Lift Force Acting on Body in Liquid in the Vicinity of Boundary Executing Tangential Oscillations

The average force acting on a cylindrical or spherical body placed near the boundary of cylindrical cavity filled with liquid and executing rotational vibrations is experimentally studied. The repulsive lift force acting on solid is found and measured using the method of body suspension in the gravity field. In horizontal cavity the repulsive force provides steady state of light cylinder near the upper boundary at a distance comparable with the thickness of the Stokes layer. The heavy sphere which hangs on thread repulses from the wall of vertical cylindrical cavity under torsional vibration. The dependence of the average lift force on the amplitude and frequency of vibrations and on distance between the body and the boundary has been investigated. Results are presented on the plane of dimensionless parameters. In the examined frequency range the lift force acting on cylinder decreases exponentially with distance from the boundary. Lift force acting on sphere decreases with distance and strongly depends on dimensionless frequency of vibration. Conclusion that lift force is generated by body oscillations excited by its viscous interaction with the oscillating boundary is done. The found phenomenon is important for control of inclusions under microgravity conditions.     

Oscillatory and Steady Dynamics of a Cylindrical Body Near the Border of Vibrating Cavity Filled with Liquid

The results of experimental study of vibrational dynamics of cylindrical solid in a rectangular cavity filled with viscous incompressible fluid are generalized. The cavity performs high-frequency translational oscillations in a horizontal plane. Experiments are carried out with bodies of different relative density: more or less than liquid’s density. The cylinder oscillates in the cavity under the influence of oscillating inertia force. An averaged force repels the body from the boundary and holds a heavy body over the bottom of the cavity and the light one at some distance from the ceiling. The vibrational lift force depends on the amplitude and frequency of vibrations as well as on the properties of liquid. It is shown that the value of the averaged lift force decreases with increasing dimensionless amplitude. Special attention is paid to the oscillatory behavior of a solid. The rotational oscillations of the body, observed in experiments simultaneously with the translational ones, and fluid motion, excited by an oscillating body, are investigated. The different modes of interaction of the body with the container’s boundary were found. The oscillatory dynamics of bodies with different relative density is studied by high-speed video-registration.     

轴向载荷条件下弹性边界约束梁结构振动特性分析

采用改进傅里叶级数展开建立了轴向载荷条件下弹性边界约束梁结构振动分析模型。通过在梁结构两端引入平动和旋转位移约束弹簧,相应设置约束弹簧刚度系数可以实现对任意边界条件及其组合的模拟。梁结构振动系统位移场采用傅里叶级数附加边界光滑函数进行构建,利用能量原理建立轴向载荷作用下梁结构总动能、总势能和外力做功项,并结合瑞利-里兹步骤获得系统特征矩阵方程。通过数值算例,验证了该模型对不同边界条件、轴向载荷作用下梁结构振动特性分析的正确性与可靠性。在此基础上,研究了边界约束弹簧横向刚度、旋转刚度、轴向载荷等系统参数及激振力对梁结构振动特性的影响。该模型具有高效、高精度等特点,为研究轴向载荷作用下复杂边界条件梁结构振动行为提供了有效分析手段。     

Interfacial Effects on Stress Transfer in Fiber-Reinforced Composites

A three-dimensional solution for a fiber-reinforced circular cylinder is presented for axisymmetric force and displacement boundary conditions. The solution, which can satisfy all the boundary conditions prescribed on the curved and end surfaces of the cylinder, can be used directly in the micromechanical analysis of fiber-reinforced composites to investigate the typical representative volume element (RVE). The element consists of a combined circular cylinder composed of a solid inner circular cylinder of transversely isotropic fiber, a concentric outer circular cylinder of isotropic matrix material, and an interface layer between the fiber and the matrix. The radial and tangential flexural compliances of the interfacial material are considered, and their effects on the stress transfer at the interface are studied parametrically. The numerical results presented show that the material properties of the interfacial layer have significant influences on the stress distribution within the RVE, particularly at the cross sections near the ends of the cylinder, where external loads are applied.     

