Large deflection of constant curvature cantilever beam under follower load

This paper describes a method to analyze for the large deflections of curved prismatic cantilever beams with uniform curvature subjected to a follower load at the tip. The large deflection, the deflection dependent follower load and the initial curved geometry are the important features of the beam considered in this work. Shear force formulation proposed by Lee [Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int J Non-Linear Mech 2002;37(3)] is used for deriving the governing equations. Using this approach, the resulting two point boundary value problem (TPBVP) can be reduced to an initial value problem (IVP). Fourth order Runge-Kutta method along with one parameter reverse shooting method is applied to the numerical solution to the problem. A novel approach presented in this paper of integrating from the free end to the fixed end of the cantilever beam simply replaces the two parameter shooting with a single parameter shooting yielding several advantages. This solution technique is demonstrated for various types of follower tip loads on curved and straight cantilever beams and is validated with existing solutions in the literature.     

MEMS微悬臂梁构件变形规律的AFM试验研究

采用原子力显微镜测试了微悬臂梁构件的弯曲变形规律。发现构件的弹性支撑是试验数据和理论计算出现误差的主要原因。引入支撑扭转等效刚度对探针-样品等效刚度计算公式进行修正。修正结果对大有效长度的构件与实测结果吻合良好。对短有效长度微悬臂梁,其误差原因主要为支撑的影响以及测试探针的大变形,论文进一步提出研究的建议。     

Seizure of elastic material sliding through a rigid die

Mechanisms causing frictional locking due to the interaction between normal load and frictional force are described. The particular type of jamming produced when an elastic material is pushed between fixed rigid plates is discussed in detail. Experiments, using rubber as the elastic material and aluminum for the rigid plates, support a theoretical analysis of this effect.     

求解任意梁的普遍化方法

介绍了一种求解任意弹性梁的新方法。该方法利用奇异函数与拉普拉斯变换相结合的方法导出弹性梁弯曲变形的普遍表达式,并利用边界条件和约束处的变形协调条件确定约束反力和变形常数(左端面的挠度和转角),对由固定和活动铰链支座、径向和角度弹性支承以及固定端等支承形式任意组合而成的,具有任意支承沉降的,承受任意载荷(集中力、集中力偶和均布力)的,具有任意阶梯形状的静定或超静定弹性梁具有普遍的适用性。该方法可以方便、准确地确定任意梁在支座处的约束反力以及任一截面的挠度和转角等参数,可用于复杂梁的计算机分析、优化设计和计算机辅助设计。     

Axial stress waves in an elastic–perfectly-plastic bar

A bar, made from an elastic–perfectly plastic material, fixed at one end, suddenly has an axial load applied at the other end. After its sudden application, the load is held constant. If the load is less than half the yield load for the bar, and in the absence of damping, the load causes a stress wave to pass up and down the bar, all behaviour being elastic. At any point within the bar length, the stress varies, in a stepwise fashion, between zero, and twice the stress corresponding to the applied load. This is the classical elastic solution. However, if the load is greater than half the yield load, when the stress wave first hits the fixed end, yielding will occur, and a simple model is proposed in this paper to allow for yielding. The model incorporates two zones separated by the stress wave, as in the elastic solution, together with a third zone, concentrated, and adjacent to the fixed support, in which all plastic straining takes place. The paper describes and verifies the model, and presents the predictions that it gives for various levels of load.     

拉压式环形梁测力与称重传感器

在中、大容量的应变式测力与称重传感器中,应用较多的是圆柱、圆筒、板环、悬臂梁、双端固支梁和轮辐式等结构,这些结构对同时检测拉伸、压缩对称循环载荷,或拉向、压向灵敏度不对称无法满足计量要求,或需要增加辅助部件才能完成计量任务。本文介绍的多梁串联配置的环形梁结构,弥补了上述弹性元件的不足,它是把产生正应力或切应力的应变梁串联式的相互连接起来,并沿着封闭的圆柱表面进行配置,外载荷以交错排列的形式施加于应变梁上,使得拉向、压向灵敏度的一致性好,易于进行拉、压对称循环栽荷测量。文中重点介绍了矩形截面正应力和工字形截面切应力环形梁弹性元件的结构特点、受力分析和理论计算,并给出了结构设计与理论计算范例。     

多层悬臂梁静电作用下的弯曲及吸合电压分析

多层悬臂粱MEMS器件具有广泛的应用,其吸合电压对器件性能有重要影响。通过选取合适的挠度试函数,并考虑多层悬臂梁中的绝缘层对等效间隙高度的影响,运用能量法分析了多层悬臂梁在静电作用下的弯曲情况。推导出了梁在发生吸合现象时,其自由端归一化的挠度值和对应的吸合电压的解析表达式。用Coventor软件中的CoSolveEM模块验证所得公式,表明模型具有较高的精度。所得结论对静电执行结构设计具有一定的参考价值。     

弹性悬臂梁摩擦力测量机构的设计

摩擦力的测量始终是摩擦磨损试验机的重要组成部分之一。在自行开发的模拟缸套 /活塞环摩擦学性能的试验机中 ,采用弹性悬臂梁配合力传感器进行摩擦力的测量。推导了弹性悬臂梁测量摩擦力的公式 ,并用有限元软件分析了弹性悬臂梁的变形 ,确定了合适的截面形状。经试验验证 ,设计的摩擦试验机能够基本真实地反映缸套 /活塞环摩擦副的运动和摩擦学规律 ,具有较强的可信度。     

可靠性设计中的安全系数

材料在弹性极限以外工作时，应按极限荷载法计算结构的承载能力。本文介绍了一阶和二阶的弹性分析法、刚塑性分析法和弹塑性分析法，对悬臂梁的荷载-位移(p-δ)曲线作了定性分析，指出在可靠性设计中，安全系数的概念与传统的按容许应力法设计中的不同。     

The Damping Effect on Critical Values of Nonconservative Loads

A systematic study of the effect of energy dissipation on critical nonconservative loads within the stability calculation is carried out. Some classical nonconservative elastic stability problems are considered: the stability of a linear form of equilibrium of a double pendulum under the action of a follower force, the stability of a cantilever beam compressed by a follower force (Beck’s problem), and the stability of a flat panel in a supersonic gas flow. The dependences of critical loads on the damping parameters are built, and the conditions of mechanical system stabilization and destabilization are determined for the cases when damping coefficients vary over a wide range and for various ratios. The external and internal frictions (according to the Voigt model) are considered for the distributed parameter systems. Conclusions about the effect of various types of energy dissipation on the critical values of nonconservative load parameters and about the conditions of nonconservative system destabilization due to the energy dissipation are formulated.     

原子力显微镜测量双光子成型点的弹性模量

提出了一种飞秒激光双光子成型点弹性模量的测量及结果分析方法.借助于原子力显微镜,选用无针尖探针对成型点的力学性能进行了测试,建立了椭球-平面接触的弹性力学模型.考虑了成型点剩余部分形变对结果分析的影响,在标定微探针弹性系数和对粘附力进行分析的基础上,提取了力曲线中所包含的力学信息,推算出了成型点的弹性模量,得到了成型点的弹性模量低于宏观材料弹性模量的结论.     

基于分布式光纤传感技术的结构变形估计方法研究

悬臂板是广泛应用于工程实践的常见结构形式,在航空航天、轨道交通、土木工程等领域均有重要应用,其变形监测问题一直是此类领域重要的研究内容之一.本文将矩形弹性悬臂薄板纯弯曲的一般问题作为研究对象,讨论求解该问题的方法,建立应变与位移的联系,并在线弹性小变形理论框架下,得到结构横向位移的有限差分表达式;采用具有高密度应变测量...     

A New AFM Nanotribology Method Using a T-Shape Cantilever with an Off-Axis Tip for Friction Coefficient Measurement with Minimized Abbé Error

A new AFM (atomic force microscopy) nanotribology method using a T-shape cantilever with an off-axis tip (Nat Nanotechnol 2:507–514, 2007) has been developed for measuring friction coefficient at nanometer scale. In this method, signals due to both bending and twisting of the T-shape AFM cantilever are detected simultaneously. For a T-shape AFM cantilever, the bending is caused by the normal load and the twisting is caused by both the normal and the lateral loads. The twisting generated by the normal load is calibrated in advance. Consequently, the twisting only due to the lateral load can be decoupled from the total lateral voltage signal. And the friction coefficient can be finally determined based on a conversion relationship between the normal and lateral voltage signals of the AFM photodetector. A practical procedure for minimizing Abbé error in friction coefficient measurement has also been introduced. The proposed new method is simple and accurate, and requires the least operation for friction coefficient measurement at nanometer scale.     

基于Mathcad求弹性梁弯曲问题的数值解

提出一种求解受复杂载荷作用的弹性梁弯曲问题数值解的新方法。该方法利用奇异函数表示弹性梁的弯曲内力和弯曲变形方程,与梁的边界条件和连续条件联立,应用数学软件Mathcad中相应的求解块和绘图工具,可以快速获得弹性梁的支座约束力、任意截面的剪力和弯矩、挠度和转角等参数以及相应的曲线图。该方法无需编程,既适用于静定或超静定梁,也适用于等截面或变截面梁,为梁的强度和刚度校核以及优化设计等提供了新途径。     

Instability of cantilever beams with non-linear elements: Butterfly catastrophe

The instability of an elastic cantilever beam combined with a non-linear element, which is subjected to axial and normal concentrated and distributed loads was studied.It was shown that the total potential energy u of the system was equivalent to a universal unfolding of a butterfly catastrophe and, therefore, its approximate locus of failure may be studied by means of the bifurcation set of this type of elementary catastrophe. The problem is a generalization of the case of cantilever beams connected with elastic elements, whose solution is in agreement with the general results. established in the paper.     

悬臂梁单晶压电发电机的实验研究

建立了悬臂梁单晶压电振子的发电测试系统,对压电晶体与磷青铜基板材料的厚度比对单晶压电振子输出电压的影响进行了有限元分析,得出了压电晶体与磷青铜基板材料的最佳厚度比并进行了实验验证,同时对具有最佳厚度比的单晶压电振子进行了压电发电能力测试。研究结果表明,当压电晶体与磷青铜金属基板的最佳厚度比为0.5,单晶压电振子的输出电压最大,有限元分析与实验结果基本吻合。单晶压电振子输出电压随着负载的增大而随之增大,而输出功率并不随负载的增大而增大。压电振子存在一个最佳负载,当负载与压电振子内阻匹配时,此时的输出功率最大,能量转化效率最高。单晶压电振子在负载为50 时,输出电压最大可达5.4 ;当负载电阻为 时,负载与压电振子内阻匹配较好,输出功率达到最大为1.18 ,产生的能量能满足网络传感器等低耗能电子产品的供能需求。     

An investigation of the collapse of thin-walled rectangular beams in biaxial bending

Two different thin-walled closed sections, one square and one rectangular were tested in biaxial bending using displacement controlled cantilever bending tests.Two different constraint conditions were used, the first kept the deflection axis fixed and left the direction of the load axis free. The second kept the load axis direction fixed and allowed the beam to deflect freely.Each configuration was repeated at 15° axis intervals and was performed twice to assure repeatability. This gave a total of 42 cantilever bending tests.The results are used to compare the beam behaviour in the transition and collapse stages between the two constraint conditions. The behaviour is also contrasted with thick-walled theory predictions, since this is the only currently available reference.     

取料机行走轨道存在的问题及解决方法

悬臂取料机轨道在运行中,发现轨道下面的调整垫片有被挤出的现象。基于提高取料机行走轨道的安装精度和使用寿命,设计了一种新型的行走轨道固定装置,不会使得固定支座轻易地移位,同时提高了固定支座的安装精度和使用寿命。     

3D polymer nanostructures fabrication by AFM tip-based single scanning with a harder cantilever

A cantilever with a larger elastic spring constant (the applied force is at the micro Newton scale) is employed to perform a single scanning test on the polycarbonate (PC) surface in contact mode of Atomic Force Microscope (AFM). This method is used as a novel nanomachining technique for the formation of three-dimensional (3D) polymer bundle structures similar to conventional sinusoidal structures. Effects of machining parameters such as the feed and the normal load on bundles formation, the period and the height of bundle structures are analyzed. Furthermore, influence of the tip geometry on microstructures formation is also studied.     

宽频压电振动能量采集器的分布参数模型与实验

为解决无线传感网络节点自供电问题,提出了一种带有弹性支撑与放大的宽频压电振动能量采集器。利用Hamilton原理和Raleigh-Ritz方法,并考虑悬臂梁末端质量块的影响,建立了压电能量采集器的分布参数机电耦合模型;数值分析了能量采集器质量比、刚度比和阻尼比等参数对系统振动特性、输出特性的影响;研制了实验原理样机,搭建了实验测试平台,验证了数学模型的正确性。研究结果表明,分布参数模型比集总参数模型具有更高的预测精度。