钟形橡胶弹簧的扭转刚度计算

钟形橡胶弹簧的扭转刚度计算赖远明，张孟喜（兰州铁道学院，兰州７３００７０）钟形橡胶弹簧广泛应用于交通运输中，如ＳＳ＿１型电力机车上的中央支承，内燃机车柴油机上的支承座等等。由于其形状复杂，目前还没有相应的扭转刚度计算公式，为此本文导出其计算公式。由于...     

纳米碳管与刚性壁的正碰撞

用分子动力学方法模拟纳米碳管与刚性壁的正碰撞过程,并与弹性动力学方法的结果进行对比在分子动力学模拟中,采用Tersoff-Brenner势描述碳管的原子间相互作用,用6~12形式的Lennard-Jones势描述碳管与刚性壁间相互作用结果表明,两种方法所得到的应力波传播速度吻合较好与弹性动力学分析结果不同的是,在发生屈曲以前,纳米碳管与刚性壁的接触时间不仅与纳米碳管的长度近似成线性关系,还与管径及碰撞初速度有关.碰撞过程中,纳米碳管端部应力并非定值,但其平均值与弹性动力学计算结果相差不大.     

纳米碳管/铝基复合材料的制备及摩擦磨损性能研究

利用粉末冶金法制备纳米碳管/铝基复合材料,研究不同纳米碳管含量对复合材料硬度和稳态摩擦磨损行为的影响,采用扫描电子显微镜观察复合材料的磨损表面形貌,并对其磨损机制进行探讨.结果表明:随着纳米碳管质量分数的增加,复合材料的硬度呈现先增大而后减小的趋势,含质量分数为2%的纳米碳管复合材料硬度比铝增加约80%;复合材料的摩擦系数逐渐降低,磨损率先减小而后增大;含质量分数为1%的纳米碳管复合材料磨损机制为磨粒磨损和粘着磨损,而含质量分数为2%的纳米碳管复合材料以剥层磨损和疲劳磨损为主.     

纳米碳管增强铜基复合材料的滑动磨损特性研究

以纳米碳管作为增强体制备了铜基复合材料,采用ＭＭ－２２０型环－块摩擦磨损试验机考察了该复合材料的滑动磨损行为,并观察分析了复合材料的组织结构、磨损表面形貌及磨屑组成．结果表明,其磨损过程存在跑合和稳态磨损２个阶段,在稳态磨损阶段主要发生氧化磨损,同时也存在磨粒磨损．工作环境影响复合材料的耐磨性．纳米碳管体积分数在１２％～１５％时,可以较好地发挥其润滑和阻止基体氧化的作用．     

范德华力对多壁纳米碳管力学性质的影响

用分子动力学方法模拟了多壁纳米碳管在压缩、弯曲变形下力与变形的关系.通过与组成多壁碳管的各单壁碳管的比较分析,揭示了多壁纳米碳管层间范德华力对碳管力学性质的影响.采用Tersoff-Brenner势描述每一单壁纳米碳管内原子间作用,采用Lennard-Jones势描述碳管壁间范德华力.计算结果表明:多壁纳米碳管的比强度明显高于单壁纳米碳管.纳米碳管的半径虽然对杨氏模量影响不大,但对纳米碳管的曲屈行为影响却相当显著.     

Ni—P—纳米碳管化学复合镀层的摩擦磨损特性

用化学镀方法制备了 Ni- P-纳米碳管复合镀层 ,研究了热处理对复合镀层微观结构及摩擦学性能的影响 .结果表明 :Ni- P-纳米碳管复合镀层比 Ni- P- Si C和 Ni- P-石墨镀层具有更好的摩擦磨损性能 ;在 6 73K条件下热处理 2 h后 ,复合镀层的耐磨性能显著改善 ;除 Ni- P-纳米碳管复合镀层的摩擦系数基本不变以外 ,其余复合镀层的摩擦系数均降低 .     

基于水平弹簧刚度折减的反压土计算方法

为促进反压土台支护技术的广泛应用,针对现行刚度折减计算方法的局限性,基于力学平衡原理,提出了基坑内开挖影响距离的计算方法。在此基础上,对反压土的水平弹簧刚度进行折减,并通过弹性地基梁法求解反压土支护问题。通过工程实例的计算与分析,验证了基于水平弹簧刚度折减方法的可靠性和适用性。结果表明:①基坑开挖影响距离不仅与基坑悬臂深度有关,还与坑内开挖深度、土的物理力学性质也密切相关;②当反压土台宽度为1～2倍土台高度时,土层弹簧刚度与土台截面面积近似呈正相关关系;③当土层均一且土性良好时,基坑开挖影响距离按经验取值3～5倍基坑悬臂深度是适用的。当地层含有厚层软土时,经验取值计算结果最大误差可达57%,现行刚度折减方法不再适用。     

求解比例加载下结构负刚度问题的虚加弹簧法

针对恒载和比例变载共同作用下软化结构按位移法求解的负刚度问题,提出了一种虚加弹簧法.在各比例加载点沿荷载方向布置刚度适当的弹簧,得到没有负刚度问题的硬化结构,对虚加弹簧的结构进行逐级加载,在每级加载时从总荷载中扣除弹簧所承担的荷载,即得到结构所承担的荷载.将后者中不符合比例加载要求的非比例成分反向施加在虚加弹簧的结构上重新求解,将得到新的非比例成分.重复此过程进行迭代运算,直至非比例成分可略,就得到本级比例加载下结构负刚度问题的解,重复此过程可得到各级加载下的解.本方法同时也适合结构硬化阶段的求解.该方法力学概念直观,编程简明,可以用于非线性结构加卸载变形全过程的数值分析.运用该方法对多种工况进行了计算,结果表明该方法可行并具有良好的收敛性.     