A standing wave-type noncontact linear ultrasonic motor

In this study, a novel standing wave-type noncontact linear ultrasonic motor is proposed and analyzed. This linear ultrasonic motor uses a properly controlled ultrasonic standing wave to levitate and drive a slider. A prototype of the motor was constructed by using a wedge-shaped aluminum stator, which was placed horizontally and driven by a multilayer PZT vibrator. The levitation and motion of the slider were observed. Assuming that the driving force was generated by the turbulent acoustic streaming in the boundary air layer next to the bottom surface of the slider, a theoretical model was developed. The calculated characteristics of this motor were found to agree quite well with the experimental results. Based on the experimental and theoretical results, guidelines for increasing the displacement and speed of the slider were obtained. It was found that increasing the stator vibration displacement, or decreasing the gradient of the stator vibration velocity and the weight per unit area of the slider, led to an increase of the slider displacement. It was also found that increasing the amplitude and gradient of the stator vibration velocity, or decreasing the weight per unit area of the slider and the driving frequency, gave rise to an increase of the slider speed. There exists an optimum roughness of the bottom surface of the slider at which the slider speed has a maximum     

轮胎振动声辐射数值分析

以225/50R17光面和纵向刻槽子午线轮胎为例,利用有限元软件ANSYS和边界元软件SYSNOISE对在面荷载激励下的轮胎振动与声辐射做了数值计算和分析。在有限元模型中,分别计算了轮胎在受径向接触面力、切向接触面力和侧向接触面力时的位移频率响应。将有限元计算的节点位移响应结果传递到边界元模型中,作为边界元模型的速度边界条件,利用边界元技术分别计算了三种工况下轮胎的辐射声功率、辐射效率和远场指向性。     

Free Vibration of the Axially Loaded System of Two Beams Connected by a Two-Directional Viscoelastic Interlayer

In this paper, the analytical method has been used for solving a problem of free vibration with clamping of an axially loaded sandwich beam. The sandwich beam consists of two external layers connected by a viscoelastic two-directional Winkler interlayer. The upper external layer is described by the Bernoulli–Euler model, which is loaded by a constant axial force. The lower external layer is modeled as the Timoshenko model. The phenomenon of free vibration has been described using a homogenous system of conjugate partial differential equations. After separation of variables in the system of differential equations, the boundary problem has been solved and three complex equations for the definition of frequency and modes of free vibration have been obtained. The free-vibration problem for arbitrarily assumed initial conditions and various axial forces has been considered.     

Slip flow on a body of revolution

This work investigates the boundary layer development and resulting net frictional drag along a general blunt-nosed body of revolution in uniform slip flow. The curvilinear boundary layer equations are subjected to a Navier slip condition near the surface. For motion near the nose, a similarity-type solution is obtained as a double series, comprising a small velocity slip parameter, from which the non-dimensional drag coefficient is obtained. In addition, the displacement effect of the boundary layer on the outer inviscid flow is determined and interpreted by means of a dimensionless parameter. The general analysis is then applied to the special case of the Rankine half-body. Considering laminar flow along the nose and downstream regions, results are presented for prescribed slip parameters and Reynolds numbers with particular emphasis on the influence of slip on the flow.     

半无限大弹性地基等效刚度公式及其应用

根据Mindlin关于一集中力作用在半空间弹性体中的位移公式,采用能量等效原理推导出半无限大弹性地基考虑基础埋深时基坑底部的法向等效刚度和切向等效刚度公式、基坑坑壁的法向等效刚度和切向等效刚度公式。同理根据Boussinesq关于半空间体在边界上受法向集中力的位移公式和Cerruti关于半空间体在边界上受切向集中力的位移公式,推导出不考虑基础埋深时地基的法向等效刚度和切向等效刚度公式,以及运用这些公式计算出半无限大弹性地基取不同地基土时的等效刚度。最后举例说明了这些等效刚度公式在分析高层和超高层建筑的上部结构、基础、地基的共同工作时的应用。     

A method of analyzing elastic constraints due to grain or interphase boundaries

Elastic constraint due to grain or interphase boundaries is considered by taking a bicrystal under a general boundary condition as an example. The concept of reference deformation is introduced on which the effect of elastic constraints is superposed to get the actual state of deformation. Reference deformation accompanies, in general, incompatibilities of both traction and displacement at the boundary. Tractional incompatibility is resolvable by solving an elasticity problem in which requisite body force is distributed along the boundary. Incompatibility of displacement can be nullified in two steps. First, an arbitrarily chosen point within the boundary is joined by a rigid translation of either one of the boundary faces. Then, the incompatibility relative to that point is nullified by introducing the surface dislocations within the boundary, the density of which is proportional to an external force and vanishes as the external force ceases to act.     

