Exact spectral elements for follower tension buckling by power series

The spectral dynamic stiffness method using exact solutions of the governing equations as shape functions has been popular for vibration and dynamic stability analyses of framed structures consisting of uniform members. Since non-uniform members do not generally have closed form solutions, special cases only have been considered. However, exact solutions are still possible for generally non-uniform members using power series. The paper studies the exact dynamic stability of columns with distributed axial force by power series. Both uniform and distributed, compression and tension, and conservative and non-conservative axial forces are considered. Interaction diagrams of various kinds of axial loads on the natural frequencies including different intensities of the distributed loads and degree of tangency are given. Follower tension buckling is reported for the first time. It is found that the power series outperforms the dynamic stiffness method in terms of versatility in applications and numerical stability at the very low and high ends of the frequency spectrum.     

On the vibration and stability of a free-free beam subjected to end-loads

In this paper the vibration and stability of a free-free beam subjected to direction-controlled axial loads at its ends are investigated. The eigencurves and mode shapes of the beam are presented for various values of the directional control parameter. It is found that the behaviour of the free-free beam subjected to compressive axial loads is unstable for any direction parameter—except for the follower loading case. However, the same beam subjected to tensile loads is stable.     

MD investigation of the collective carbon atom behavior of a (17, 0) zigzag single wall carbon nanotube under axial tensile strain

The collective dynamic behavior of carbon atoms of a (17, 0) zigzag single wall carbon nanotube is investigated under tensile strains by molecular dynamics (MD) simulations. The “slip vector” parameter is used to study the collective motion of a group of atoms and the deformation behavior in three different directions (axial, radial, and tangential) of a (17, 0) carbon nanotube. The variations of radial slip vectors indicate almost all carbon atoms of the (17, 0) carbon nanotube will stay on the cylindrical surface before the yielding of the single wall carbon nanotube (SWNT). Furthermore, the tangential vectors show kinking deformation for the (17, 0) zigzag tube only rarely appears when the crack occurs. Non-symmetrical deformation around a carbon atom along the axial direction also can be found. The variations in the slip vector values of each atom display a symmetrical crack along the horizontal direction and normal to the tube axis. Chain-like structures with 3–4 atoms can be observed, with the number of chain-like structures decreasing before the breakage of the SWNT. The mechanical properties and dynamic behavior of a (17, 0) zigzag SWNT under tensile strain are also compared with that of a (10, 10) armchair tube in our previous study (Weng et al. 2009).     

材料力学基本实验中应变片粘贴误差分析

根据任意方向的应变公式,分析了材料力学基本实验中应变片粘贴方向、位置误差对测量结果的影响。     

Dependence of the thermal conductivity of a polymer chain on its tension

The heat transfer along a finite polyethylene macromolecule with fixed ends has been simulated. It has been shown that the thermal flux arising in the chain essentially depends on the distance between its ends. The thermal flux along the chain increases due to its stretching and decreases when its ends become closer to each other. There is a critical value for the approach of the ends at which the coil-globule transition begins. Upon a closer approach, a globule in the chain is formed and, upon a smaller approach, the chain always freely bends in space. It is at this critical approach of the ends that the tension in the chain and heat transfer along it are the weakest. Making the ends more remote or closer, one can change the thermal flux by more than two orders of magnitude. This effect is connected with the strong dependence of the morphology of the polymer chain on its tension. In nanotechnologies, such a polymer molecule with a variable distance between its fixed ends can be used as a regulated phonon resistor, i.e., as a phonon rheostat.     

FREE VIBRATIONS OF SELF-STRAINED ASSEMBLIES OF BEAMS

This paper examines the natural frequencies and modes of transverse vibration of two simple redundant systems comprising straight uniform Euler-Bernoulli beams in which there are internal self-balancing axial loads (e.g., loads due to non-uniform thermal strains). The simplest system consists of two parallel beams joined at their ends and the other is a 6-beam rectangular plane frame. Symmetric mode vibration normal to the plane of the frame is studied. Transcendental frequency equations are established for the different systems. Computed frequencies and modes are presented which show the effect of (1) varying the axial loads over a wide range, up to and beyond the values which cause individual members to buckle (2) pinning or fixing the beam joints (3) varying the relative flexural stiffness of the component beams. When the internal axial loads first cause any one of the component beams to buckle, the fundamental frequency of the whole system vanishes. The critical axial loads required for this are determined. A simple criterion has been identified to predict whether a small increase from zero in the axial compressive load in any one member causes the natural frequencies of the whole system to rise or fall. It is shown that this depends on the relative flexural stiffnesses and buckling loads of the different members. Computed modes of vibration show that when the axial modes reach their critical values, the buckled beam(s) distort with large amplitudes while the unbuckled beam(s) move either as rigid bodies or with bending which decays rapidly from the ends to a near-rigid-body movement over the central part of the beam. The modes of the systems with fixed joints change very little (if at all) with changing axial load, except when the load is close to the value which maximizes or minimizes the frequency. In a narrow range around this load the mode changes rapidly. The results provide an explanation for some computed results (as yet unpublished) for the flexural modes and frequencies of flat plates with non-uniform thermal stress distributions.     