层合板界面层的弹簧界面元等效刚度计算模型

弹簧界面元是一种最常用的层合结构界面脱层数值模拟的计算模型.但目前对应于给定的复合材料层合板界面层,弹簧界面元的长度和等效刚度的确定却没有严格的方法,所以时常因为弹簧元刚度定义的不当而导致脱层数值模拟结果的不稳定甚至计算困难.本文给出了一种基于层合板粘接层的实际厚度和材料特性确定弹簧界面元的长度和等效刚度的计算模型.通...     

不同类型水平弹簧组合刚度非线性吸振器的性能分析及稳定性研究

动力吸振器作为一种振动控制单元被广泛运用于各种工程场合, 但传统的线性吸振器只能实现窄带振动控制. 文章在线性吸振器的基础上引入对称水平弹簧构建线性刚度与非线性刚度相结合的组合刚度非线性吸振器, 以提升吸振器的吸振性能. 考虑实际工程中可能的安装方式, 分别建立水平弹簧接地安装和不接地安装的组合刚度非线性吸振器模型, 利用谐波平衡法结合弧长延拓法解析求解动力学响应, 并与数值结果相互验证, 证明了求解结果的准确性. 随后分析比较两种组合刚度非线性吸振器与线性吸振器以及非线性能量阱之间的吸振性能, 发现水平弹簧接地安装类型的组合刚度非线性吸振器在保留线性吸振器优势的同时又改善其吸振频带窄的缺点, 且与非线性能量阱相比在主共振频率附近的较宽频内吸振性能更优. 在此基础上, 讨论了水平弹簧参数以及吸振器阻尼对主结构振动幅频响应和稳定性的影响, 最后观察分析主结构幅频响应曲线不稳定区内的复杂动力学行为. 研究结果表明合适的设计参数能够使得主结构振动峰值较低的同时, 频响曲线不稳定运动区域的范围也较小.     

A cohesive law for carbon nanotube/polymer interfaces based on the van der Waals force

We have established the cohesive law for interfaces between a carbon nanotube (CNT) and polymer that are not well bonded and are characterized by the van der Waals force. The tensile cohesive strength and cohesive energy are given in terms of the area density of carbon nanotube and volume density of polymer, as well as the parameters in the van der Waals force. For a CNT in an infinite polymer, the shear cohesive stress vanishes, and the tensile cohesive stress depends only on the opening displacement. For a CNT in a finite polymer matrix, the tensile cohesive stress remains the same, but the shear cohesive stress depends on both opening and sliding displacements, i.e., the tension/shear coupling. The simple, analytical expressions of the cohesive law are useful to study the interaction between CNT and polymer, such as in CNT-reinforced composites. The effect of polymer surface roughness on the cohesive law is also studied.     

Carbon nanotubes/TiO2 nanotubes composite photocatalysts for efficient degradation of methyl orange dye

A series of carbon nanotubes/TiO2 nanotubes （CNTs/TNTs） composite photocatalysts were successfully prepared by incorporation of CNTs in HNO3 washing process. These photocatalysts were characterized by XRD, N2 physical adsorption, UV-vis diffuse reflectance spectroscopy, TEM and Raman spectroscopy, respectively, and their photocatalytic activities were tested by using methyl orange （MO） as a model compound. Also, the effects of amount of CNTs incorporated, calcination temperature and amount of catalyst on the photocatalytic activity of the composite photocatalyst were systematically investigated. The results show that the CNTs/TNTs composite exhibits much higher photocatalytic activity than that of the TNTs or CNTs alone.     

Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes

It is of fundamental value to understand the thermo-mechanical properties of carbon nanotubes. In this paper, by using molecular dynamics simulation, a systematic numerical investigation is carried out to explore the natural thermal vibration behaviors of single-walled carbon nanotubes and their quantitative contributions to the apparent thermal contraction behaviors. It is found that the thermo-mechanical behavior of single-walled carbon nanotubes is exhibited through the competition between quasi-static thermal expansion and dynamic thermal vibration, while the vibration effect is more prominent and induces apparent contraction in both radial and axial directions. With increasing temperature, the anharmonic interatomic potential helps to increase the bond length, which leads to thermally induced expansion. On the other hand, the higher structural entropy and vibrational entropy of the system cause the carbon nanotube to vibrate, and the apparent length of nanotube decreases due to various vibration modes. Parallel analytical and finite element analyses are used to validate the vibration frequencies and provide helpful insights. The unified multi-scale study has successfully decoupled and systematically analyzed both thermal expansion and contraction behaviors of single-walled carbon nanotube from 100 to 800 K, and obtained detailed information on various vibration modes as well as their quantitative contributions to the coefficient of thermal expansion in axial and radial directions. The results of this paper may provide useful information on the thermo-mechanical integrity of single-walled carbon nanotubes, and become important in practical applications involving finite temperature.     

