利用 Laplace 变换确定双层厚壁长圆筒的轴对称界面碰撞压力

利用Ｌａｐｌａｃｅ变换，考虑轴对称弹性波的影响，采用特征函数展开法求解双层厚壁长圆筒受爆炸载荷作用下的轴对称弹性碰撞冲击问题，着重研究前几次碰撞冲击引起的轴对称界面碰撞压力。并对轴对称界面碰撞压力与间隙量、爆炸载荷幅值、爆炸载荷衰减系数之间的关系以及相关的动力响应作了初步的分析。     

Dynamic analysis of thick short length FGM cylinders

In this paper a thick short length hollow cylinder made of functionally graded materials (FGMs) under internal impact loading is considered. The inner surface of the cylinder is pure ceramic, the outer surface is pure metal, and the material composition varies continuously along its thickness. Finite Element Method based on Rayleigh-Ritz energy formulation has been applied to study the propagation of elastic waves in FG thick hollow cylinders. The Newmark direct integration method is applied to solve the time dependent equations. The time histories of displacements, stresses, wave propagation in two directions and velocities of radial stress wave propagation for various values of volume fraction exponent have been investigated. Also by using fast Fourier transform, the first natural frequencies for FG cylinders with simply-simply and clamped-clamped ends conditions are illustrated. The model has been compared with result of a plane strain FG thick hollow cylinder which is subjected to an internal impact loading, and it shows very good agreement.     

Hopf bifurcation and chaotic motions of a tubular cantilever subject to cross flow and loose support

The Hopf bifurcation and chaotic motions of a tubular cantilever impacting on loose support is studied using an analytic model that involves delay differential equations. By using the damping-controlled mechanism, a single flexible cantilever in an otherwise rigid square array of cylinders is analyzed. The analytical model, after Galerkin discretization to five d.o.f., exhibits interesting dynamical behavior. Numerical solutions show that, with increasing flow beyond the critical, the amplitude of motion grows until impacting with the loose support placed at the tip end of the cylinder occurs; more complex motions then arise, leading to chaos and quasi-periodic motions for a sufficiently high flow velocity. The effect of location of the loose support on the global dynamics of the system is also investigated.     

Elastic analyses of heterogeneous hollow cylinders

Two different kinds of heterogeneous elastic hollow cylinders are studied in the present paper. One is a multi-layered cylinder with different values in different layers for both elastic modulus and Poisson’s ratio. Another is an elastic hollow cylinder with continuously graded material properties. By introducing two recursive algorithms, the extrusion stresses between two neighbor layers in the multi-layered cylinder submitted to uniform pressures on the inner and outer surfaces can be simply determined. Then the exact solutions of the multi-layered structure can be found based on Lamé’s solution. For the hollow cylinder with continuously graded properties, the displacement method is used. Both Whittaker equation and hyper-geometric equation are derived and successfully solved, and then the exact solutions are found. The results obtained in the present paper are compared with the numerical solutions and good agreements are found. At the end of the present paper, some inherent properties of these two different kinds of heterogeneous elastic hollow cylinders are presented and discussed. The results obtained in the present paper are useful in the design and analysis for composites reinforced by unidirectional fiber layers.     

Elastodynamic response of a wedge to surface pressures

An elastic wedge of interior angle κπ, where 1 < κ ? 2, is subjected to the impact of spatially uniform pressures on its faces. The application of the pressures produces a system of longitudinal waves, transverse waves and head waves. In this paper the elastodynamic stress singularity in the circumferential stress at the vertex of the wedge is analyzed. The analysis is based on self-similarity of first-order time derivatives of the displacement potentials. By means of appropriate transformations the statement of the problem is reduced to two Laplace's equations, whose solutions in half-planes are coupled along the real axes. The solutions to this system are obtained by using elements of analytic function theory, together with summations over Chebychev polynomials along the real axes.     

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.     

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.     

LIQUID SLUG MOTION IN A VOIDED LINE

Transient individual liquid slug motion in a voided line is investigated both numerically and experimentally. In a series of experiments, slugs of various lengths are propelled into an empty pipe under varying air pressures controlled at an upstream reservoir. The pressure–time histories created by the impacting slugs at an elbow located at the end of the pipe reach are measured, and the peak pressures are in reasonable agreement with results reported in an earlier study. An analytical model is developed to predict the slug acceleration and its impulse at the elbow. Comparisons between measured and predicted parameters reveal the random nature of the slug motion and subsequent impact.     

