TiNi相变悬臂梁的横向冲击特性实验研究

利用改装的霍普金森压杆装置对TiNi形状记忆合金圆截面悬臂梁进行了横向冲击实验研究,并与45#钢悬臂梁的实验结果进行了对比,目的是探索相变对结构动态响应的影响。结果表明:在同样冲击条件下,TiNi悬臂梁的吸能效率优于钢悬臂梁;发现冲击过程中,TiNi试件根部内侧可能形成局部相变铰,使阻力曲线的斜率发生变化;卸载后相变铰消失,TiNi悬臂梁试件基本回复原状,钢试件则留下显著的残余变形。TiNi悬臂梁的冲击特性受热弹性马氏体相变和逆相变的支配,不同于传统的弹塑性机制。     

A node-based smoothed point interpolation method for dynamic analysis of rotating flexible beams

We proposed a mesh-free method, the called node-based smoothed point interpolation method (NS-PIM), for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection. This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations, but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange’s equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method (FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions.     

SELF-CORRECTED PID VIBRATION CONTROL BASED ON DUAL-FREEDOM DUAL-DRIVE INTELLIGENT CANTILEVER BEAM 1)

随着科技不断进步,智能结构的振动控制在航天航空、机械制造、车辆与船舶等领域得到了广泛应用。由于多输入多输出存在多样性和复杂性,严重威胁系统稳定性。为了解决这一问题,针对两输入单输出的双驱动智能悬臂梁系统提出一种自适应控制策略,首先基于压电线性本构方程,应用假设模态方法建立双驱动智能悬臂梁的力学模型,得到了基于闭环控制系统的状态方程,同时利用递推最小二乘法在线辨识系统参数设计比例积分微分(proportional--integral--derivative, PID)控制器实现自校正PID控制。通过数值仿真对比在有无PID 控制下两输入单输出双驱动智能悬臂梁系统的振动情况,分析自校正PID 控制的控制效果。通过实验验证自校正PID 控制对双输入单输出的双驱动智能悬臂梁系统的控制效果;再设置两组不同的单输入单输出自校正PID控制实验作对比。结果表明：自校正PID 控制方法可以较为有效地抑制智能悬臂梁的自由振动,相比单输入单输出的两组,两输入单输出自校正PID控制的效果更为明显和有效。     

Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods

This study applies two analytical approaches, Laplace transform and normal mode methods, to investigate the dynamic transient response of a cantilever Timoshenko beam subjected to impact forces. Explicit solutions for the normal mode method and the Laplace transform method are presented. The Durbin method is used to perform the Laplace inverse transformation, and numerical results based on these two approaches are compared. The comparison indicates that the normal mode method is more efficient than the Laplace transform method in the transient response analysis of a cantilever Timoshenko beam, whereas the Laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi-span Timoshenko beam. Furthermore, a three-dimensional finite element cantilever beam model is implemented. The results are compared with the transient responses for displacement, normal stress, shear stress, and the resonant frequencies of a Timoshenko beam and Bernoulli–Euler beam theories. The transient displacement response for a cantilever beam can be appropriately evaluated using the Timoshenko beam theory if the slender ratio is greater than 10 or using the Bernoulli–Euler beam theory if the slender ratio is greater than 100. Moreover, the resonant frequency of a cantilever beam can be accurately determined by the Timoshenko beam theory if the slender ratio is greater than 100 or by the Bernoulli–Euler beam theory if the slender ratio is greater than 400.     

Optical Sensing Limits in Contact and Bending Mode Atomic Force Microscopy

Interferometry and optical deflection offers the best force sensing accuracy using standard cantilever probes in atomic force microscopy. Here, we examine the mechanics of cantilever deformation in the bending and contact mode and the optical sensing principles involved. Under typical conditions, the optical deflection method was found to require displacement measurements that were a thousand times less accurate in order to sense the same amount of force as compared with interferometry used in the regular mode. It also allowed better positioning tolerance for the probe beam in order to retain a high level of accuracy in force sensing. These and other attendant findings serve to provide a clearer outlook for the development of improved accuracy sensors in atomic force microscopy in the contact and bending mode.     

均布荷载作用下悬臂磁电弹性梁的解析解

对磁电弹性平面问题进行了研究，给出了用拟调和位移函数表达的通解，进而以试凑法按平面应力问题推导出了均布荷载作用下悬臂磁电弹性粱的解析解，所得解有易于理解、便于校对、形式统一简洁的特点。本文还将计算结果与压电材料和弹性材料相应结果进行了分析、比较，为验证各种数值计算方法提供了参考依据。     

APPROXIMATE SOLUTIONS FOR TRANSIENT RESPONSE OF CONSTRAINED DAMPING LAMINATED CANTILEVER PLATE

The series composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates, and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work.By solving Lagrange＇s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then the transient response of constrained damping of laminated cantilever plate is obtained, when the concentrated force is withdrawn suddenly.The theoretical calculations are compared with the experimental data, the results show：both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results.Also, the response time of steel cantilever plate, unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison, which shows that the constrained damping structure can effectively suppress the vibration.     

基于三阶剪切变形理论的悬臂输流管道自由振动

采用三阶剪切变形理论,结合有限元法研究了悬臂输流管道的自由振动问题．利用虚功原理建立了输流管系统的有限元方程,同时将悬臂端弹性支承以势能的形式引入到系统方程中,求解了系统前三阶的复频率．分别探讨了流体速度和弹簧刚度对系统复频率实部和虚部的影响,重点分析了弹簧刚度与前三阶固有频率间的关系．在弹性支承刚度为零的特例下,对比了本文结果与Timoshenko梁理论的结果,证明了本文方法的可靠性．研究发现系统固有频率的实部恒为负值,表明一端带有弹性支承的约束形式有利于提高悬臂输流管道自由振动的稳定性;流体的流动对管道振动起到了阻尼作用,在流动速度足够大的情况下,各阶振动固有频率均趋于零;当弹簧刚度为无穷大,且流体速度足够大时,输流管道将发生失稳．     

On new symplectic superposition method for exact bending solutions of rectangular cantilever thin plates

A novel superposition method based on the symplectic geometry approach is presented for exact bending analysis of rectangular cantilever thin plates. The basic equations for rectangular thin plate are first transferred into Hamilton canonical equations. By the symplectic geometry method, the analytic solutions to some problems for plates with slidingly supported edges are derived. Then the exact bending solutions of rectangular cantilever thin plates are obtained using the method of superposition. The symplectic superposition method developed in this paper is completely rational compared with the conventional analytical ones because the predetermination of deflection functions, which is indispensable in existing methods, is dispelled.     

深海采矿系统中悬臂式立管涡激振动分析

不同于传统的海洋立管, 深海采矿系统中的垂直提升管道可以被视为一个底部无约束的柔性悬臂式立管, 工作过程中同样面临涡激振动和柔性变形问题. 本文采用一种无网格离散涡方法和有限元耦合的准三维时域求解数值模型, 系统性地研究了不同流速下悬臂式立管的涡激振动问题. 结果表明: 悬臂式立管的横向振动模态阶数随折合速度增加而增大, 在一定折合速度范围内主导振动模态保持不变; 当主导模态转变时, 对应的横向振幅会发生突降, 但是当新的高阶模态被激发后, 立管振幅随来流速度增加而再次逐渐增大; 在相同的振动模态下, 立管底部位移均方根值随折合速度线性增加, 主导振动频率在模态转变时会出现跳跃现象; 特别地, 本文讨论了三阶主导模态下悬臂式立管的振动响应, 无约束的立管底部呈现出较大的振动能量, 且振幅的驻波特征随折合速度增加而逐渐增强; 本文比较了两端铰支立管与悬臂式立管的涡激振动响应特征, 两者在振幅和主导振动频率两方面均表现出了相同的变化趋势.      

Dynamics of a partially confined,discharging, cantilever pipe with reverse external flow

The potential for fluid-elastic instability of hanging cantilevered pipes subjected to simultaneous internal and external axial flows is investigated. Such systems may lose stability by amplified oscillations (flutter) or buckling (static divergence). The system of interest is a flexible tubular cantilever hanging concentrically within a rigid outer tube of larger diameter. Flow inside the cantilever is directed from the clamped end to the free end. Upon exiting the cantilever, the fluid flows in the opposite direction in the annular region between the outer tube and the cantilever. The rigid outer tube is of variable length and it can cover part of the length of the cantilever. This system has applications in brine production and salt-cavern hydrocarbon storage. A linear model is derived based on the work of Paidoussis, Luu and Prabhakar; the presence of the shorter outer rigid tube is taken into account in a simplified way. Series solutions are obtained using a Galerkin method with Euler–Bernoulli beam eigenfunctions as comparison functions. Experimental results are presented and compared with the theoretical model. Additional computations are performed to quantify the effect of confinement (i.e. the narrowness of the annular region) on the cantilever stability, as well as the effect of confined-flow length, for both the short laboratory-sized system and long brine-string-like systems. An increase in these parameters gives rise to flutter for short systems, or a succession of flutter and divergence for long systems. In addition, the effect of the system length is investigated. Increasing length results in asymptotic behaviour, with both the critical flow-velocity and associated frequency reaching limiting values. Sufficiently long systems lose stability by divergence rather than flutter.     

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Plastic size effects in single crystals are investi-gated by using finite strain and small strain discrete dislo-cation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip sys-tems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete disloca-tion plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. How-ever, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bend-ing stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.     

Flexural vibrations of double tapered atomic force microscope cantilevers studied by considering the contact position and using the differential quadrature method

The resonant frequency of flexural vibrations for a double tapered atomic force microscope (AFM) cantilever has been investigated by using the Timoshenko beam theory. In this paper, the effects of various parameters on the dimensionless frequency of vibrations of the AFM cantilever have been studied. The differential quadrature method (DQM) is employed to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when the Timoshenko beam parameter or the cantilever thickness increases, and high-order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the higher-order modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. Furthermore, with increasing the breadth taper ratio, the frequency increases. The DQM results are compared with the exact solution for a rectangular AFM cantilever.     

Mechanical Fatigue Measurement via a Vibrating Cantilever Beam for Self-Supported Thin Solid Films

In this paper, we develop a novel experimental apparatus, referred to as the resonant frequency device, and establish methodology to measure the fatigue properties of thin solid films. Arranging thin-film strips of our specimens into the mechanical setting of a cantilever beam and using state-of-the-art piezo actuators to generate oscillation at the clamp of the cantilever, we create a system suitable for studying the material properties of the cantilever, such as Young's modulus, fatigue and possibly, loss tangent. Deformation of the cantilever is our controlled variable in the present study, and measured with fiber-optic probes pointed at the specimen and at the piezo driver. Stress is calculated from relative deformation of the cantilever specimen with respect to the piezo actuator via a photograph of the cantilever under vibration with a curve fitting method. A LabView computer program is developed for the fatigue tests to accurately count number of cycles applied on the specimens, and a feedback mechanism is adopted to maintain displacement during the tests. Here, we present our experimental setup, procedure and theoretical models for material-property extraction. For small displacement, the two-dimensional Euler–Bernoulli beam theory is adopted. With large displacement, the system behaves as the Duffing oscillator due to geometrical nonlinearity. In addition, some experimental observations of the piezo actuators and fiber optics are reported. The method is applied to evaluate the fatigue properties of nanolayered copper-niobium composites and significant increase in the fatigue endurance limit compared to the constituent materials in the bulk form is noted.     

Suppression of multiple modal resonances of a cantilever beam by an impact damper

Impact dampers are usually used to suppress single mode resonance. The goal of this paper is to clarify the difference when the impact damper suppresses the resonances of different modes. A cantilever beam equipped with the impact damper is modeled. The elastic contact of the ball and the cantilever beam is described by using the Hertz contact model. The viscous damper between the ball and the cantilever beam is modeled to consume the vibrational energy of the cantilever beam. A piecewise ordina...     

端部受斜撞击作用悬臂梁的弹塑性动力响应模式

基于大变形动力控制方程并利用有限差分离散分析,研究了斜撞击作用下弹塑性悬臂梁的动力响应．通过对屈服函数以及弯矩、轴力在动力响应过程中分布规律的分析,阐明了斜撞击下恳臂梁的弹塑性动力响应模式和斜撞击的轴向分量对变形机制的影响．研究表明,弹塑性响应过程可划分为四个阶段,对应的变形模式为：“压缩塑性区扩展”模式,“广义移行塑性铰”和“压缩塑性区收缩”混合模式,“驻定塑性铰”模式,“弹性自由振动”模式．与刚塑性分析所假定的两相变形模式比较,弹塑性应响分析证实了响应早期的瞬态轴向压缩模式和梁根部“驻定塑性铰”模式的存在性,肯定了刚塑性分析所假定变形模式的主要特征．斜撞击的轴向分量在撞击发生的瞬时主导了梁的变形,使梁呈现同承受横向冲击明显小同的变形规律．随着响应的深入,轴向分量迅速衰减,其对截面屈服的贡献非常微弱,由横向分量引起的弯曲挠动在大部分时间内主导和控制梁的变形．数值计算结果表明,斜撞击载荷的质量、撞击速度和角度是影响梁动力响应的重要因素．     

Non-linear bending of beams with uniformly distributed loads

The non-linear bending of both cantilever and simply supported beams subjected to a uniformly distributed load has been studied. The exact solutions for the slopes have been obtained and the solution for the maximum deflection and the horizontal projection of the beam length for the cantilever case are compared with a known approximate solution.     

Approximate analytical solutions and experimental analysis for transient response of constrained damping cantilever beam

Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived using Lagrange＇s equation. Dynamic response of the constrained damping cantilever beam is obtained according to the principle of virtual work, when the concentrated force is suddenly unloaded. Frequencies and transient response of a series of constrained damping cantilever beams are calculated and tested. Influence of parameters of the damping layer on the response time is analyzed. Analyitcal and experimental approaches are used for verification. The results show that the method is reliable.     

Bending of uniformly cantilever rectangular plates

An exact solution is given for the bending of uniformly loaded rectangular cantilever plates by using the idea of generalized simply supported edge together with the method of superposition. As illustrative examples, a square plate and a rectangular plate with the ratio of the clamped edge to the neighbouring free edge equal to two are solved numerically. The results are compared with those obtained from approximate methods to confirm the validity of the method presented.