TORSIONAL PROPERTIES OF METALLIC NANOSPRINGS

Based on molecular mechanics and the embedded-atom potential, the torsional mechanical behaviors of metallic copper nanosprings are investigated in this paper. The torsion coefficient of the nanospring is obtained by fitting the curve of potential energy versus torsion angle according to a parabolic law. It is found that the geometry of nanospring has a strong influence on the torsion coefficient. With the increase of the wire radius and the helix radius, the torsion coefficient of the nanospring increases. However, it decreases with the increase of the helix pitch and turns. It is also found that the classic spring theory is invalid to torsional nanosprings. The calculated torsion coefficient is higher than the predication from the classic spring theory and is lower than that of the corresponding solid rod. In addition, the continuum mechanics is shown to be inapplicable to describe the torsional behavior of nanosprings. These findings might provide a better understanding of the usability and functionality of nanosprings in nanodevices.     

An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation

Carbon nanotubes (CNTs) display unique properties and have many potential applications. Prior theoretical studies on CNTs are based on atomistic models such as empirical potential molecular dynamics (MD), tight-binding methods, or first-principles calculations. Here we develop an atomistic-based continuum theory for CNTs. The interatomic potential is directly incorporated into the continuum analysis through constitutive models. Such an approach involves no additional parameter fitting beyond those introduced in the interatomic potential. The atomistic-based continuum theory is then applied to study fracture nucleation in CNTs by modelling it as a bifurcation problem. The results agree well with the MD simulations.     

An approach to multi-body interactions in a continuum-atomistic context: Application to analysis of tension instability in carbon nanotubes

The tensile strength of single-walled carbon nanotubes (CNT) is examined using a continuum-atomistic (CA) approach. The strength is identified with the onset of the CNT instability in tension. The focus of this study is on the effects of multi-body atomic interactions. Multiscale simulations of nanostructures usually make use of two- and/or three-body interatomic potentials. The three-body potentials describe the changes of angles between the adjacent bonds – bond bending. We propose an alternative and simple way to approximately account for the multi-body interactions. We preserve the pair structure of the potentials and consider the multi-body interaction by splitting the changing bond length into two terms. The first term corresponds to the self-similar deformation of the lattice, which does not lead to bond bending. The second term corresponds to the distortional deformation of the lattice, which does lead to bond bending. Such a split of the bond length is accomplished by means of the spherical–deviatoric decomposition of the Green strain tensor. After the split, the continuum-atomistic potential can be written as a function of two bond lengths corresponding to the bond stretching and bending independently. We apply an example exponential continuum-atomistic potential with the split bond length to the study of tension instability of the armchair and zigzag CNTs. The results of the study are compared with those obtained by Zhang et al. (2004. J. Mech. Phys. Solids 52, 977–998) who studied tension instability of carbon nanotubes by using the Tersoff–Brenner three-body potential, and with recent experimental results on the tensile failure of single walled carbon nanotubes.     

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical buckling load. The present investigation may be of some help in further understanding the mechanical properties of MWNTs.     

A study on the bending stiffness of single-walled carbon nanotubes and related issues

Single-walled carbon nanotubes (SWCNTs) are usually modeled as elastic tubes and their bending stiffness D is often related to their axial stretching modulus E (Young's modulus) as in mechanics of materials (i.e. D=EI where I is the moment of inertia of the tube). However, recent studies show that large discrepancies may exist when this relationship is used to predict Young's modulus of carbon nanotubes (CNTs) through bending dominated deformations. In the present paper, the bending stiffness of SWCNTs and some related issues are investigated by the combined use of the molecular-mechanics (M-M) model and the deformation mapping technique. Based on the analysis results, the contradictions mentioned above can be explained well. Furthermore, an analytical expression for the bending stiffness of SWCNTs is also presented. It shows that the bending stiffness of a SWCNT is approximately proportional to the cube of its radius which agrees well with the existing molecular dynamics simulation and continuum theory based results.     

Numerical model for composite material with polymer matrix reinforced by carbon nanotubes

Due to the high stiffness and strength, as well as their ability to act as conductors, carbon nanotubes are under intense investigation as fillers in polymeric materials. The nature of the carbon nanotube/polymer bonding and the curvature of the carbon nanotubes within the polymer have arisen as particular factors in the efficacy of the carbon nanotubes to actually provide any enhanced stiffness or strength to the nanocomposite. Here the effects of carbon nanotube curvature and interface interaction with the matrix on the nanocomposite stiffness are investigated using nanomechanical analysis. In particular, the effects of poor bonding and thus poor shear lag load transfer to the carbon nanotubes are studied. In the case of poor bonding, carbon nanotubes waviness is shown to enhance the composite stiffness.