基于INM模型的天津机场飞机噪声污染预测与防治研究

随着我国航空运输业的不断发展,飞机噪声污染问题已经成为限制民航发展的主要问题之一。调查统计了天津机场2018 年实际航空业务量和规划航空业务量,利用INM模型计算飞机噪声并绘制等值线图,根据计算结果分析飞机噪声对周边环境的污染情况。计算结果表明,受航空业务量增加和第三跑道建设的影响,天津机场周边受飞机噪声影响的面积和人数显著增加。结合国际民航组织（ICAO）针对飞机噪声控制提出的“平衡做法”,研究天津机场可以采用的噪声污染防治措施,主要包括减少噪声源、土地使用的合理规划和管理、采用减噪飞行程序。     

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

This paper provides a formulation for indirect BIEs in plane elasticity using single or double layer potentials and complex variable. There are two ways to obtain two kinds of layer and the relevant indirect BIEs. In the first way, the displacement expression at domain point is directly obtained from the Somigliana identity with necessary modification. In the second way, after placing some density functions, for example, the body force or the dislocation doublet, along the layers, one can obtain the displacement expression at domain point. For both single and double layers, the continuous or discontinuous properties for the displacement and traction are studied in detail when a moving point is passing through the boundaries. Formulations of the Dirichlet and the Neumann problems are proposed. The ranges for solving the boundary value problem by using the single or double layer potentials are clearly indicated. For the case of single layer, the degenerate scale problems for the finite multiply connected region and infinite multiply connected region are studied. For the case of double layer, a hypersingular BIE for crack can be formulated by assuming that the density functions are vanishing along a portion of boundary.     

Punch and crack problems in transversely isotropic bodies

An exact solution is proposed for the mixed boundary-value problem in a transversely isotropic half-space. Here, certain arbitrary shear tractions are prescribed inside a circular region, outside of which certain arbitrary tangential displacements are given. The normal stresses are supposed to be known all over the boundary. A particular case is considered, in detail, where normal stresses vanish all over the boundary with the shear tractions vanishing inside the circular region. A closed form expression is obtained for the tangential displacements inside the circular region directly through the displacements outside. As an example, a penny-shaped crack in an infinite transversely isotropic body is considered with arbitrary shear tractions acting on both sides of the crack. The formulae for the tangential displacements inside the circle and the shear stresses outside are obtained. Special cases where uniform shear and a concentrated tangential force arise are also discussed.     

盘形滚刀垂向振动特性分析与试验

盘形滚刀的垂向振动对于全断面隧道掘进机的贯入度和破岩效率有一定的影响,为了研究影响滚刀垂向振动的因素,首先建立盘形滚刀垂向三自由度振动模型,得到盘形滚刀刀圈与刀体、圆锥滚子轴承和刀轴的等效质量和刚度,利用MATLAB软件对该振动模型进行仿真,得到滚刀各部分的振动位移,并通过试验得到滚刀各部分振动位移与仿真的结果趋势一致。结果表明:滚刀的刀圈加刀体的最大振动位移量为2.8×10^-4 m,轴承最大振动位移为2.1×10^-4 m,当滚刀的轴承刚度增大3倍时,各部分最大振动位移减少约50%,增大刀圈刀体刚度时,各部分最大振动位移减少约12%,盘形滚刀减振需要增加轴承和刀圈刀体的刚度。研究结果为盘形滚刀的振动测量提供了一种有效方法,对滚刀的设计具有重要的指导意义。     

用GDQ空-时半解析法分析圆弧拱强迫振动

从圆弧拱的强迫振动控制方程出发,在空间域采用广义微分求积法,将广义微分求积法中的节点参数在时域内取为响应的时间级数,通过时域配点求解该六阶偏微分方程得到全域内的响应位移场,分析了圆弧拱的平面内强迫振动问题。运用Matlab语言编制圆弧拱强迫振动时程分析的计算程序,并进行了相应的算例分析,数值计算结果表明该方法对于求圆弧拱的强迫振动问题具有较高的精度和效率。     

双圆柱尾流致涡激振动的质量比效应及其机理

双圆柱尾流激振受多种因素影响,情况复杂,质量比m*(相同体积的圆柱与流体质量的比值)对双圆柱尾流激振的影响规律尚未澄清。采用数值模拟方法,在低雷诺数下(Re=100),研究了三种质量比(m*=2,10,20)对串列双圆柱尾流致涡激振动特性和尾流流场结构的影响规律,分析了下游圆柱的升力与位移的相位差,探讨了涡激升力与能量输入的内在联系。结果表明:质量比对串列圆柱尾流致涡激振动有重要影响。随着质量比的增大,横流向最大振幅减小,并发生在较小折减速度下,振动锁定区域范围变窄;质量比越小,升力与位移之间的相位差对下游圆柱振幅的影响越显著;在较小质量比时尾流出现“2S”、不规则和平行涡街模态,而在较大质量比时只有“2S”和平行涡街模态。     

