Numerical estimation of the influence of joint stiffness on free vibrations of frame structures via the scattering of waves at elastic joints

In the structural design of mechanical products, natural frequencies must be controlled to reduce noise and vibration. In particular, the stiffness of the joints which assemble the structural components affects the natural frequencies. Therefore, it is important to predict the influence of joint stiffness on natural frequencies. Generally, these effects are determined by iterative finite element analyses of assembled structural models. Because this results in high computational costs, the sensitivity of natural frequencies to joint stiffness should be determined by a different approach to make the structural design process more efficient. Therefore, this paper proposes the use of reflection and transmission coefficients of elastic joints to predict the dependency of natural frequencies on joint stiffness. First, we formulate the reflection and transmission coefficients of joint stiffness, and then organize the coefficients using a ray tracing method. These formulations enable us to discuss the mechanisms which determine the natural frequency of a structure based on a wave approach using the phase-closure principle. Therefore, by applying the phase-closure principle to the frame structure, we investigate the formation of bending modes, which suggests that the effects of joint stiffness on natural frequencies correspond to the dependence of the reflection and transmission coefficients on joint stiffness. Therefore, these coefficients are useful indicators for estimating the influence of joint stiffness.     

Linear normal stress under a wheel in skid for wheeled mobile robots running on sandy terrain

Wheeled mobile robots are often used on high risk rough terrain. Sandy terrains are widely distributed and tough to traverse. To successfully deploy a robot in sandy environment, wheel-terrain interaction mechanics in skid should be considered. The normal and shear stress is the basis of wheel-soil interaction modeling, but the normal stress in the rear region on the contact surface is computed through symmetry in classical terramechanics equations. To calculate that directly, a new reference of wheel sinkage is proposed. Based on the new reference, both the wheel sinakge and the normal stress can be given using a quadratic equation as the function of wheel-soil contact angle. Moreover, the normal stress can be expressed as a linear function of the wheel sinkage by introducing a constant coefficient named as sand stiffness in this paper. The linearity is demonstrated by the experimental data obtained using two wheels and on two types of sands. The sand stiffness can be estimated with high accuracy and it decreases with the increase of skid ratio due to the skid-sinkage phenomenon, but increases with the increase of vertical load. Furthermore, the sand stiffness can be utilized directly to compare the stiffness of various sandy terrains.     

A Novel Method for Dynamic Short-Beam Shear Testing of 3D Woven Composites

A new test method for performing dynamic short-beam shear tests using a momentum trapped Hopkinson pressure bar is proposed. Angle-interlock 3D woven composite specimens were tested under quasi-static and dynamic loading conditions to determine the effect of loading rate on damage evolution. The equilibrium condition in the composite specimen under dynamic loads was verified using finite element analysis of the experiment. A high speed camera was used to capture delamination initiation and propagation during both quasi-static and dynamic experiments. Analysis of the load-deflection curves and the high speed images revealed a good correlation between the modes of damage initiation and propagation with the features in the loading response. The apparent inter-laminar shear strength and the bending stiffness increased with rate of loading. While the damage was observed to propagate at a relative steady rate during quasi-static loading, the high rate of energy input during dynamic loading resulted in a rapid propagation of damage and a subsequent loss of stiffness in the composite as noted in the load-deflection curve.     

基于永磁体间的磁性负刚度的分析与优化

为了有效地降低磁性负刚度结构的非线性程度,从简单三磁体结构出发,引入新型负刚度结构模型——五磁体对称结构,运用MATLAB建立新型负刚度结构的磁力学模型并应用Ansoft Maxwell进行仿真验证。研究永磁体间的相对位置参数对五磁体对称结构的负刚度曲线走势的影响,在微幅振动下对基于磁引力的负刚度曲线拟合后使用谐波平衡法求解动力学方程。最终得出结论:在给定的条件下,五磁体负刚度结构的负刚度曲线的非线性相较于简单三磁体结构,一定程度上得到了改善,且其隔振性能相较于传统线性隔振系统有了大幅提高,为磁性负刚度结构的负刚度曲线非线性的优化和应用提供了理论上的参考。     

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.     

An Experimental Setup for Combined In-Vacuo Raman Spectroscopy and Cavity-Interferometry Measurements on TMDC Nano-resonators

Experimental Mechanics - Nanoelectromechanical (NEMS) systems fabricated using atomically thin materials have low mass and high stiffness and are thus ideal candidates for force and mass sensing...     

一般情况下小垂度索的刚度方程及其应用

索单元的刚度随变形而变化,索结构的力学分析是一个典型的几何非线性问题,因而在数值分析中单索的刚度方程显得尤为重要。由于许多文献不常见的单索刚度方程在推导时忽略了索单元元弦向倾的影响,用来进行结构计算尚存在一定的误差。本文因此考虑了影响单元刚度的弦倾角等因素,推导了一般情况下小垂度索的显式表达刚度方程,并运用该刚度方程进行结构数值分析,与采用近似刚度方程的分析结果进行了比较,给出了近似刚度方程与本文     

Dramatically stiffer elastic composite materials due to a negative stiffness phase?

Composite materials of extremely high stiffness can be produced by employing one phase of negative stiffness. Negative stiffness entails a reversal of the usual codirectional relationship between force and displacement in deformed objects. Negative stiffness structures and materials are possible, but unstable by themselves. We argue here that composites made with a small volume fraction of negative stiffness inclusions can be stable and can have overall stiffness far higher than that of either constituent. This high composite stiffness is demonstrated via several exact solutions within linearized and also fully nonlinear elasticity, and via the overall modulus tensor estimate of a variational principle valid in this case. We provide an initial discussion of stability, and adduce experimental results which show extreme composite behavior in selected viscoelastic systems under sub-resonant sinusoidal load. Viscoelasticity is known to expand the space of stability in some cases. We have not yet proved that purely elastic composite materials of the types proposed and analyzed in this paper will be stable under static load. The concept of negative stiffness inclusions is buttressed by recent experimental studies illustrating related phenomena within the elasticity and viscoelasticity contexts.     

Effect of formulation of alginate beads on their mechanical behavior and stiffness

The aim of this work was to determine the effect of formulation of alginate beads on their mechani-cal behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusion-dripping method. Single wet beads were compressed at a speed of 40 mm/min,and their elastic limits were investigated,and the corresponding force versus displacement data were obtained. The Young's moduli of the...     

Transverse Stiffness of a Sinusoidally Corrugated Plate∗

Abstract

An analytical model for the initial transverse stiffness of a sinusoidally corrugated plate is derived, incorporating deformations due to extension, shear, and bending. A nondimensional plot is developed for determining transverse stiffness based on thickness and corrugation for a range of plate geometries. This model shows that for most corrugated plates the transverse stiffness is dramatically decreased from that of an uncomigated plate of the same thickness. For thin plates, a simple approximate polynomial expression for initial transverse stiffness is obtained. For thick plates with a small degree of corrugation, transverse stiffness is not negligible relative to longitudinal stiffness. The exact model is verified using a linear-elastic two-dimensional finite element model.     

偏心迷宫密封动静特性研究

建立了不同偏心状态下迷宫密封三维数值分析模型，应用基于微元理论的密封动力特性系数识别方法计算密封静态和动态特性. 结果表明:转子偏心会降低密封抑制流体泄漏的效果；密封腔内周向压力高点随偏心率增大逐渐偏离最小间隙处. 低偏心率(≤ 0.5)下，静态直接刚度K与静态交叉刚度k变化较小，高偏心率(> 0.5)下K和k的绝对值减小. 随着偏心率的增大，密封小间隙侧流动黏性效应增强是产生负静态直接刚度的主要原因. 密封偏心涡动时，低偏心率(< 0.6)下刚度和阻尼系数变化较小，随偏心率和涡动频率的升高直接刚度逐渐变为负值；随偏心率的增大，交叉刚度在正交两个方向上大小不再相等，有效阻尼降低，高偏心率(≥ 0.6)下有效阻尼受偏心率影响更显著.      

