Existence of longitudinal waves in anisotropic poroelastic solids

In anisotropic fluid-saturated porous solids, four waves can propagate along a general phase direction. However, solid particles in different waves may not vibrate in mutually orthogonal directions. In the propagation of each of these waves, the displacement of pore–fluid particles may not be parallel to that of solid particles. The polarization for a wave is the direction of aggregate displacement of the particles of the two constituents of a porous aggregate. These polarizations, for different waves, are not mutually orthogonal. Out of the four waves in anisotropic poroelastic medium, two are termed as quasi-longitudinal waves. The prefix ‘quasi’ refers to their polarization being nearly, but not exactly, parallel to the direction of propagation. The existence of purely longitudinal waves in an anisotropic poroelastic medium is ensured by the stationary characters of two expressions. These expressions involve the elastic (stiffness and coupling) coefficients of a porous aggregate and the components of phase direction. Necessary and sufficient conditions for the existence of longitudinal waves are discussed for different anisotropic symmetries. Conditions are also discussed for the existence of the apparent longitudinal waves, i.e., the propagation of wave motion with the particle displacement parallel to the ray direction instead of the phase direction. A graphical solution of a numerical example is shown to check the existence of these apparent longitudinal waves for general directions of phase propagation.     

Stability of some stationary solutions to the forced KdV equation with one or two bumps

Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. The first-order approximation of long nonlinear surface waves over one or two bumps results in a forced Korteweg?Cde Vries (fKdV) equation. Solutions of the stationary fKdV equation are constructed and their stability is studied, either analytically or numerically. These various solutions include solitary waves over a single bump, solitary waves with two humps over a double bump, table-top solutions over a double bump and fronts.     

Reflection of an air shock wave from a foam layer

Within the framework of an equilibrium model of disperse media, the problem on reflection of an air shock wave from a foam layer located in the neighborhood of a rigid wall is investigated. An exact solution is constructed for the initial stage of reflection from a homogeneous layer. The effect of the type of gas which fills foam bubbles on the characteristics of reflected waves is studied. The results of numerical calculations are given, which are obtained using the modified Godunov method     

直立堤上任意方向入射波的波压力研究

为了研究在不同入射波向时直立堤上的波压力,基于FLOW-3D,该文建立了三维数值波浪水池,并进行了物理模型试验。模型采用推板造波及孔隙消波的方法形成稳定的波浪场,数值模拟结果与试验结果吻合较好。研究表明:墙面测点的波压力与波吸力均随入射角度的增大而增大;墙底各测点浮托力的变化规律较为复杂,合田公式不能准确描述;墙面波压力的分布与合田公式基本相符;墙底浮托力的分布并不是合田公式描述的三角形,而是近似梯形分布;斜向波作用下的墙面波吸力分布图相似于正向入射时的分布。研究结论可为防波堤设计提供参考依据。     

无限介质包围的充液管道中导波的频散特性

利用波传播方法从理论上分析了无限介质包围的充液管道中导波的频散特性.基于经典的薄壳振动理论,求出了不同传输路径中的波数表达式,并利用数值方法对振动方程进行解析研究,分析管道参数和无限介质对导波频散特性的影响.结果表明,管道厚径比、管壁厚度、无限介质和管壁材料与导波频散密切相关.其中管道厚径比和管壁材料对流体主导波(s1...     

一种由横波激发的特殊非线性声现象

目前对非线性超声的研究多集中在纵波激发的谐波性质以及对材料微观结构变化的实验检测上,横波激发的非线性声波性质少有研究。对横波激发的一维非线性声波方程入手,利用摄动法求解该方程,并改写为一阶偏微分方程,然后利用交错网格的有限差分形式进行数值求解。结果表明:采用横波激发,能产生线性横波和非线性纵波,且纵波的高次谐波内有两个信号,分别以纵波和横波两种速度传播。若采用较长的激发信号,纵波谐波能形成"拍"现象,成为一种奇特的声传播现象。     