Pipe-Wall Friction in Vertical Sand-Slurry Flows

This article describes the results of extensive laboratory tests of vertical flows of three sand fractions (0.12, 0.37, and 1.84 mm sands) in a 150 mm pipe. The tests revealed an interesting phenomenon of a surprisingly low contribution of the medium sand to the total friction of the mixture flow in the vertical pipe. The frictional pressure drop in highly concentrated flows at high velocities was lower for slurries of the medium sand than for slurries of both the fine sand and the coarse sand. The solids friction at the pipe wall is analyzed taking into account effects of particle-particle interactions and particle-liquid interactions in the boundary layer of a vertical flow of settling slurry. The analysis suggests that the observed phenomenon is associated with the hydrodynamic liquid lift force acting on solid particles traveling near a pipe wall. This off-wall force seems to be more effective for the medium sand particles than for the fine sand particles and coarse sand particles interacting with liquid in the boundary layer of the mixture flow. The excessive frictional pressure drop due to the presence of solids in vertical flows seems to be primarily produced by the combined effect of the Bagnold collisional force (the force that colliding particles exert against the pipe wall) and the liquid lift force acting on solid particles in the near-wall zone of the slurry flow.     

Dynamic Performance of Stacked Packaging Units

Stacked packaging units is the main form of distribution packaging of products. Its dynamic performance is not fully understood. This paper investigated the influence of the constraint, input vibration, location and contact nonlinearity on the dynamic performance of three layers stacked packaging units. The dynamic contact force between surfaces and acceleration response of products were obtained. In sine sweep vibrations, the constraint to stacked packaging units has an obvious influence on the dynamic characteristics. The acceleration response of product is associated with the vibration mode. The force amplification factor is in general between 1.5 and 2, but it can close to 3 on top layer in the case of no fixed. In random vibrations, non‐Gaussian data of dynamic contact force appear when Gaussian data of input vibration pass through the stacked packaging units, resulting a Weibull distribution of force level‐crossing. The force level‐crossing diagram becomes more abrupt with the decreasing of input vibration level, smoother from the top contact surface to middle and bottom ones, and moves right and becomes smoother with the constraint strengthen. In the case of lower input level, Gaussian distribution of force level‐crossing appears. The force power spectral density (PSD) between bottom box and table is much larger than that between boxes, which is significantly influenced by the first resonance frequency. However, the acceleration PSD of product is significantly influenced by both the first and second resonance frequencies, and controlled by the vibration mode. It depends much on the value of input acceleration PSD around the resonance frequencies.     

A new approach for displacement functions of a curved Timoshenko beam element in motions normal to its initial plane

In existing literature, either analytical methods or numerical methods, the formulations for free vibration analysis of circularly curved beams normal to its initial plane are somewhat complicated, particularly if the effects of both shear deformation (SD) and rotary inertia (RI) are considered. It is hoped that the simple approach presented in this paper may improve the above‐mentioned drawback of the existing techniques. First, the three functions for axial (or normal to plane) displacement and rotational angles about radial and circumferential (or tangential) axes of a curved beam element were assumed. Since each function consists of six integration constants, one has 18 unknown constants for the three assumed displacement functions. Next, from the last three displacement functions, the three force–displacement differential equations and the three static equilibrium equations for the arc element, one obtained three polynomial expressions. Equating to zero the coefficients of the terms in each of the last three expressions, respectively, one obtained 17 simultaneous equations as functions of the 18 unknown constants. Excluding the five dependent ones among the last 17 equations, one obtained 12 independent simultaneous equations. Solving the last 12 independent equations, one obtained a unique solution in terms of six unknown constants. Finally, imposing the six boundary conditions at the two ends of an arc element, one determined the last six unknown constants and completely defined the three displacement functions. By means of the last displacement functions, one may calculate the shape functions, stiffness matrix, mass matrix and external loading vector for each arc element and then perform the free and forced vibration analyses of the entire curved beam. Good agreement between the results of this paper and those of the existing literature confirms the reliability of the presented theory. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of a crack at a weak interface

The problem of two elastic half-planes joined along the common part of their boundary by a cracked weak interface is considered. The central part of the joint is detached, while in the remaining part there is a continuous distribution of springs which assures continuity of stress which is proportional to the displacement gap. The adherents are homogeneous and isotropic, while the interface is allowed to be orthotropic with principal directions normal and tangential to the interface, respectively. The body is subjected to constant normal and tangential loads applied at infinity and at the crack faces. Using classical solutions for elastic half-planes as Green functions, the integral equation governing the problem is obtained and solved numerically. Attention is paid to the analysis of the solution around the crack tip, and an asymptotic estimate showing that the derivative of the solution is logarithmically unbounded is obtained analytically. Accordingly, it is shown that there may exist, at most, logarithmic stress singularities. It is further shown how, contrary to the case of perfect bonding, stress singularities are not related to the normal propagation of the crack, but possibly to the crack deviation. The crack propagation is analyzed by the energy Griffith criterion, and it is shown that some drawbacks of linear elastic fracture mechanics disappear in the case of weak interface.