Spicules and the effect of rigid rods on enclosing membrane tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g., the growth of microtubules, actin filaments, or sickle hemoglobin fibers towards a membrane. We calculate the axial force f exerted by the tube, and its average radius, taking into account steric interactions between the fluctuating membrane and the enclosed rod. We find a smooth crossover of the axial force between f approximately square root of (sigma) and f approximately sigma as the membrane tension sigma increases and the tube radius shrinks. This crossover occurs around the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension, and (ii) constructing dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.     

Spatial symmetrical vibrations and stability of circular arches with flexibly supported ends

In this work, exact formulae have been obtained for determining the lowest natural frequencies and critical loads of elastic circular arches with flexibly supported ends for symmetrical vibration in the direction perpendicular to the initial curvature of the arch. This investigation is concerned with three cases of load behaviour during the process of deformation. The values of the frequencies and critical loads are shown to be dependent on the opening angle of the arch, on the stiffness of the flexibly supported ends and on the ratio of the flexural rigidity to the torsional rigidity of the arch cross-section.     

Asymmetry of the water flux induced by the deformation of a nanotube

The behavior of nano-confined water is expected to be fundamentally different from the behavior of bulk water.At the nanoscale,it is still unclear whether water flows more easily along the convergent direction or the divergent one,and whether a hourglass shape is more convenient than a funnel shape for water molecules to pass through a nanotube.Here,we present an approach to explore these questions by changing the deformation position of a carbon nanotube.The results of our molecular dynamics simulation indicate that the water flux through the nanotube changes significantly when the deformation position moves away from the middle region of the tube.Different from the macroscopic level,we find water flux asymmetry(water flows more easily along the convergent direction than along the divergent one),which plays a key role in a nano water pump driven by a ratchet-like mechanism.We explore the mechanism and calculate the water flux by means of the Fokker-Planck equation and find that our theoretical results are well consistent with the simulation results.Furthermore,the simulation results demonstrate that the effect of deformation location on the water flux will be reduced when the diameter of the nanochannel increases.These findings are helpful for devising water transporters or filters based on carbon nanotubes and understanding the molecular mechanism of biological channels.     

Stability and free vibration analyses of cantilever shear buildings with semi-rigid support conditions and multiple masses

The stability and free vibration analyses of a cantilever shear building with generalized support conditions and with multiple masses (rotational and translational) rigidly attached at both ends and along its height are presented. The proposed model includes the simultaneous effects of: (1) lateral and rotational elastic restraints at the base support; (2) a uniform distributed mass and rotary inertia plus lumped rotary and translational masses rigidly attached at both extremes and along its height; (3) linearly distributed axial load plus the concentrated vertical axial loads caused by the lumped masses; and (4) shear deformations and shear forces induced by the applied axial forces. A parametric study is carried out that shows the importance of all variables included in this work on the stability and dynamic behavior of cantilever shear buildings, particularly the effects of the attached lumped masses and the rotational and translational constraints at the base support. A comparison with results presented by other researchers in previous studies shows that the proposed method and corresponding equations can be very useful in the assessment design of cantilever shear buildings. The main objective is to present readily solutions on the static stability and free vibration of cantilever shear buildings with generalized support conditions and multiple masses rigidly attached. The proposed method and corresponding expressions for the natural frequencies and modal shapes, buckling modes and axial critical loads are extensions of those presented recently by the senior author.     

The mechanical property of single-walled carbon nanotube under combined electromechanical loading

The mechanical properties and failure process of single-walled carbon nanotube (SWCNT) under combined electric field and tensile loading are investigated using the semi-empirical quantum mechanical method. The local and global structural deformation and variation of mechanical properties of SWCNT under different directions and intensity of external electric field are discussed systematically. It is shown that the electric field induced deformation in the radial and axial directions of the SWCNT are strongly dependent on the direction of electric field. The analysis of mechanical properties shows that the structure stiffness, tensile strength and failure strain of the SWCNT all decrease with the increase of the field intensity, which is particularly evident under the longitudinal electric field. The Young's modulus of SWCNTs vary with the tube diameter and are affected by the electric field. The increase of the length of the tubes intensifies the charge concentration at the tube ends under the electric field and lead to the decrease of mechanical properties of SWCNTs. The failure process of SWCNTs under the coupling effect of electric field and tensile loading is found to be controlled by the field strength and also affected by the electric charge accumulation.     

Strain-rate-induced bcc-to-hcp phase transformation of Fe nanowires

Using molecular dynamics simulation method, the plastic deformation mechanism of Fe nanowires is studied by applying uniaxial tension along the [110] direction. The simulation result shows that the bcc-to-hcp martensitic phase transformation mechanism controls the plastic deformation of the nanowires at high strain rate or low temperature; however,the plastic deformation mechanism will transform into a dislocation nucleation mechanism at low strain rate and higher temperature. Furthermore, the underlying cause of why the bcc-to-hcp martensitic phase transition mechanism is related to high strain rate and low temperature is also carefully studied. Based on the present study, a strain rate-temperature plastic deformation map for Fe nanowires has been proposed.     

