部破片轴向飞散的集中度,提高战斗部的轴向杀伤威力,提出使用波形控制器控制破片的飞散方向。基于爆轰波在波形控制器界面发生反射的规律以及Shapiro公式,设计了波形控制器的形状,使用LS-DYNA有限元软件和ALE(arbitrary Lagrange-Euler)算法对破片的飞散过程进行数值计算,结合战斗部原理样机静爆试验,验证了使用波形控制器改善破片飞散特性方法的合理性。对比了有无波形控制器时破片飞散过程的差异,对无波形控制器以及波形控制器材料分别为尼龙、聚氨酯和聚四氟乙烯（polytetrafluoroethylene,PTFE）时杀伤战斗部的破片飞散速度和破片飞散角规律进行了分析。结果表明：波形控制器可以减小战斗部中心和两端位置的破片飞散速度大小差异,使中心到两端位置的破片飞散方向角变化均匀,破片在轴向的分布更加均匀;不同材料的波形控制器对破片飞散特性影响不同,波形控制器的使用减小了破片飞散角,增大了破片分布密度,提升了破片飞散的集中度。破片飞散角数值计算值与试验计算值误差在6.53%之内,与无波形控制器的杀伤战斗部原理样机相比,含波形控制器且材料为尼龙、聚氨酯和P...     

基于辛理论的载流碳纳米管能带分析

基于连续介质力学理论和辛弹性理论,将载流碳纳米管等效为铁木辛柯梁,采用哈密顿变分原理建立了载流碳纳米管的振动控制方程;引入对偶变量将振动控制方程从拉格朗日体系导入到哈密顿体系下;通过波传播方法分析了载流碳纳米管的能带结构;研究了流体密度、流速对载流碳纳米管能带结构的影响;同时计算了载流碳纳米管的散射矩阵. 研究发现:管内流速以及流体密度对剪切频率和弯曲频率有着非常重要的影响. 研究结果表明:载流碳纳米管的剪切频率和弯曲频率因流体的加入而减小,并随流速及流体密度的增大而减小;通过对数值结果的分析发现:载流碳纳米管由于管内流体、流速以及流体密度的作用,会使得载流碳纳米管变的更“软”. 其中,哈密顿体系下所得出的载流碳纳米管弯曲频率随管内流体密度的增加而变小,有别于在拉格朗日体系下非局部梁理论所得的结论. 同时,数值结果表明散射矩阵是酉矩阵,辛体系下的入射波功率流与反射波功率流相等,即功率流守恒,体现了辛弹性力学理论的优越性.      

Ultrasound scattering from a turbulent round thermal pure plume

This research work brings about additional contribution to validate the ultrasound scattering technique as a nonintrusive probe in the Fourier space for measurements performed in unsteady flows. In particular, this work reports experimental evidence of scattering from a turbulent thermal plume utilized as a testing flow. This technique is based upon the scattering of an ultrasound wave hitting and interacting with an unstable flow. The coupling among the acoustic mode with vorticity and entropy modes is derived from nonlinear terms of Navier–Stokes and energy equations. Scattering mechanism occurs when characteristic length scales of flows are comparable with wavelength of sound. Thus, it is possible to probe the flow at different length scales by changing the incoming frequency. The results allow verifying some theoretical predictions, such as the existence of a nonscattering angle. It was also observed, that both the phase and the Doppler shift of the Fourier's signal are linear, respectively, with respect to the time and the frequency of the incident wave. The Doppler shift allowed us to determine the advection velocity and has proved to be sensitive to the direction of the wave vector, to the scattering angle and also, we show that it is possible to have both positive and negative angles. The advection velocity increases with temperature and its values are coherent with those obtained with traditional techniques. Broadening and Doppler shift of the scattering signal allowed us to define the turbulence intensity, whose values are in agreement with those found in thermal plumes, where well-known techniques are currently used. This study has shown that the turbulence intensity increases weakly with temperature, nevertheless it seems more sensitive to the size of the structure under observation.     