一种考虑初始垂度影响的非线性索单元

本文首先运用Mathematic的符号运算功能，通过解偏微分方程给出了不等高单索的显式解析解，然后把该解析解应用于索微元的应变计算中，在此基础上用虚功原理推导了考虑初始垂度影响的两节点非线性索单元，并给出了索单元的单刚矩阵的具体形式，通过与两节点直线索单元的单铡矩阵的形式的比较，明确了该曲线非线性索单元的修正项，并给出了垂度影响因子的变化曲线。比较直观的给出了垂度对索单元刚度各项的影响程度。该非线性索单元既有多节点索单元精度高的特点，又有节点少，刚度元素较易求解以及有限元列式简洁等特点。本文通过两个数值算例表明，本文的非线性索单元是正确的，也表明了所编制的非线性计算程序是正确和可靠的。     

颗粒增强复合材料的屈服极限

基于渐近均匀化方法,导出了颗粒增强复合材料的屈服准则,给出了初始屈服应力的解析表达式。因为颗粒增强体的弹性模量远比弹塑性基体的弹性模量高,这个模量差在增强体和基体中产生了装配刚度。解局部问题可以得到该装配刚度。从屈服应力的表达式可以看出,增强体和基体两者的平均装配刚度和剪切模量之比决定了屈服应力的提高程度。给出了两个数值算例。采用菱形十二面体单胞求解了局部问题。取单胞形状为菱形十二面体的优点是增强体的体积比可以高达74%。     

Design,Manufacture, and Quasi-Static Testing of Metallic Negative Stiffness Structures within a Polymer Matrix

A composite material system comprised of a monostable negative stiffness (NS) structure within a polymer matrix was designed, fabricated, and experimentally evaluated. The monostable negative stiffness (NS) structure was designed using a combination of analytical and numerical models and manufactured in stainless steel. The NS structure was arranged in parallel with different polymer matrices to experimentally evaluate the effects of the matrix properties on the overall stiffness and energy dissipation of the composite NS-matrix system when loaded in uniaxial compression. A strong influence of the matrix properties on the stiffness and energy absorption capacity of the composite system was observed. Unlike conventional composites for which there is a natural tradeoff between stiffness and energy absorption capacity, the composite NS-matrix system enhanced stiffness while simultaneously improving energy absorption relative to a neat matrix, but only when the stiffness of the matrix was carefully matched to the stiffness of the NS structure.     

似叠罗汉槽干气密封的结构优选与性能研究

针对现有干气密封在高速条件下所存在的泄漏率大、气膜刚度不足等问题,在干气密封螺旋槽结构的基础上,基于叠加组合思想提出一种似叠罗汉槽端面密封结构.基于气体润滑理论,建立了似叠罗汉槽端面的几何模型和数学模型,采用有限差分法求解二维稳态雷诺方程,获得了密封端面压力分布.以气膜刚度最大作为优化目标,对比分析了不同结构型式的优选叠加组合槽干气密封与普通螺旋槽干气密封的密封性能参数,数值分析了周向槽宽比、径向槽宽比和槽深比等结构参数对似叠罗汉槽干气密封性能的影响规律,获得了似叠罗汉槽主要结构参数的优选值范围.结果表明:在高速低压条件下,相较于普通螺旋槽干气密封,似叠罗汉槽干气密封在泄漏率基本不变的同时能显著提升气膜刚度,综合密封性能显著提升,且转速越高,压力越小,这种性能优势越明显.     