利用光纤光栅实现力学量二维实时感测的研究

将一根光纤上写入两个不同波长的布位格光栅，沿矩形悬臂梁的中性而与表面的交线粘贴于靠近固定端两个相邻侧面，利用不纤光栅波长绝对编码的特性，实现了应力（或应变）与位移的二维实时传感测量。理论分析和实验结果证明，通过监测粘贴梁上的两个光纤光栅波长变化的大小和指向，能够实时感测应力、位移等力学量的大小和方向。在与梁轴垂直的方向上，获得应力实验灵敏度分别为5．32nm/N和3．21nm/N，位移实验灵敏度分别为0．30nm/mm和0．48nm/mm。     

风扇通流设计中环量分布形式的探讨

本文以时间推进通流设计方法为工具,设计了两个压比3.0级别的风扇转子,探讨了环量轴向分布形式对设计的影响.两个设计采用不同的环量分布,一为环量沿轴向线性变化,另一为环量沿轴向按余弦曲线变化,三维粘性计算结果表明,在峰值效率点,后者压比、效率和流量都高于前者.后者叶尖形成预压缩效果更为显著的叶型,对激波有更好的控制,激波后分离区小,更适合用于高负荷风扇的设计.     

空调器新型轴流风扇叶尖涡的研究

本文采用Navier-Stokes方程和Spalart-Allmaras湍流模型,对只在叶轮尾缘带有导流罩的低压轴流风扇进行了三维稳态内流模拟,详细分析了叶顶流场中叶尖涡的产生和发展轨迹。研究结果表明,叶尖涡在距叶尖前缘约1/4叶顶轴向弦长的吸力面附近形成,在叶轮出口附近消失,在切向约占3/4流道,近似形成一个涡环,阻塞主流.在回转面上,叶尖涡涡核先沿流线方向发展,在导流罩附近逐渐转为切向方向发展;在径向方向,叶尖涡先沿外径方向发展,在导流罩附近转向内径方向移动。空调室外机系统的不对称结构引起叶尖涡在叶轮旋转过程中的相对位移.流量的变化对叶尖涡的轴向位置影响较大,而对其径向位置的影响不明显;小流量时叶尖涡的轴向移动能力减弱,切向移动能力增强,消失位置向前缘方向移动.     

Discrete element simulation of localized deformation in stochastic distributed granular materials

The deformation in granular material under loading conditions is a problem of great interest currently. In this paper, the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modified distinct element method under the plane strain conditions, and the influences of the confining pressure, the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded, based on the numerical simulation testing, that two crossed shear sliding planes may occur inside the granular assembly, and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes, it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last, the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

液体物性对雾化射流液雾粒径的影响

对不同液体在空气中湍动雾化射流的气液两相流场进行了数值模拟.建立了一次雾化的一维模型,分析了粘度、表面张力和气液质量流量比对液雾粒径的影响趋势,采用基于粒子追踪法的二次雾化三维模型,分析了物性和各种工况对液雾粒径沿轴向分布的影响程度.计算结果和已公开发表的实验数据进行比对,得到了较好的吻合,在此基础上,分析了影响气泡雾化喷嘴雾化质量的主要因素.     

激光等离子体细丝的场分布和共振吸收

本文对激光等离子体细丝的场分布和共振吸收进行了理论研究.在冷等离子体的条件下,首先求得场方程以及电场的径向分量和轴向分量的解析表示式;然后,通过数值计算发现:在等离子体细丝的径向场存在一个隧道效应,即在径向共振点r_o附近,场出现极大值.     

管壁导热对脉管内自然对流换热影响的研究

本文计算了不同脉管倾角和管壁材料下脉管管壁导热对自然对流换热的影响。发现脉管壁面导热对换热的影响不仅体现在增加了壁面的纯导热部分,更主要的上强化了脉管内的自然对流;壁面和内部气体的温度差异沿脉符轴向的变化是管壁导热强化自然对流的主要原因。     

First-principles investigation on ideal strength of B2 NiAl and NiTi alloys

For B2 NiAl and NiTi intermetallic compounds, the ideal stress–strain image is lack from the perspective of elastic constants. We use first-principles calculation to investigate the ideal strength and elastic behavior under the tensile and shear loads. The relation between the ideal strength and elastic constants is found. The uniaxial tension of NiAl and NiTi along <001> crystal direction leads to the change from tetragonal path to orthogonal path, which is driven by the vanishing of the shear constant C(66). The shear failure under {110}{111} shear deformation occurring in process of tension may result in a small ideal tensile strength(~ 2 GPa) for NiTi. The unlikeness in the ideal strength of Ni Al and Ni Ti alloys is discussed based on the charge density difference.