Nonlinear faraday waves in a parametrically excited circular cylindrical container

IntroductionIn 1 83 1 ,Faraday[1]reportedhisexperimentalobservationofsurfacewavesindifferentfluidscoveringahorizontalplatesubjectedtoaverticalvibration ,andheobservedthesurfacestandingwavesoffluidsliketheteethofaveryshortcoarsecomb .Heremarksthatthesesurfacewaveshaveafrequencyequaltoonehalfthatoftheexcitation .ThisisthefamousFaradayexperiment.WedesignatethosefluidsurfacewavesformedbyverticallyexcitationandhaveafrequencyequaltoonehalfthatoftheexcitationasFaradaywaves.FollowingthisproblemMatth…     

Experimental investigation of a twice-shocked spherical gas inhomogeneity with particle image velocimetry

Results are presented from an experimental investigation into the interaction of a planar shock wave with a vortex ring. A free-falling spherical soap bubble is traversed by the incident shock wave and develops into a vortex ring as a result of baroclinically deposited vorticity (?r×?p 1 0{\nabla\rho\times\nabla p \neq 0}). The vortex ring translates with a velocity relative to the particle velocity behind the shock wave due to circulation. After the shock wave reflects from the tube end wall, it traverses the vortex ring (this process is called “reshock”) and deposits additional vorticity. Planar Mie scattering is used to visualize the atomized soap film at high frame rates (up to 10,000 fps). Particle image velocimetry (PIV) was performed for an argon bubble in nitrogen accelerated by a M = 1.35 shock wave. Circulation was determined from the PIV velocity field and found to agree well with Kelvin’s vortex ring model.     

Effect of baffles on sloshing modulated fluid force and torque fluctuations on the dewar driven by gravity gradient acceleration in microgravity

The dynamical behavior of fluids affected by the asymmetric gravity gradient acceleration is studied. In particular the effect of surface tension on partially liquid filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without a baffle have been investigated. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient acceleration indicate that the gravity gradient acceleration is equivalent to the combined effect of a twisting force and torsional moment acting on the spacecraft. As viscous force (between liquid and solid interface), and surface tension force (between liquid-vapor-solid interface) greatly contribute to the damping effect of slosh wave excitation, a rotating dewar with baffle provides more areas of liquid-solid and liquid-vapor-solid interfaces than that of a rotating dewar without baffle. Results show that the damping effect provided by the baffle reduces the amplitude of slosh wave excitation, lowers the fluid force, torque, and the moment arm of fluid torque fluctuations than that without baffle, and also lowers the degree of asymmetry in the liquid-vapor distribution.     

Experiment and theory on a twisted ring under quasi-static loading

Consider an initially straight rod of circular cross section bent into a circular ring so that the cross sections of the two ends meet face to face. In this paper we study, theoretically and experimentally, the behavior of the ring as the relative rotation between the two end cross sections increases quasi-statically. The variables of interest are the relative rotation angle and the corresponding twisting moment. In theoretical aspect the ring is modeled as an elastica and its deformation is calculated by shooting method. It is found that a ring with dimensionless rod radius 0.001 jumps to a two-point self-contact deformation when the relative rotation angle reaches a critical value. As the rotation angle continues to increase, the deformation evolves smoothly to three-point contact and finally to point-line-point contact. In the experiment we build a simple device to control the relative rotation angle between the two end cross sections. Measurements of twisting moment and relative rotation angle are recorded and compared with theoretical prediction. Reasonable agreement between experiment and theory is observed. Especially the jump phenomenon is confirmed. Installation misalignment and plastic deformation of the rod are the main causes of discrepancy between theory and experiment.     

Wave attenuation in a vessel equipped with damper plates

The effect of vertical damper plates mounted at the center of a rectangular vessel normal or at an angle to a wave flow is experimentally investigated for the first mode of the standing surface waves excited at the parametric resonance. The variation of the resonance curves and the wave attenuation degree are discussed. The fluid depth effect on the wave motion damping is evaluated.     

