Three-Dimensional Lumped Mass/Lumped Spring Modeling and Nonlinear Behavior of a Levitated Droplet

The nonlinear dynamics time evolution of an electromagnetically levitated (EML) droplet is considered in this study. The droplet is modeled as a three dimensional system with lumped masses and elastic springs. A new expression for the spring elastic constants in a global stiffness matrix has been derived, and equations of motion presented. The chaotic behavior of the system is analyzed for different coil configurations. The stability of the motion is studied using the Lyapunov exponents. Computations were performed for droplets of aluminum and copper.     

Complete Characterization and Synthesis of the Response Function of Elastodynamic Networks

The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function W(ω), depending on the frequency ω, mapping the displacements of some accessible or terminal nodes to the net forces at the terminals. We give necessary and sufficient conditions for a given function W(ω) to be the response function of an elastodynamic network, assuming there is no damping. In particular we construct an elastodynamic network that can mimic a suitable response in the frequency or time domain. Our characterization is valid for networks in three dimensions and also for planar networks, which are networks where all the elements, displacements and forces are in a plane. The network we design can fit within an arbitrarily small neighborhood of the convex hull of the terminal nodes, provided the springs and masses occupy an arbitrarily small volume. Additionally, we prove stability of the network response to small changes in the spring constants and/or addition of springs with small spring constants.     

张拉整体结构的动力学等效建模与实验验证

为了实现张拉整体结构高效动力学计算, 并考虑其大范围运动中柔性杆局部动态屈曲, 提出了一种受压细长杆动力学降阶模型, 采用五节点弹/扭簧集中质量离散模型等效连续杆的静力学和动力学特性. 首先, 通过静力学等效分析推导了弹簧拉压刚度和扭簧弯曲刚度表达式, 可准确预测杆件受压屈曲和近似预测其后屈曲行为. 第二, 通过动能等效分析推导了集中质量表达式, 可准确预测杆在线速度场下的运动. 第三, 通过弯曲振动固有模态等效分析确定弯曲刚度和节点质量的分布参数, 合适的分布参数取值组合可将降阶模型前两阶固有频率相对误差均降低至1%以内. 第四, 在全局坐标系下建立张拉整体结构瞬态动力学方程, 并利用静力凝聚法实现方程高效迭代求解. 最后, 分别对球形张拉整体结构准静态压缩、模态分析和碰撞动力学进行仿真和实验对比分析, 证明了提出的动力学降阶模型可有效预测张拉整体结构的静力学行为、固有振动特性及瞬态动力学响应, 并分析了结构参数变化对其力学特性的影响规律. 本文提出的动力学等效建模与计算方法, 可望用于软着陆行星探测器、大型可展开空间结构及点阵材料等复杂张拉整体系统的动力学分析与控制.      

汽车多自由度悬架的非线性振动特性

以研究主、副簧组成的悬架系统出发,建立了分段线性非线性悬架系统的动力学模型,运用KB方法求出了此类系统运动的解析解。其幅频响应曲线表明,当缓冲簧间隙适当时,系统非线性特征十分明显,相当于一种缓冲器的趋硬弹簧的作用。同时讨论了非线性弹簧刚度、阻尼系数、地面不平度对共振曲线的影响,分析了轮胎的等效刚度、阻尼系数和质量对系统振动的影响,得到了此类主、副簧组成的悬架结构的运动形式及特征。由理论分析和数值计算画出的幅频特性曲线基本吻合,可为汽车悬架系统的分段线性非线性振动的参数识别、稳定区域的分析研究和优化设计提供理论依据。     

Free vibration characteristics of a rectangular plate carrying multiple three-degree-of-freedom spring–mass systems using equivalent mass method

This paper aims at presenting a technique to replace each three-degree-of-freedom (3-dof) spring–mass system (or substructure) by a set of equivalent masses so that the dynamic characteristics of a rectangular plate (or main structure) carrying any number of elastically mounted lumped masses may be obtained from the same plate carrying the same sets of rigidly attached equivalent masses. Because the three degrees-of-freedom (dof’s) of the substructure are embedded in its equivalent masses, the total dof of the entire vibrating system (i.e., the main structure together with all the substructures) is independent on the total number of the substructures attached to the main structure in the presented equivalent mass method (EMM). However, in the conventional finite element method (FEM), the total dof of the entire vibrating system increases by three when one more substructure is attached to the main structure. Compared with FEM, the merits of EMM are double: Firstly, since the total dof of the entire vibrating system in EMM is smaller than that in FEM, some computer storage memory may be saved. Secondly, since the dof’s for all the substructures are eliminated, the associated natural frequencies and mode shapes are excluded from those of the main structure and some effort required for the analysis of computer-output data may also be saved. It is evident that the last merits of EMM will be more predominant if the total number of substructures attached to the main structure is large.     

干气密封推环用弹簧蓄能密封圈工作特性研究

干气密封推环用密封圈关系到补偿环的浮动性和追随性. 通过建立弹簧蓄能密封圈的二维轴对称等效模型,对有、无凸台两种结构的弹簧蓄能密封圈,模拟了不同工况下的密封特性及摩擦特性. 研究表明:两种结构弹簧蓄能密封圈的峰值接触压力随介质压力、预压缩率的增加而增大,都具有良好的自紧密封特性. 推环微动时密封圈的摩擦力较大,不能忽略. 推环轴向微动时,有凸台结构与无台结构的弹簧蓄能密封圈表现出不同摩擦行为;无台弹簧蓄能密封圈,在推环沿±Z方向微动时,摩擦特性曲线相似. 而有凸台的弹簧蓄能密封圈,当推环沿Z方向微动时,分离距离更大;推环沿-Z方向微动时,具有更小的最大静摩擦力,且滑动摩擦力与最大静摩擦力差值较小,滑动平稳,有利于补偿环恢复到设计工作位置.      

Sliding friction in the presence of ultrasonic oscillations: superposition of longitudinal oscillations

Summary  It was often observed that friction forces can be reduced significantly if ultrasonic oscillations are superposed to the macroscopic sliding velocity. This phenomenon can be used to improve machining processes by addition of ultrasonic vibration to tools or workpieces, and forms the basis for many processes of ultrasonic machining. On the other hand, ultrasonic vibrations can be used to generate motion. The thrusting force of ultrasonic motors is provided to the rotor through friction. In the present paper, a simple theoretical model for friction in the presence of ultrasonic oscillations is derived theoretically and validated experimentally. The model is capable of predicting the reduction of the macroscopic friction force as a function of the ultrasonic vibration frequency and amplitude and the macroscopic sliding velocity. Received 22 November 2000; accepted for publication 6 February 2001     

超低频振动能量收集器中夹片弹簧结构的建模与验证

针对一类基于夹片弹簧的压电振动能量收集器,利用材料力学莫尔积分理论建立了振荡俘能结构中夹片弹簧的等效刚度模型,通过万能拉伸试验机验证了模型精度。在此基础上,讨论了夹片弹簧刚度线性简化的两种途径：拉伸曲线线性拟合和固有频率修正。研究结果表明,从夹片弹簧拉伸曲线上看,将其等效成线性弹簧具有一定的合理性;而在实际振动能量收集器结构中,若振动加速度相对较小,通过固有频率修正法对夹片弹簧刚度进行线性简化,其幅频响应特性与非线性模型的特性相近。该研究成果为压电振动能量收集器的动力学和机电耦合模型简化提供了理论支撑。     

Consideration of the masses of helical springs in forced vibrations of damped combined systems

The common point about many systems modeled as Bernoulli-Euler beams with attachments is that the own masses of the helical springs are neglected. Some researchers accounted for the masses of the springs during free vibrations of those systems. Further to these studies, the present study deals with the investigation of the effect of not taking into account the masses of the helical springs in damped combined systems during their forced vibrations. It is shown that the spring mass effect may be important in regions near to the resonance frequencies. Further, this effect influences the phase angles more than the amplitudes.     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。     

Using spring repulsions to model entanglement interactions in Brownian dynamics simulations of bead–spring chains

We develop a bead–spring Brownian dynamics model for simulating the topological interactions between polymers and thin obstacles and apply this method to electrophoretically translating DNA strands interacting with an immovable post. The use of a bead–spring method allows for the simulation of entanglement interactions of polymer chains too long to be simulated using bead–rod or pearl necklace models. Using stiff “FENE-Fraenkel” springs, we are able to model short chains as well. Our new method determines the shortest distance between a spring and the post, calculates a repulsive force inversely related to this distance using an exponential potential, and corrects for the rare situation when a spring passes beyond the post despite the repulsive interaction. As an example problem, we consider single-chain collisions with a single post in weak electric fields. We explore a wide range of chain lengths (25–1,515 Kuhn steps), and we find that the average delay produced by the collision is a function of both the chain length and the Peclet number. Chains of all lengths reach the same upper limit at high Peclet number, but they follow separate curves with similar slopes at lower Peclet number. Our results are consistent with published results for a 25-Kuhn-step chain at Peclet number Pe = 10. Our new method is a general one that allows us to compute the effects of entanglements in systems with rare entanglements and long chains that cannot be simulated by other more microscopic methods.     

Considerations on the spring analogy

This paper presents an investigation on the spring analogy. The spring analogy serves for deformation in a moving boundary problem. First, two different kinds of springs are discussed: the vertex springs and the segment springs. The vertex spring analogy is originally used for smoothing a mesh after mesh generation or refinement. The segment spring analogy is used for deformation of the mesh in a moving boundary problem. The difference between the two methods lies in the equilibrium length of the springs. By means of an analogy to molecular theory, the two theories are generalized into a single theory that covers both. The usual choice of the stiffness of the spring is clarified by the mathematical analysis of a representative one‐dimensional configuration. The analysis shows that node collision is prevented when the stiffness is chosen as the inverse of the segment length. The observed similarity between elliptic grid generation and the spring analogy is also investigated. This investigation shows that both methods update the grid point position by a weighted average of the surrounding points in an iterative manner. The weighting functions enforce regularity of the mesh. Based on these considerations, several improvements on the spring analogy are developed. The principle of Saint Venant is circumvented by a boundary correction. The prevention of inversion of triangular elements is improved by semi‐torsional springs. The numerical results show the superiority of the segment spring analogy over the vertex one for a small rotation of an NACA0012 mesh. The boundary correction allows for large deformation of the mesh, where the standard spring analogy fails. The final test is performed on a Navier–Stokes mesh. This mesh contains high aspect ratio mesh cells near the boundary. Large deformation of this mesh shows that the semi‐torsional spring improvement is imperative to retain the validity of this mesh. Copyright © 2000 John Wiley & Sons, Ltd.     

Model of the UIC link suspension for freight wagons

Summary The paper presents a model of the UIC link suspension for freight wagons with emphasis on its longitudinal and lateral characteristics, which influence the lateral dynamics of the vehicle. The functioning of the suspension in the horizontal plane is realised by a number of technical (pivoted) pendulums composing linkages. The main feature of the joints of linkages is internal rolling/sliding in the presence of dry friction. The dissipation of energy by dry friction in the joints is the only source of damping, which influences the lateral dynamics of the vehicle. After detailed modelling of the technical pendulum, phenomenological models of the suspension are built, which reproduce the characteristics of the suspension using simple elements. A three-parameter model with one dry-friction slider and two linear springs reproduces the lateral characteristic of the suspension. A nine-parameter model with four dry-friction sliders and five springs reproduces the longitudinal characteristic. The models, using a method of non-smooth mechanics, may be directly implemented to vehicle/track dynamic simulations.Professor Hans True of TU Denmark for stressing the importance of the problem of the UIC suspension modelling for successful upgrading of freight wagons.     

Modeling and dynamics analysis of helical spring under compression using a curved beam element with consideration on contact between its coils

Helical springs are indispensable elements in mechanical engineering. This paper investigates helical springs subjected to axial loads under different dynamic conditions. The mechanical system, composed of a helical spring and two blocks, is considered and analyzed. Multibody system dynamics theory is applied to model the system, where the spring is modeled by Euler–Bernoulli curved beam elements based on an absolute nodal coordinate formulation. Compared with previous studies, contact between the coils of spring is considered here. A three-dimensional beam-to-beam contact model is presented to describe the interaction between the spring coils. Numerical analysis provides details such as spring stiffness, static and dynamic stress for helical spring under compression. All these results are available in design of helical springs.     

Analysis of the applicability of a modified Kol'skii's method for dynamic tests of soils in a deformable casing

Results of an experimental and theoretical analysis of Kol'skii's method for dynamic tests of soft soils in an elastic casing are presented. The model proposed by S. S. Grigoryan for a plastically compressible medium with parameters determined in shock-wave experiments was used as the model of a soft soil. The high-rate deformation of the soil was simulated using a modified “Dunamics-2” program package. The numerical calculations performed showed that the compliance of the casing and friction practically do not influence the measured characteristics of the soil and the basic premises of Kol'skii's method are adequate for soft soil too. Institute of Mechanics, Nizhinii Novgorod State University, Nizhnii Novgorod 603600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 155–162, May–June, 2000.     

Investigation of the heat transfer and Reynolds analogy in a turbulent boundary layer at a high freestream turbulence level

The results of a systematic experimental study of the flow turbulence level effect on the heat transfer and Reynolds analogy coefficients over a wide range of the relevant parameters (the turbulence intensity and scale and the Reynolds number) are presented. The notion of the equivalent flow turbulence, which unifies the above-mentioned parameters, is introduced. It is established that the skin friction and heat transfer coefficients increase with the equivalent turbulence, while the Reynolds analogy coefficient remains unchanged. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 61–71, January–February, 2000.     

Qualitative analysis of forced response of blisks with friction ring dampers

A damping strategy for blisks (integrally bladed disks) of turbomachinery involving a friction ring is investigated. These rings, located in grooves underside the wheel of the blisks, are held in contact by centrifugal loads and the energy is dissipated when relative motions between the ring and the disk occur. A representative lumped parameter model of the system is introduced and the steady-state nonlinear response is derived using a multi-harmonic balance method combined with an AFT procedure where the friction force is calculated in the time domain. Numerical simulations are presented for several damper characteristics and several excitation configurations. From these results, the performance of this damping strategy is discussed and some design guidelines are given.     

Synchronization of two coupled pendula in absence of escapement

A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is examined. The mechanical model consists of two coupled pendula both oscillating on a moving board attached to a spring. The final result performs selection among the peculiar parameters of the physical process (the length, the ratio of masses, the friction and damping coefficients, and the stiffness of the spring), providing a tendency to synchronization.     

Study on the static properties of spiral springs under static loading

Applied Mathematics and Mechanics - Spiral springs have a wide range of applications in various fields. As a result of the complexity of friction, few theoretical analyses of spring belts under...     

对称扭杆弹簧系统隔振性能研究2000-04-03收稿.

对扭杆弹簧隔振系统的研究表明,扭臂的质量对系统的性能有比较大的影响。虽然系统可获得长的共振周期,但由于扭臂的质量不为零,地基振动的加速度被直接耦合进系统,从而严重地降低了系统的隔振性能。