Improvements for the ultra weak variational formulation

In this paper, we investigate strategies to improve the accuracy and efficiency of the ultra weak variational formulation (UWVF) of the Helmholtz equation. The UWVF is a Trefftz type, nonpolynomial method using basis functions derived from solutions of the adjoint Helmholtz equation. We shall consider three choices of basis function: propagating plane waves (original choice), Bessel basis functions, and evanescent wave basis functions. Traditionally, two‐dimensional triangular elements are used to discretize the computational domain. However, the element shapes affect the conditioning of the UWVF. Hence, we investigate the use of different element shapes aiming to lower the condition number and number of degrees of freedom. Our results include the first tests of a plane wave method on meshes of mixed element types. In many modeling problems, evanescent waves occur naturally and are challenging to model. Therefore, we introduce evanescent wave basis functions for the first time in the UWVF to tackle rapidly decaying wave modes. The advantages of an evanescent wave basis are verified by numerical simulations on domains including curved interfaces.Copyright © 2013 John Wiley & Sons, Ltd.     

The structure of a turbulent boundary layer

According to the wave mechanism of turbulence, pulsation in the hydrodynamic parameters results from a superposition of perturbations arising at the wall and then spreading in the flow in the form of spherical wave packets. At the flow boundary, where the fluid velocity is characterized by a large gradient, the acoustic rays of these waves exhibit bending and reversal toward the wall, whereby the trajectories with various initial orientations are interweave and the wave packets are broken. The pulsation of parameters in the region of wave packet breakage results in the formation of a turbulent boundary layer. Upon the reflection of waves, the flow velocity oscillations immediately at the wall cease that corresponds to a laminar sublayer of the turbulent boundary layer.     

Existence of longitudinal and transverse waves in anisotropic thermoelastic media

Four waves propagate in an anisotropic thermoelastic medium. The fastest among them is a quasi-longitudinal wave. The slowest of them is a thermal wave. The remaining two are called quasi-transverse waves. The prefix ‘quasi’ refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these four waves are not mutually orthogonal. Hence, unlike anisotropic elastic media, the existence of a longitudinal wave may not imply the existence of a transverse wave, by default. The existence of a purely longitudinal wave in an anisotropic thermoelastic medium is ensured by the stationary characters of three expressions. These expressions involve components of phase direction with elastic (stiffness and coupling) and thermal coefficients of the thermoelastic medium. The existence of a purely transverse wave is ensured by the two equations restricting the choice of thermoelastic (stiffness and coupling) coefficients. The existence of longitudinal and transverse waves along the coordinate axes and in the coordinate planes are discussed for general anisotropy. The discussion is extended to orthotropic materials, and the existence of pure phases is explored along few specific phase directions.     

基于谱有限元的自由阻尼梁结构损耗因子分析

使用谱有限元分析了自由阻尼梁中扩散波类型及其损耗因子,通过对其特征波形的分析探讨了各个频率下每种波的激励条件,然后使用有限元对自由阻尼长梁做谐响应分析得到各个单元的应变能,根据应变能法计算得到该长梁分别在垂直和水平激励下的结构损耗因子,对结构损耗因子同激励起的波类型之间的关系进行了讨论,最后分析了边界反射对结构损耗因子的影响。研究表明：垂直激励主要激励起最高阶弯曲波或者某些低阶纵波,水平激励主要激励起最高阶纵波;边界反射对结构损耗因子的影响随着梁长增大以及激励点远离边界而变小;不同边界条件的结构损耗因子一般情况下比较接近,但在一些频率点处会存在一定的差异;自由阻尼梁的结构损耗因子主要由激励所能激励起的波类型所决定,在一定程度上受到边界反射影响。     

Gravity-driven film flow down an inclined wall with three-dimensional corrugations