The puzzle of whip cracking – uncovered by a correlation of whip-tip kinematics with shock wave emission

During whip cracking the whip-tip reaches a supersonic velocity for a period of about 1.2 ms, thereby emitting a head wave with a parabolic-shaped geometry. A detailed study of this mechanism which encompasses the motion analysis of the whip-tip as well as the determination of the local origin of the shock emission requires a sophisticated recording technique. A pre-trigger framing high-speed video camera system was used which was triggered by an acoustical sensor and synchronized with a pulsed copper-vapour laser. The phenomena were visualized by the direct shadowgraph method and recorded cinematographically as digital images at a frame rate of 9 kHz using a CCD-matrix with pixels. The resulting series of frames allowed, for the first time, (i) a reconstruction of the whip-tip trajectory, (ii) a determination of the tuft velocity and acceleration, (iii) a correlation of whip-tip kinematics with shock wave emission, and (iv) a motion analysis of the turning and unfolding mechanism of the tuft. The tuft at the whip-tip was accelerated within a distance of about 45 cm from a Mach number of to a maximum of , thereby reaching a maximum acceleration of 50,000 g. The shock is emitted at the moment when the cracker, arriving at the turning point of the lash, is rapidly turned around. After emission of the shock wav within a short distance of only 20 cm. Received 3 March 1997 / Accepted 21 July 1997     

Diffraction of torsional elastic waves by a peripheral edge crack around a spherical cavity

This paper deals with the problem of finding the stress distribution in the neighborhood of a peripheral edge crack in a spherical cavity. The crack is excited by a torsional standing wave.The problem is solved by using integral transforms and is reduced to the solution of a singular integral equation. The solution of this equation is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors are displayed graphically.     

Elastic responses of a flotation ring in water waves

The gravity-type fish cage is extensively applied in open-sea fishery aquaculture. Its practicality is closely related to the reliability of the flotation ring which is its main load-bearing component. Therefore, it is necessary to study the elastic responses of the flotation ring in ocean waves. Here, an analytical method is proposed to analyze the elastic deformations of a circular ring subjected to water waves. The governing equations of six degree-of-freedom motions and elastic deformations are obtained according to Euler's laws and curved beam theory. In order to examine the method, a series of physical model tests were carried out. The surge and heave displacements of the ring between the predicted results and experimental measurements are compared, and good correlation is represented. The effects of the propagation directions of the incident wave on elastic responses of the ring are then analyzed. It is concluded that small deformations of the ring occur when the configuration of the mooring cables is symmetrically arranged along the propagation direction of the incident waves. Additionally, the out-of-plane stiffness is suggested to be strengthened in order to diminish the corresponding deformations.     

Effect of mesh phase on wave vibration of spur planetary ring gear

The distinctive wave vibration of a ring gear affected by mesh effect is investigated based on the inherent symmetry of spur planetary gears. Compared to prior analysis, this work mainly examines the forced flexural and extensional vibrations. The superposition principle and the Fourier series are introduced to jointly deal with the wave vibrations. The dynamics of the ring gear shows that the effect of the mesh phase on the wave vibration is mainly embodied by the specific relationships between the tooth number, the planet number, the largest common factor of them, the planets’ circumferential position, and the excited wave numbers in the typical rotational, translational and planet modes. For the equal systems, the three modes can be possibly excited depending on the specific mesh phase. And the dominant vibration orders of them are 0, 1 and 2, respectively. The non-zero lowest order is equal to the largest common factor of the two numbers. But for the diametrical ones, only the first two modes can be excited, and the dominant orders of them are 0 and 1, respectively. And the lowest non-zero wave number is 2 for even tooth number and 1 for odd tooth number. As a typical application, these relationships can be used to predict and suppress some potential wave resonances of the ring gear by optimizing the ring-planet mesh phase. The main results are demonstrated with finite element examples and comparisons with the existing literature.     

Limit currents in a plasma betatron

The radial motion of a plasma column is considered for electron acceleration in a plasma betatron. The limit value of the relativistic currents which can be obtained in devices of this type is computed.G. I. Budker [1] proposed using the runaway effect in a plasma with a strong electric field for converting a cold ring plasma into an intense compensated beam of relativistic electrons. To confine such a beam within an annular vacuum chamber one can use either a betatron-type magnetic field or the field of the image currents produced in the metal shell enclosing the vacuum chamber with the electron beam. In the latter case, as estimates show, the number of accelerated electrons must already be considerable; this leads to an increase in the difficulties which impede the successful acceleration of all plasma electrons.Accordingly, most of the experiments on accelerating plasma electrons have employed betatron fields in devices called plasma betatrons [2–4], A feature of these accelerators is total compensation of the space charge of the accelerated electrons and hence an increased possibility of obtaining high accelerated currents. In this article, we compute the magnitude of the limit currents which may be obtained in a plasma betatron as a function of its parameters and operating conditions.The first results in this direction, published in 1949 [5], were rough estimates. Subsequently, other more accurate calculations were published [6], but these, in our opinion, did not give sufficient information on the characteristic quantities.The author thanks A. E. Bazhanov for his help in interpreting Eq. (16).     

Experimental and numerical investigation of nonlinear thermocapillary oscillations in an annular geometry

The present work investigates thermocapillary flow in a cylindrical configuration using large Prandtl number liquids. The flow is studied using coordinated simulations and experimental optical methods such as PIV and flow visualization. In this way, properties of the oscillatory state can be obtained in great detail. Considerable attention is given to the search for the parameters influencing the onset of the instability. It is found that the onset of oscillations can be correlated using a thermocapillary Reynolds number. The oscillations take the form of a standing wave close to the onset, which is replaced by a travelling wave for stronger forcing. The selection of azimuthal wave number of the oscillatory mode is determined from geometrical parameters, and resembles the wave number selection in vortex ring instabilities. Throughout we obtain good agreement between experiments and simulations using a mathematical model with an undeformed adiabatic free surface.     

外载荷作用下水泥砂浆复合材料中的弹性波波速分析

为研究水泥基复合材料中弹性波频散特性,应用主频分别为50kHz、300kHz和1MHz三种声波探头,对钢纤维体积含量分别为0.5%、1.0%和3.0%的三种钢纤维增强水泥砂浆试件进行了单轴压缩下的弹性波测试实验。结果表明:在加载初始阶段,P波波速随着载荷增大而明显增大,但这种增大趋势逐渐减弱,并达到一个较稳定的值。随着钢纤维体积含量增加,波速有增大趋势。S波具有类似趋势,但其增幅比P波小得多。三种材料均表现出一定的频散效应。为消除材料在初始加载过程的非线性特性影响,采用了相对波速的方法,并讨论了相对波速的频散效应。结合多组份未胶结模型和Hashin-Shtrikman上限模型,应用一种无量纲理论模型,对比分析了弹性波波速频散规律。     

半空间SH波方程非线性井间双参数反演

以半空间的ＳＨ波方程出发,采用Ｂｏｒｎ迭代法求解半空间弹性介质中密度和剪切模量分布的非线性反演问题。首先,采用矩量法和正则化方法,给出井间反演积分方程的离散形式,然后应用Ｂｒｏｎ迭代法求解非线性反演问题。     

Quasiperiodic and exponential transient phase waves and their bifurcations in a ring of unidirectionally coupled parametric oscillators

Phase waves rotating in a ring of unidirectionally coupled parametric oscillators are studied. The system has a pair of spatially uniform stable periodic solutions with a phase difference and an unstable quasiperiodic traveling phase wave solution. They are generated from the origin through a period doubling bifurcation and the Neimark?CSacker bifurcation, respectively. In transient states, phase waves rotating in a ring are generated, the duration of which increases exponentially with the number of oscillators (exponential transients). A power law distribution of the duration of randomly generated phase waves and the noise-sustained propagation of phase waves are also shown. These properties of transient phase waves are well described with a kinematical equation for the propagation of wave fronts. Further, the traveling phase wave is stabilized through a pitchfork bifurcation and changes into a standing wave through pinning. These bifurcations and exponential transient rotating waves are also shown in an autonomous system with averaging and a coupled map model, and they agree with each other.     