On the Direct and Radiated Components of the Collisional Particle Pressure in Liquid-Solid Flows

In a recent study the collisional particle pressure was measured for liquid fluidized beds and liquid-solid flows. The particle pressure was defined as the additional pressure generated by the presence of the particulate-solid phase in a liquid-solid mixture. The particle pressure generated by collisions of particles was found to be composed of two main contributions: one from pressure pulses generated by direct collisions of particles against the containing walls (direct component), and a second one from pressure pulses due to collisions between individual particles that are transmitted through the liquid (radiated component). This paper presents a summary of the technique to measure the particle pressure and the main results of that study.Additional experiments were performed to further study each one of the components of the particle pressure. The direct component was studied by impacting particles on the active face of the pressure transducer. The magnitude of the measured impulse was found to be related to the impact velocity, the mass and the size of the impacting particle. By comparing the measurements with the predictions from Hertzian theory, a quantification of the interstitial fluid effects could be obtained. The radiated component was investigated by generating binary collisions of particles in the vicinity of the transducer. The magnitude of the measured impulse was found to be a function of fluid density, particle size and impact velocity. Predictions based on impulse-pressure theory were obtained and compared with the experimental measurements. The model results showed good agreement with the experimental measurements.     

气相爆轰波冲击气固界面的透反射特性

为了研究气相爆轰波冲击气固界面过程中透射波和反射波的相关特性,建立爆轰波冲击气固界面的一维理论模型,对不同初始压力条件下爆轰波到达气固界面后的界面两侧的压力和界面速度变化进行分析。利用时空守恒元求解元方法对气相爆轰波冲击气固界面过程进行数值模拟,分析气体部分反射波的压力分布和速度变化规律及透射入固体中应力波的波形和波速特征,并搭建气相爆轰波冲击活塞实验装置进行进一步验证。结果表明:气体爆轰波到达气固界面后,在固体中透射指数形式的弹性波,并在界面处向气体区反射一道激波。爆轰波后的稀疏波与反射激波相交,削弱反射激波,最终形成稳定激波回传。气固界面在稀疏波和反射稀疏波的作用下,压力和速度逐渐下降,最终也形成稳定状态。在不同混气初始压力情况下,爆轰波冲击过程中产生的最高压力和爆压的比值基本保持不变。理论模型对特征点相关物理量的计算值和实验数据符合的较好。     

Dynamic thermal shock in a layered cylinder with initial interface pressure

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Impact phenomena of rotor-casing dynamical systems

Rubbing and impacting between a rotor and adjacent motion-constraining structures is a serious malfunction in rotating machinery. A shaver rotor-casing system with clearance and mass imbalance is modelled with two second-order ordinary differential equations and inelastic impact conditions. The dynamics is investigated analytically, as well as by numerical simulation. A Lyapunov exponent technique is developed to characterize the topologically different behavior as the parameters are varied. The dry friction coefficient and the eccentricity of the rotor imbalance were chosen to be the two variable parameters, the effect of which on the system dynamics is illustrated through phase plots, bifurcation diagrams, as well as Poincaré maps. The results demonstrate the existence of both rubbing and impacting behavior. Depending on values of the parameters, rubbing motion in both the clockwise and counter-clockwise directions may occur. Within the impact regime, the impact behavior could be periodic, quasi-periodic or chaotic, as confirmed by the calculation of Lyapunov exponents.     

Extreme wind pressure estimation based on the r largest order statistics mode

提出一种基于r个最大次序统计量(r largest order statistics, r-LOS)模型的极 值风压估算方法, 该模型包括广义极值(generalized extreme value distribution, GEV)联合分布形式及Gumbel联合分布形式. 提出了独立风压峰值 r-LOS序列构造方法、最优r值确定方法、r-LOS GEV模型和r-LOS Gumbel模型的优选方法. 将r-LOS模型方法应用于某低矮工业建筑刚性模型测压试验的极 值风压估算. 当采用多段风压时程估算极值风压时, r-LOS Gumbel模型优于r-LOS GEV模型和经典Gumbel模型. 当采用单段风压时程时, 与基于改进Hermite模型的峰值因子 法、Sadek-Simiu法相比, r-LOS Gumbel模型方法能更加精确地估算极值风压, 适用于非高斯风压的极值估算, 可以给出极值风压分位点的解析解. 分析表明, r-LOS Gumbel模型方法是一种多段时程和单段时程条件下均适用的极值风压估算方法.     

空心率对中空夹层钢管混凝土组合柱耐撞性能影响

以外层为不锈钢的中空夹层钢管混凝土柱为研究对象,采用有限元分析软件,模拟该类构件在低速横向冲击下的动力响应,讨论空心率对其耐撞性能的影响,并提出稳固性因数来评估结构的耐撞性能,同时展开3组实验对有限元模拟典型算例进行校正。试件的耐撞性能主要从抗冲击能力与冲击过程中结构的稳固性方面讨论。研究结果表明:空心率在0~0.73范围内,其对冲击力平台值影响不明显,试件抗冲击能力没有明显变化;空心率大于0.73,冲击力平台值明显下降,试件抗冲击能力明显减弱。空心率在0~0.6范围内,试件冲击过程中的结构稳固性因数保持在一个较高水平;空心率0.6~1.0范围内,试件冲击过程的结构稳固性因数明显降低,且呈单调下降趋势。     