Wave interaction with multiple articulated floating elastic plates

Flexural gravity wave scattering by multiple articulated floating elastic plates is investigated in the three cases for water of finite depth, infinite depth and shallow water approximation under the assumptions of two-dimensional linearized theory of water waves. The elastic plates are joined through connectors, which act as articulated joints. In the case when two semi-infinite plates are connected through a single articulation, using the symmetric characteristic of the plate geometry and the expansion formulae for wave-structure interaction problem, the velocity potentials are obtained in closed forms in the case of finite and infinite water depths. On the other hand, in the case of shallow water approximation, the continuity of energy and mass flux are used to obtain a system of equations for the determination of the full velocity potentials for wave scattering by multiple articulations. Further, using the results for single articulation and assuming that the articulated joints are wide apart, the wide-spacing approximation method is used to obtain the reflection coefficient for wave scattering due to multiple articulated floating elastic plates. The effects of the stiffness of the connectors, length of the elastic plates and water depth on the propagation of flexural gravity waves are investigated by analysing the reflection coefficient.     

????Hilbert-Huang?任?????????????????Ч?????

通过Hilbert-Huang变换得到地震波的时间-频率-振幅分布图,并对地震动动力特性进 行分析,创造性地提出了用地震动峰值能量的最大值(即时频密度函数的最大值)和峰值系 数作为评估地震动震动效应强弱的定量指标,初步建立了地震动震动效应评估的判据;并用实 例验证了该判据的可行性和可靠性.     

弹性波绕任意形状界面孔的散射

求解了弹性波绕任意形状界面孔的散射问题．通过入射波、反射波或折射波及孔的散射波场的叠加,得到了界面孔在SH波绕射下的总波场．总波场波函数的级数项待定系数可采用边界配点法来确定,该法不受边界正交性的限制,能够适用于任意形状的边界．最后,对界面椭圆孔进行了实例计算,得到了椭圆孔边的动应力集中系数．     

缺陷岩体中弹性波传播的多次散射效应分析

弹性波在岩体中传播时与岩体缺陷相互作用形成复杂的传播图案。为研究缺陷对弹性波多次散射作用的影响,建立了双椭圆缺陷模型,基于Green函数基本解,采用边界积分的计算方法,得到了反映缺陷界面条件的刚度矩阵,分析了弹性波在双椭圆缺陷间的多次散射效应。结果表明：与单椭圆缺陷模型相比,双缺陷的相互作用使得弹性波频散和衰减效应增强,定量给出了缺陷的影响区域,从而明确了多次散射效应的尺度界限。进一步探讨了弹性波传播的多尺度效应,结果表明频散的Rayleigh峰、Mie峰和衰减的峰值频率同椭圆长轴和入射波波长两个尺度密切相关,存在明确的定量关系。相应的数值模拟结果表明,弹性波和缺陷相互作用在缺陷界面上诱发界面波,该界面波也存在频率相关性,影响了弹性波宏观传播的频散和衰减特征。     

Vibration modelling of structural networks using a hybrid finite element/wave and finite element approach

The vibration modelling of waveguide structures is considered. These structures comprise waveguides connected via joints. Traditionally, analytical models of the wave behaviour of such structures can be developed if they are simple (beams or rods connected at point joints, etc.). However, if the waveguides are of complicated constructions (truss-like, layered media, etc.) or the joints are complicated (e.g. of significant physical dimensions), obtaining the wave characteristics might be a formidable task. In this paper, such structures are modelled using a hybrid finite element/wave and finite element (FE/WFE) approach. The waveguides are modelled using the WFE method and thus their wave characteristics are obtained regardless of the complexity of their cross-section. The joints are modelled using standard FE, and the WFE and FE models are coupled to yield the scattering properties of the joints. The propagation and scattering models are assembled to describe the behaviour of the structure using relatively small models, while also providing information for other applications such as structure-borne sound, statistical energy analysis, etc. Numerical examples are presented to illustrate the approach.     

A time-domain energy theorem for the scattering of plane elastic waves

A time-domain energy theorem for the scattering of plane elastic waves by an obstacle of bounded extent is derived. The obstacle is embedded in a homogeneous, isotropic, perfectly elastic medium. As to the elastodynamic behavior of the obstacle no assumptions have to be made; so, lossy, non-linear and time-variant behavior is included. As to the wave motion, three different kinds of time behavior are distinguished: (a) transient, (b) periodic, and (c) pertuating, but with finite mean power flow density. For these cases, the total energy (case (a)) or the time-averaged power (cases (b) and (c)) that is both absorbed and scattered by the obstacle is related to a certain time interaction integral of the incident plane wave (P or S) and the spherical-wave amplitude of the scattered wave of the same type (P or S) in the far-field region, when observed in the direction of propagation of the incident wave.     

Sound scattering and its cancellation by an elastic spherical shell in free space and near a free surface

Sound scattering by an elastic spherical shell is analysed using linear acoustics and linear structural dynamics. It is suggested to utilize the shell’s structural dynamics to reduce or even eliminate the scattered sound field, thus making it practically acoustically invisible. This can be achieved using a prescribed external pressure distribution acting on the shell’s wall. Exact analytical solutions are found for that external pressure distribution, eliminating the scattered wave when the sphere is in free space or near a free surface and is subject to an incoming planar monochromatic sound wave. The latter is assumed to propagate in a direction perpendicular to the free surface (if it exists). The case of a few pressure-actuators acting on the shell’s wall is also modelled and an optimal solution which reduces the sound scattering by these actuators is found. An aluminium shell of 1 m radius and 5 mm thickness, situated in fresh water is analysed for sound frequencies of up to 10 kHz. The scattered wave fields are presented as well as the external pressure distributions that eliminate these scattered sound field, i.e. achieving acoustic cloaking. Significant reduction in the scattered wave energy and the target strength of more than 10 dB are also realized using a few pressure-actuators as long as the distance between the actuators is no more than three times the incident wave length for the investigated cases.     

多个椭圆柱波浪力的一种解析解

波浪在大尺寸结构表面产生不可忽略的散射波, 该散射波在多柱体体系中继续传播, 并在同体系中的其他柱体上产生高次散射波. 本文基于椭圆坐标系和绕射波理论首先推导了波浪作用下椭圆单柱体产生的散射波压力公式, 随后考虑该散射波在多柱体系中的传播, 将其视为第二次入射波, 推导出柱体上第二次散射波压力公式, 同理可以推导出高次散射波压力公式, 最后得到椭圆多柱体波浪力解析解, 并用数值解验证了本文解析方法的正确性. 本文以双柱体和四柱体体系为例, 分析了不同参数(波数、净距、波浪入射角度等)下, 高次散射波对柱体上波浪作用的影响. 结果表明: 波数较大的情况下, 高次散射波引起柱体上的波浪力不能忽略; 结构间距较大的情况下, 虽然高次波的作用有减小的趋势但仍然明显; 高次散射波来自多个柱体对入射波的散射, 柱体数目的增加后, 高次波的影响会增加, 结构所受的高次波作用因参数变化而起的波动会变剧烈; 高次波对上游柱体波浪力的贡献较对下游柱体的贡献大.      

Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere

In this paper, the off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid immovable (fixed) sphere is investigated. It is shown here that shifting the sphere off the axis of wave propagation induces a dependence of the scattering on the azimuthal angle. Theoretical expressions for the incident and scattered field from a rigid immovable sphere are derived. The near- and far-field acoustic scattering fields are expressed using partial wave series involving the spherical harmonics, the scattering coefficients of the sphere, the half-conical angle of the wave number components of the beam, its order and the beam-shape coefficients. The scattering coefficients of the sphere and the 3D scattering directivity plots in the near- and far-field regions are evaluated using a numerical integration procedure. The calculations indicate that the scattering directivity patterns near the sphere and in the far-field are strongly dependent upon the position of the sphere facing the incident high-order Bessel vortex beam.     

SH波绕界面孔的散射

用波函数展开方法研究了SH波绕界面孔的散射问题。由入射、反射和透射波组成的自由波场与孔的散射场叠加成总波场。按照一定方式将两个半平面散射波场延拓于全平面，通过Hankel-Fourier展开方法求得了任意形状孔散射场的级数解。以椭圆形孔为例计算了孔边缘的动应力集中系数。     

Nonlinear hyperbolic wave propagation in a one-dimensional random medium

We use an asymptotic expansion introduced by Benilov and Pelinovski to study the propagation of a weakly nonlinear hyperbolic wave pulse through a stationary random medium in one space dimension. We also study the scattering of such a wave by a background scattering wave. The leading-order solution is non-random with respect to a realization-dependent reference frame, as in the linear theory of O’Doherty and Anstey. The wave profile satisfies an inviscid Burgers equation with a nonlocal, lower-order dissipative and dispersive term that describes the effects of double scattering of waves on the pulse. We apply the asymptotic expansion to gas dynamics, nonlinear elasticity, and magnetohydrodynamics.