Kelvin结构开孔泡沫材料的弹性性能研究

采用一修正的十四面体结构模型(Kelvin结构模型)对开孔泡沫金属的弹性性能进行研究,对低密度开孔泡沫材料表现出不可压的特性进行了分析。该模型考虑作用在泡沫筋条上的弯矩、剪力和轴向力,以及轴向力的平衡。修正模型的数值计算结果与实验结果及其他模型的结果进行了对比,结果表明修正模型计算的杨氏模量比原有模型的略有提高,筋条截面为星形的修正模型计算的结果与实验比较符合。在密度等同的条件下,筋条截面惯性矩越大的开孔泡沫材料,其弹性模量也越大,而泊松比则越小。Kelvin结构的开孔泡沫材料的泊松比随相对密度的减小而趋于0.5。     

液固半无限空间低频点声源的地震波动

将舰船地震波简化为液固半无限空间低频点声源引起的地震波动,基于简正波理论,通过计算围道内的留数得到了位移势函数的表达式.分析了液体层内声传播损失和固体层表面的位移、加速度的频率特性曲线,为分析舰船地震波的形成机理以及波动特征提供了一定的理论基础.     

On the universality of nonthermal electron acceleration due to quasi-turbulent wakefields

Nonthermal acceleration of relativistic electrons in a wakefield induced by large amplitude light waves is discussed. It is considered that large amplitude light waves are excited as the precursor waves in the upstream of relativistic perpendicular shocks in the universe, and that the wakefield is excited by the light ponderomotive force. Thus, the wakefield acceleration is possible in the astrophysical circumstances. We model such shock environments in a laboratory plasma by substituting an intense laser pulse for the large amplitude light waves. By performing 2-D particle-in-cell simulations, we discuss the properties of the wakefield acceleration in various laser and plasma conditions. With the relativistic intensities of the laser pulses, the electrons are nonthermally accelerated by the wakefield. When the pulse length and the spot size are comparable to the electron inertial scale, the energy distribution functions of the electrons can be monoenergetic. On the other hand, when the pulse spatial scales are much larger than the electron inertial scale, which occurs in the case of the shock precursor light waves, the distribution functions are universally represented by power law spectra with an index of 2, independent of the laser intensity, the plasma density, and the laser pulse size.     

Propagation,Dispersion, and Localization of Elastic Waves in Low-Symmetric Anisotropic Waveguides

The results of a theoretical investigation into ultrasonic linear normal wavefields in anisotropic three-dimensional bodies with mechanical orthorhombic symmetry are presented. A detailed study is made of the dispersion dependencies for higher normal wave modes in a single-layered orthorhombic plate-type waveguide. Moreover, the distribution of complex branches corresponding to the edge standing wave modes is studied and their role in the transformation of the entire spectrum upon a change in the travel direction in the waveguide plane is analyzed. A new type of localization of the higher modes of high-frequency short-range normal waves in a crystal layer is described. An efficient method is developed for studying the spectrum of ultrasonic normal waves in a circular cylindrical waveguide made of an orthorhombic monocrystal     

Elastic stability and the zero moment condition

The work presented in this paper is concerned with the zero moment stability theory of Beatty. We find that while the zero moment condition can be justified as a possible aid in the analysis of certainspecific problems, we also indicate that this condition should not be considered as a general and primitive restriction on stability theory at the foundation level.     

Study of axial acoustic radiation force on a sphere in a Gaussian quasi-standing field

Based on the finite series method, the Gaussian standing or quasi-standing beam is expressed in terms of spherical wave functions and a weighting parameter, which describe the beam shape and location relative to the particle. An expression is derived for the radiation force on a sphere centered on the axis of a Gaussian standing or quasi-standing wave propagating in an ideal fluid. Rigid, fluid, elastic, and viscoelastic spheres immersed in water are treated as examples. In addition, a method is proposed to compute the axial acoustic radiation force when the sphere is translated axially. Results indicate the capability of the proposed method to manipulate and separate spheres based on their mechanical and acoustical properties. The interaction of a Gaussian quasi-standing beam with a sphere can result in periodic axial force under specific operating conditions. The results presented here may provide a theoretical basis for the development of acoustical tweezers in a Gaussian standing beam, which would be useful in micro-fluidic lab-on-chip applications.