Summary The gravity-driven flow of a liquid film down an inclined wall with three-dimensional doubly periodic corrugations is investigated in the limit of vanishing Reynolds number. The film surface may exhibit constant or variable surface tension due to an insoluble surfactant. A perturbation analysis for small-amplitude corrugations is performed, wherein the wall geometry is expressed as a Fourier series consisting of a linear superposition of two-dimensional oblique waves defined by two base vectors. Each of the constituent perturbation flows over the individual oblique waves is further decomposed into a two-dimensional flow transverse to the oblique waves and a unidirectional flow parallel to the waves. Both the transverse and the parallel flow are calculated by carrying out an analysis in oblique coordinates, similar to that conducted for two-dimensional flow. The particular cases of flow down a wall with oblique two-dimensional, orthogonal three-dimensional, and hexagonal three-dimensional corrugations are considered. The results illustrate the surface velocity field and the distribution of the surfactant. The three-dimensional wall geometry is found to reduce the surface deformation with respect to its two-dimensional counterpart by increasing the effective wave numbers and decreasing the effective capillary number encapsulating the effect of surface tension.     

有限长叉指换能器激发表面波及体波声场的数值模拟

采用数值方法,模拟了有限长叉指换能器(IDT)在半无限大压电晶体中激发的表面波和体波声场在晶体界面上的分布情况。在数值模拟所得结果的基础上,将频率域内的位移分量做傅立叶反变换得到时间域内声波脉冲振幅随时间的分布,并对界面上三个位移分量含有的声波模式进行分析,其中场位移分量1沿波的传播方向,位移分量2为平行于IDT指条方向,位移分量3沿基片表面法线方向。分析结果表明,界面上各位移分量中除Rayleigh波外,还含有不同比例的体波成分。其中,在位移分量1和位移分量3中占主要成分的是准纵波,在位移分量2中占主要成分的是准慢切变波。它们均按照指数方式在表面上进行传播衰减,其中准慢切变波的衰减速度小于准纵波的衰减速度。IDT指条数相对较多时的体波振幅要大于指条数相对较小时的体波振幅,且在距离IDT较近的范围内IDT指条数相对较多时体波衰减更快。     

Sand bed configurations under 2‐D standing waves

Abstract

Laboratory experiments conducted in a wave basin with movable sand bed have shown that, under the action of 2‐D standing water waves, longitudinal sand bars with small ripples riding on their tops are formed beneath the nodes of standing waves. Wavelengths of the sand bars are approximately equal to one‐half of those of standing water waves. The formation of sand bars under standing waves over an initially horizontal sand bed is explained by the suction and impinging effects of the wave action. A mathematical model for describing the induced density of sediment‐water mixture due to wave action is proposed. By employing the induced‐density model and mass conservation of sediment‐water mixture, a numerical simulation model is constructed. Bed configurations resulting from the actions of 2‐D standing waves are studied by using the simulation model. The simulation results of sand bed configuration under the action of 2‐D standing waves are in good agreement with those obtained from laboratory experiments.     

Electromagnetic theory of an open resonator.

Particular higher-order sources give rise to electromagnetic Gaussian beams, which are linearly polarized and have their maximum in the propagation direction. For this dipolar beam the cross-sectional shape changes in the propagation direction. Nodal surfaces exist on which the tangential component of the electric field vanishes in the standing wave that is formed by the two oppositely directed dipolar, electromagnetic Gaussian beams. These surfaces are identified as the mirror shapes for an open resonator that supports this standing wave. For standing waves that have a particular cross-sectional shape at the waist the cross section of the beam near the mirror surfaces is circular. The resonant frequencies for the fundamental transverse mode of such a resonator have been determined as a function of the geometry and the axial mode number. By a perturbation technique the resonant frequency of an open resonator with spherical mirrors has been obtained. This result is valid in only the paraxial approximation. Illustrative numerical results are included.     

