计及轴颈倾斜的径向滑动轴承湍流润滑分析

分析了轴颈倾斜状态下,径向滑动轴承的湍流润滑性能. 基于轴颈倾斜的统一Reynolds方程和能量方程,应用有限差分法求解了不同轴颈倾斜方位角、轴颈倾斜度、偏心率和平均雷诺数下的径向滑动轴承湍流润滑性能. 结果表明:轴颈倾斜方位角α=0°时,随着轴颈倾斜度的增大,轴承油膜的压力峰向轴承一端移动,轴承一端的轴向油膜温度梯度增大;α=90°时,随着轴颈倾斜度的增大,轴承油膜压力逐渐出现双峰分布,且向轴承两端移动,轴承两端的轴向温度梯度也不断增大. 在相同轴颈倾斜度增量下,轴承最大油膜压力、最高油膜温度、承载力和稳定工作力矩的增量随轴承中央截面偏心率的增大而增大. 相同轴颈倾斜度增量下,轴承最大油膜压力增量、最高油膜温度增量、承载力增量、摩擦系数减量和稳定工作力矩增量随平均雷诺数的增大而增大. 可见,径向滑动轴承湍流润滑分析中有必要考虑轴颈倾斜因素的影响.      

尖头碎片撞击小尺寸储罐的模拟实验

化工园区内,容器爆炸事故易引发多米诺效应,产生的碎片击中临近目标设备或装置可能造成事故后果升级。通过开展尖头碎片撞击小尺寸储罐模拟实验,得到了不同轴向撞击角的尖头碎片撞击不同壁厚小尺寸储罐的穿透形貌、穿透能量以及穿孔直径。结果表明:（1）尖头碎片以0°轴向撞击角穿透罐壁形成的穿孔正面近似圆形,以15°、30°及45°轴向撞击角撞击形成的穿孔正面近似椭圆形且有2个条形翻边,穿孔背面均呈现花瓣型开裂;（2）轴向撞击角越大,壁厚越大,所需的穿透能量越大;（3）轴向撞击角与壁厚对穿孔轴向直径影响显著,但穿孔环向直径变化幅度不大。最后,根据穿甲力学理论和动量守恒定理,推导出适用于0°~45°轴向撞击角的尖头碎片剩余速度理论计算公式。     

NUMERICAL SIMULATIONS OF HYDRODYNAMIC BEHAVIORS IN CONICAL SPOUTED BEDS

The axial and radial distributions of static pressures and vertical particle velocities of conical spouted beds have been simulated and compared with experimental data. Simulation results show that, among all factors investigated, the Actual Pressure Gradient (the APG term) in conical spouted beds, introduced as the default gravity term plus an empirical axial solid phase source term, has the most significant influence on static pressure profiles, followed by the restitution coefficient and frictional viscosity, while other factors almost have no effect. Apart from the solid bulk viscosity, almost all other factors affect the radial distribution of the axial particle velocity, although the influence of the APG term is less significant. For complex systems such as conical spouted beds where a fluidized spout region and a defluidized annulus region co-exist, the new term introduced in this work can improve the CFD simulation. Furthermore, for other systems with the Actual Pressure Gradient different from either fluidized beds or packed beds, the new approach can also be applied.     

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads is studied in the paper. Through deriving accurate expressions of inertial force and initial hoop tension, a rotating conical shell model is presented based upon the Love's thin shell theory. Considering the periodic axial loads, equations of motion of the system with periodic stiffness coefficients are obtained utilizing the generalized differential quadrature (GDQ) method. Hill's method is introduced for parametric instability analysis. Primary instability regions for various natural modes are computed. Effects of rotational speed, constant axial load, cone angle and other geometrical parameters on the location and width of various instability regions are examined.     

Analysis of bending and buckling of pre-twisted beams: A bioinspired study

Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elas- tic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self- weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.     

Microbuckle initiation from a patch of large amplitude fibre waviness in a composite under compression and bending

A finite element couple stress formulation is used to predict microbuckle initiation from a patch of fibre waviness in a unidirectional fibre composite under remote compression and bending. Attention is focused on the knock-down in strength due to large amplitude waviness, with the effects of the physical size of the imperfection included by incorporating the fibre bending resistance within the formulation. The predicted strengths deviate significantly from the simpler kinking theory which neglects the role of fibre bending. Initial imperfections in the form of an infinite band and a circular wavy patch are considered: when these imperfections are of large spatial extent and possess a large misalignment angle, the compressive strength approximates the steady state band broadening stress for an infinite band. The effect of an imposed spatial gradient of stress within the composite is explored by determining the compressive strength of beams of finite height B for the loading cases of pure bending and axial compression. It is found that the compressive strength is sensitive to the magnitude of the imposed stress gradient: the compressive strength of the outer fibres of the beam in bending increases with diminishing height of the beam. This size dependence is much reduced for the case of uniform compression.     