Minimum weights of pressurized hollow sandwich cylinders with ultralight cellular cores

Long, open-ended, hollow sandwich cylinders with ultralightweight cellular cores are optimized under uniform internal pressure for minimum weight design. Five different core topologies are considered: Kagomé truss, single-layered pyramidal truss, double-layered pyramidal truss, single-layered corrugated core and double-layered corrugated core. The highly porous cellular materials are homogenized to obtain effective constitutive relations. Close-formed solutions are presented for the forces and stresses in individual structural members of the sandwich, which are then validated by finite element calculations. Optimization of the sandwich-walled hollow cylinder is achieved using a quadratic optimizer, subjected to the constraints that none of the following failure modes occurs: facesheet yielding; facesheet punch shearing (active only for truss-cored sandwiches); core member buckling; core member yielding. In comparison with hollow cylinders having solid walls, truss-core sandwich cylinders and single-layer corrugated core sandwich cylinders are found to have superior weight advantages, especially for more heavily loaded cases. With the consideration of both weight efficiency and failure modes, sandwich-walled hollow cylinders having Kagomé truss core with pyramidal sub-geometry have the best overall performance in comparison with other core topologies.     

The Art, Craft and Science of Modelling Jet Impact in a Collapsing Cavitation Bubble

One of the key characteristics of the asymmetric collapse of a cavitation bubble near a rigid boundary is the development of a high speed liquid jet that penetrates the interior of the bubble, impacting on the other side to yield a toroidal bubble. After the formation of the toroidal bubble, a vigorous splash may occur that can lead to pressures on the boundary an order of magnitude greater than the impact pressures associated with the jet. Qualitative agreement with available experimental data is found although, as the bubble approaches minimum volume, shock waves are also observed which further complicate our full understanding of the mechanisms for damage.     

Nonstationary heat transfer in a hollow composite cylinder

Solution of a nonstationary heat-transfer problem for bounded end-conjugated hollow dissimilar cylinders is presented. In the volume of the cylinders, time- and coordinate-dependent heat release of known intensity takes place. The problem is solved using finite integral transformations over two coordinates.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 130–140, March–April, 2005.     

飞机模型高速撞击钢筋混凝土载荷特性实验研究

为得到大型商用飞机撞击的冲击载荷特性及其计算方法,基于火箭橇加载试验平台,搭建了飞机模型撞击钢筋混凝土运动靶体测试系统,开展了两种不同尺寸飞机模型的撞击试验,利用高速摄影技术获得了飞机模型撞靶前的姿态、着速及飞机模型撞靶的破坏过程。采用加速度测试系统和激光干涉测速系统,分别得到撞击过程中运动靶体的加速度和速度历史,据此得到靶体受到的冲击载荷-时间曲线,二者吻合,验证了测试系统的可靠性。通过飞机模型上安装的机载存储过载测试系统,获得了撞击过程中飞机模型的负加速度-时间曲线,由此确定了修正的Riera理论模型中的静载荷项,并进一步计算得到靶体受到的冲击载荷-时间曲线,与通过测试靶体的加速度或速度得到的结果一致,验证了使用修正的Riera理论模型计算飞机模型冲击载荷的合理性及计算方法的正确性,同时确定了适合于本试验中飞机模型的修正系数α。     

Simple Regimes of Fluid Motion in the Neighborhood of the Intersection of Bifurcations Initiating Nonisothermal Taylor Vortices and Azimuthal Waves

Steady-state, self-oscillating, and two-frequency quasi-periodic regimes of fluid motion between heated rotating cylinders are investigated in a small neighborhood of the point of intersection of the neutral curves of monotonic axisymmetric and oscillatory three-dimensional instability of the nonisothermal Couette flow. Methods developed in studies [2–4], which make it possible to reduce the problem to the investigation of an autonomous dynamical fourth-order system whose coefficients can be found numerically by integrating a series of linear boundary-value problems for systems of ordinary differential equations, are used.     

Stress state of a hollow round cylinder with side holes under different pressure and temperature impact

The stress–strain state of a hollow cylinder (pipe) with lateral holes is considered. The pipe is under the action of internal and external hydrostatic pressures P₁ and P₂ and also a temperature effect. Such a pipe is used in oil–gas recovery, rocket engineering, chemical machinery industry and etc. There is no detailed analytic solution of this problem in literature to date. The number of holes through which a liquid or gas can flow into the pipe interior (and vice versa) depends on the loads, the size of the cross-section and the material of the pipe. The proper selection of the arrangement of holes and their diameters is determined from an analytic solution. In addition, the maximum boundary loads (of pressures) at which the pipe cracks is also found.