Characteristics of waves in a functionally graded cylinder

An analytical‐numerical method is presented for analysing characteristics of waves in a cylinder composed of functionally graded material (FGM). In this method, the FGM cylinder is divided into a number of annular elements with three‐nodal‐lines in the wall thickness. The elemental material properties are assumed to vary linearly in the thickness direction so as to better model the spatial variation of material properties of FGM. The Hamilton principle is used to develop the dispersion equations for the cylinder, and the frequency and the group velocity are established in terms of the Rayleigh quotient. The method is applied to analyse several FGM cylinders, and its efficiency is demonstrated. Numerical results demonstrate that the ratio of radius to thickness has a stronger influence on the frequency spectra in the circumferential wave than on that in the axial wave, that negative group velocity presents at a range of smaller wave numbers and that the range varies as the wave normal and the ratio of radius to thickness of FGM cylinders. Copyright © 2001 John Wiley & Sons, Ltd.     

The reflection of nonlinear irregular surface water waves

This paper concerns the reflection of irregular surface water waves from an impermeable vertical wall and investigates the similarities between this case and the direct, head-on collision of two identical wave groups travelling in opposite directions. A new set of experimental measurements is presented and compared with fully nonlinear numerical predictions based upon a multiple-flux boundary element method (BEM). Comparisons concern both the spatial and the temporal water surface elevations in the vicinity of the focused wave event; the latter occurring at the location of the wall. Linear and second-order irregular wave theories, commonly adopted as the basis for design solutions, are shown to significantly under-predict both the wave steepness and the maximum crest elevation in the vicinity of the wall. In contrast, the fully nonlinear numerical predictions are shown to be in very good agreement with the experimental measurements; the present results having been achieved without the need for smoothing, filtering or regridding.     

Artificial boundary conditions for atomic simulations of face-centered-cubic lattice

We design a class of matching boundary conditions for atomic simulations of the face-centered-cubic lattice. Such a condition takes the form of a linear constraint for atoms near the boundary. A normal matching boundary condition is obtained by matching the dispersion relation in the long wave limit. A two-angle matching boundary condition is constructed through operator multiplication with the help of apparent wave propagation. The edge atoms and the corner atoms are treated in a consistent manner. Reflection coefficient analysis and wave-packet tests verify the effectiveness of the proposed boundary conditions for general incidence, not limited to long waves. The treatment is local in both space and time, yielding negligible additional numerical cost. Vector wave formulation is also presented, and applied to nanoindentation simulations.     

Instability of periodic stationary waves in an active nonlinear medium with high-frequency losses

The stability of stationary waves in nondispersive nonlinear active media with high-frequency losses is studied. It is shown that waves with wavelength greater than some minimum value λ_min can exist in such a medium. All stationary waves are unstable with respect to small perturbations of their profile, but as the wavelength increases, the lifetime of the wave increases and for waves with long wavelengths λ the lifetime can be long enough that these waves can in some sense be regarded as stable. Pis’ma Zh. Tekh. Fiz. 24, 80–87 (January 26, 1998)     

分层流体中水平运动潜体产生的内波分析

从线性化的Euler方程和连续方程出发，采用线性自由面条件，通过傅里叶变换法研究水平运动点源在分层流体中产生的内波．利用源汇分布法分析运动潜体产生的lee渡，采用稳定相法计算远场速度．计算结果表明，高模态内渡的渡域角小于低模态内波的渡域角，内渡的渡域角小于Kelvin波的渡域角；随航速增大lee波主要表现为散波．     

用改进的Boussinesq方程模拟潜堤上的波浪变形

研究了一种改进的Boussinesq方程,采用预报校正格式对该方程进行了数值离散,并对淹没潜堤上的波浪变形进行了数值模拟,从数值模拟结果和实测值的比较结果来看,该方程能较好地模拟波浪在潜堤上传播时波面的变形过程,可以用于实际中的波浪问题计算。这种改进的Boussinesq方程本身及其求解方法需做进一步的完善。研究结果为实际应用Boussinesq方程来研究复杂地形上的波浪传播提供一定的理论指导。