Fractional visco-elastic Euler–Bernoulli beam

Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some case studies.     

陶瓷材料SHPB实验的改进垫块法

高强度陶瓷材料SHPB实验中,利用圆柱或圆台形垫块可避免压杆的端面塑性变形,但存在陶瓷试件中轴向的应力不均匀现象,从而影响实验结果的有效性。本文通过数值模拟分析了两种垫块方式引起的试件中轴向应力分布的特点,并以此为基础提出了一种更为合理的垫块方法。利用商业软件LS-DYNA,数值模拟了改进垫块方法的陶瓷材料SHPB实验。结果显示,基本上消除了陶瓷试件中轴向应力不均匀现象。应用一维应力波理论,分析了实验中的波传播过程,得到了对实验数据的修正处理方法,并证明了所提的修正方法是可行有效的。     

Semi-analytic solution of Eringen’s two-phase local/nonlocal model for Euler-Bernoulli beam with axial force

Eringen’s two-phase local/nonlocal model is applied to an Euler-Bernoulli nanobeam considering the bending-induced axial force, where the contribution of the axial force to bending moment is calculated on the deformed state. Basic equations for the corresponding one-dimensional beam problem are obtained by degenerating from the three-dimensional nonlocal elastic equations. Semi-analytic solutions are then presented for a clamped-clamped beam subject to a concentrated force and a uniformly distributed load, respectively. Except for the traditional essential boundary conditions and those required to be satisfied by transferring an integral equation to its equivalent differential form, additional boundary conditions are needed and should be chosen with great caution, since numerical results reveal that non-unique solutions might exist for a nonlinear problem if inappropriate boundary conditions are used. The validity of the solutions is examined by plotting both sides of the original integro-differential governing equation of deflection and studying the error between both sides. Besides, an increase in the internal characteristic length would cause an increase in the deflection and axial force of the beam.     

Flexural–torsional buckling of misaligned axially moving beams. I. Three-dimensional modeling,equilibria, and bifurcations

The equations of motion for the flexural–flexural–torsional–extensional dynamics of a beam are generalized to the field of axially moving continua by including the effects of translation speed and initial tension. The governing equations are simplified on the basis of physically justifiable assumptions and are shown to reduce to simpler models published in the literature. The resulting nonlinear equations of motion are used to investigate the flexural–torsional buckling of translating continua such as belts and tapes caused by parallel pulley misalignment.The effect of pulley misalignment on the steady motion (equilibrium) solutions and the bifurcation characteristics of the system are investigated numerically. The system undergoes multiple pitchfork bifurcations as misalignment is increased, with out-of-plane equilibria born at each bifurcation. The amount of misalignment to cause buckling and the post-buckled shapes are determined for various translation speeds and ratios of the flexural stiffnesses in the two bending planes. Increasing translation speed decreases the misalignment necessary to cause flexural–torsional buckling. In Part II of the present work, the stability and vibration characteristics of the planar and non-planar equilibria are analyzed.     

Free vibrations of rotating composite conical shells with stringer and ring stiffeners

In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.     

A new efficient method to evaluate exact stiffness and mass matrices of non-uniform beams resting on an elastic foundation

In this paper, a new efficient method to evaluate the exact stiffness and mass matrices of a non-uniform Bernoulli–Euler beam resting on an elastic Winkler foundation is presented. The non-uniformity may result from variable cross-section and/or from inhomogeneous linearly elastic material. It is assumed that there is no abrupt variation in the cross-section of the beam so that the Euler–Bernoulli theory is valid. The method is based on the integration of the exact shape functions which are derived from the solution of the axial deformation problem of a non-uniform bar and the bending problem of a non-uniform beam which are both formulated in terms of the two displacement components. The governing differential equations are uncoupled with variable coefficients and are solved within the framework of the analog equation concept. According to this, the two differential equations with variable coefficients are replaced by two linear ones pertaining to the axial and transverse deformation of a substitute beam with unit axial and bending stiffness, respectively, under ideal load distributions. The key point of the method is the evaluation of the two ideal loads which in this work is achieved by approximating them by two polynomials. More specifically, the axial ideal load is approximated by a linear polynomial while the transverse one by a cubic polynomial. The numerical implementation of the method is simple, and the results are compared favorably to those obtained by exact solutions available in literature.     