A compliant mechanism with variable stiffness achieved by rotary actuators and shape-memory alloy

The aim of this article is to study the consequences of the active stiffening of a compliant mechanism on the workspace created by the deformation of its structure. In connection with recent soft robotics research integrating shape-memory alloys (SMAs), the variation in stiffness over time is here obtained by the thermal activation of a nickel–titanium SMA spring. The workspace is created by the deformation (in the strength of materials sense) controlled by two rotary actuators acting on a structure comprising two angled flexible beams. In addition to a natural variation in the elasticity modulus of the SMA component during its thermal activation, its shape reconfiguration adds a structural deformation modifying the workspace. The existence of a common area between the workspaces of the mechanism corresponding to the non-activated and activated modes of the SMA is preserved. Several compliance maps are determined from measurements using a laser tracker targeting a given position of the loaded structure. The impact of SMA pre-stretch on stiffness variability is compared to that of a change in Young’s modulus. Variations in the stiffness distributions between the two modes reveal interesting properties (stiffness sign inversion, anisotropy) for the future optimal design of compliant mechanisms with high versatility, associating the spatial positions of the effector with variable stiffness values.     

基于多层模拟方法的双层梁断裂有限元分析

本文提出一种用于含分层的双层梁线弹性断裂分析的有限元方法．将上下子梁均模拟为多个子层,采用只有平动位移自由度的新型梁单元,假设单元内的位移沿纵向和横向均线性变化,推导了该单元的单元刚度矩阵．将开裂部分和未开裂部分的子梁进行单元刚度矩阵组装,施加相应的等效结点力,得到整体平衡方程,并结合边界条件进行求解．为验证该方法的有效性和精度,开展非对称双悬臂梁(Asymmetric Double Cantilever Beam, ADCB)和单臂弯曲梁(Single Leg Bending, SLB)试样的断裂分析,利用虚拟裂纹闭合技术(Virtual Crack Closure Technique, VCCT)得到了试样的能量释放率及其分量,并将求得的结果与解析解和二维有限元解进行对比．计算结果表明,相对于传统双层模拟方法,该多层模拟方法能够精确、高效地计算各类梁试样的能量释放率及其分量,并且无需引入界面连续条件．     

基于组件法的穿心螺栓连接CFST柱节点初始刚度计算

本文基于EC3中的组件法，分析并建立了不同类型穿心螺栓连接CFST柱节点的力学模型，提出了EC3中未涉及的加强角钢的组件模型以及穿心螺栓连接刚度系数计算公式，推导了不同节点的初始刚度计算公式，试验结果和公式结果的对比表明，采用EC3给出的受拉螺栓刚度系数将大大低估穿心螺栓连接CFST柱节点的初始转动刚度，而采用本文所提出的考虑穿心螺栓预紧力的受拉螺栓刚度系数计算公式则与试验结果吻合较好．     

Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model

Summary In the paper, dynamic interaction between elastic high-speed-train car wheelset and track is studied using a discrete-continuous mechanical model. The model enables to investigate the influence of the parametric excitation from the track as well as static and dynamic unbalances of wheels and brake disks on the dynamic response of the wheelset running at various speeds on the track of various average vertical stiffness. From the results of numerical simulation it follows that particularly severe periodic resonances occur for the track of large stiffness, yielding high vertical dynamic contact forces between the wheels and rails. The maximum dynamic response has been obtained for parameters corresponding to the conditions at which the phenomenon of grumbling noise generation is usually observed in reality. Received 21 January 1997; accepted for publication 29 February 1997     

Mechanical Testing of Solid–Solid Interfaces at the Microscale

In order to determine the influence of internal interfaces on the material’s global mechanical behavior, the strength of single interfaces is of great interest. The experimental framework presented here enables quantitative measurements of the initiation and propagation of interfacial cracks on the microscale. Cantilever beams are fabricated by focused ion beam milling out of a bulk sample, with an interface of interest placed close to the fixed end of the cantilever. Additionally, a U-notch is fabricated at the location of the interface to serve as a stress concentrator for the initiation of the crack. The cantilevers are then mechanically deflected using a nanoindentation system for high resolution load-displacement measurements. In order to determine the onset and propagation of damage, the stiffness of the cantilevers is recorded by partial unloads during the test as well as by making use of a continuous stiffness technique. A finite element model is used to normalize the load and stiffness in order to establish the framework for comparisons between different interfaces.