Acoustic radiation force on a rigid cylinder in an off-axis Gaussian beam near an impedance boundary

The exact equations of the axial and transverse acoustic radiation force functions of a Gaussian beam arbitrarily incident on an infinite rigid cylinder close to an impedance boundary and immersed in an ideal fluid are deduced by expressing the incident wave, the scattering wave and the boundary reflected wave in terms of the cylindrical wave function. The effects of the beam waist, the sound reflection coefficient, the cylinder position and the distance from the impedance boundary on the acoustic radiation force are studied using numerical simulations. The simulation results show that the amplitude of the acoustic radiation force function increases with beam width. Moreover, the values of the acoustic radiation force in both the axial and transverse directions reach those of a plane wave when the beam width is considerably larger than the wavelength of the Gaussian beam. The properties of the impedance boundary and the position of the cylinder in the Gaussian beam have a considerable effect on the magnitude and direction of the force. The simulation results, particularly in the case of a transverse force, indicate the presence of a negative acoustic radiation force that is related to the nondimensional frequency and position of the cylinder in the Gaussian beam.     

Non-linear buckling behavior of FGM truncated conical shells subjected to axial load

In this study, the non-linear buckling behavior of truncated conical shells made of functionally graded materials (FGMs), subject to a uniform axial compressive load, has been investigated using the large deformation theory with von the Karman-Donnell-type of kinematic non-linearity. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of functionally graded truncated conical shells are obtained and are solved by superposition and Galerkin methods and the upper and lower critical axial loads have been found analytically. Finally, the influences of the compositional profile variations and the variation of the shell geometry on the upper and lower critical axial loads are investigated. Comparing the results of this study with those in the literature validates the present analysis.     

楔形杆中弹塑性波的一种渐近展开式

据我们所知,楔形杆中弹塑性波尚未有很好的分析方法。对弹性波有文献[1,2]等,其中文献[1]研究了圆锥壳轴向撞击的波动问题,发现楔形杆是其很好的近似,故后者的研究对圆锥壳具有重要意义。文中采用拉氏变换方法求得两种特殊情况下(波阵面和冲击端附近,的渐近解,而一般情形下的解未能得到。也有人用WKB方法讨论了类似问题,但仅限于波长很短的情形,局限性很大。另外,文献[5]用正则摄动法研究了楔形杆的自振问题。 本文针对楔形杆(和圆锥壳)的特点建议了一种渐近展开式,并求解了弹性波和弹塑性波问题,并与其他一些方法及其结果进行了比较。     

The propagation of elastic stress waves in a conical shell under axial impulsive loading

The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation due to their different velocities. Southwest Institute of Structural Mechanics     

Holographic interferometry measurements of transient bending waves in tubes and rings

Propagating bending waves are studied in a tube of steel and in a ring of aluminum. The waves are generated by the impact of a ballistic pendulum. Holographic interferometry, with a double-pulsed ruby laser as light source, is used to record the waves. A conical mirror is placed axially inside the tube. Axial illumination and axial observation directions, make it possible to view all sides of the tube simultaneously with a high sensitivity to radial deformation. The interferograms, which have an unusual perspective, are captured with a CCD-camera and then spatially transformed into an unwrapped strip of the tube wall. This makes the interpretation of the measurements simpler. The geometry of the tube causes the wave pattern to propagate with different speed and amplitude along and across the tube, even when the material itself is isotropic. A finite-element simulation of the impact is compared to the corresponding experiment. An impact on a ring with a defect is performed in order to study the effect on the wave pattern. The proposed method could be used in nondestructive testing of pipes.     

A dynamic photoelastic investigation of stress-wave propagation in cones

The embedded-polariscope method was employed to isolate the central plane in cylindrical and conical models subjected to axial loads. Light-field isochromatic-fringe patterns associated with each of the five models studied were recorded by using a multiple-gap camera. Results obtained indicate that the maximum stress decays with distance propagated approximately as indicated by the elementary one-dimensional wave theory.     

Elastodynamic analysis of low tension cables using a new curved beam element

In this paper, we address and overcome the difficulties associated with the use of the classic cable theory to treat low tension cables by developing a new three-noded locking-free nonlinear curved beam element. Based upon nonlinear generalized curved beam theory, large deformations and rotations in the new element are formulated in terms of Updated Lagrangian framework. Consistently coupled polynomial displacement fields are used to satisfy the membrane locking-free condition and the requirement of being able to recover the inextensible bending modes. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The stability and accuracy of the new element are further validated by experiments of an instrumented free-swinging steel cable experiencing slack and low tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions.