Hertz接触问题的解的唯一性条件

讨论了接触面为圆面的Ｈｅｒｔｚ接触问题。若压力分布是轴对称的，则该接触问题的解必是唯一的。且在上述条件下，该接触问题的积分方程可化为两个推广的Ａｂｅｌ积分方程组，此方程组的解便给出此接触问题的解。     

摩擦过程中真实接触面积的灰色分析

灰色系统理论是近几年以随机过程为研究对象而形成和发展起来的，在农业和自动控制等方面的研究与应用发展较快．为了使这种理论应用于摩擦学研究领域，从光全反射测量和计算机数值计算两方面，考察了粗糙表面接触时真实接触面积的随机特性，指出摩擦过程中的真实接触面积是一种含有随机成分的变化量，研究目标应当侧重于真实接触面积的变化趋势和范围，而不是它的精确解．在此基础上，首次利用灰色系统理论，分别对静态和动态接触条件下真实接触面积的变化规律进行了灰色分析，建立了精度比较高的预测真实接触面积的灰色模型ＣＭ（１，１）．这种模型对动、静接触面积的计算值与实测值具有良好的一致性，可以用于动态跟踪描述摩擦过程中真实接触面积的变化规律     

Formulating Dynamic Multi-Rigid-Body Contact Problems with Friction as Solvable Linear Complementarity Problems

A linear complementarity formulation for dynamic multi-rigid-body contact problems with Coulomb friction is presented. The formulation, based on explicit Euler integration and polygonal approximation of the friction cone, is guaranteed to have a solution for any number of contacts and contact configuration. A model with the same property, based on the Poisson hypothesis, is formulated for impact problems with friction and nonzero restitution coefficients. An explicit Euler scheme based on these formulations is presented and is proved to have uniformly bounded velocities as the stepsize tends to zero for the Newton–Euler formulation in body co-ordinates.     

On the Impact of Elastic Bodies with Adhesive Forces

We analyze the problem of an elastic sphere impacting against another elastic body for the case when adhesive forces act between the bodies. Depending on the parameter describing the (relative) influence of the adhesive forces, the bodies will either separate or continue to be in contact and perform an oscillatory motion after the rebound. The value of the adhesive forces parameter defining separation and capture is calculated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dry Friction Model of Percussive Drilling

It is postulated that the main mechanism of the enhancement of material removal rate (MRR) in percussive drilling is associated with generating impact forces, which act on the workpiece and help to develop micro-cracking in the cutting zone. The inherent non-linearity of the discontinuous impact process is modelled as a frictional pair, to generate the pattern of the impact forces. A novel formula for calculating the MRR is proposed, which explains the experimentally observed fall in MRR at higher static forces.     

Modelling of Ground Moling Dynamics by an Impact Oscillator with a Frictional Slider

This paper describes current research into the mathematical modelling of a vibro-impact ground moling system. Due to the structural complexity of such systems, in the first instance the dynamic response of an idealised impact oscillator is investigated. The model is comprised of an harmonically excited mass simulating the penetrating part of the mole and a visco-elastic slider, which represents the soil resistance. The model has been mathematically formulated and the equations of motion have been developed. A typical nonlinear dynamic analysis reveals a complex behaviour ranging from periodic to chaotic motion. It was found out that the maximum progression coincides with the end of the periodic regime.     

粗糙表面法向接触刚度的分形模型

提出了以往有关粗糙表面法向接触刚度理论研究工作的缺陷与不足,并在一定的前提假设下,基于球体与平面的接触理论和粗糙表面的分形接触理论,从理论上给出了具有尺度独立性的粗糙表面法向接触刚度分形模型,并进行了数字仿真研究。     

两圆柱体表面接触承载能力的分形模型研究

结合M-B分形模型和Hertz接触模型理论,建立了新型两圆柱体分形接触模型,通过与M-B模型和Hertz模型的对比分析及接触强度实例计算,证明模型所反映两接触体的应力状态.结果表明,所建立的模型反映出载荷与面积呈指数关系,指数不仅与分形维数D有关,而且还与圆柱体的接触半径及接触方式有关.此模型的建立可作为相关机械产品（如齿轮和轴承等）的强度分析和优化设计的理论基础.     

On chaotic motions of systems with dry friction

The principles of formation of closed and quasiperiodic orbitally stable trajectories in systems with dry friction are formulated. A frictional oscillator with periodic forcing is considered. It is established that random and stable oscillations exist. It is discovered that orbital instability and irregular oscillations are associated with the instability domain near a singular point Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 123–132, September 2008.     

结合部切向接触刚度分形模型研究

根据球体与平面接触的切向接触刚度和粗糙表面的接触分形理论，从理论上首次建立了结合部切向接触刚度分形模型，该模型具有尺度独立性。通过对所建模型的数字仿真，直观地给出了结合部切向接触刚度与其影响因素之间的非线性关系，并与实验研究结果具有较好的一致性，从而说明了该模型是合理的。     

Nonlinear vibrations of cantilevered circular cylindrical shells in contact with quiescent fluid

Large-amplitude vibrations of liquid-filled cantilevered (clamped–free) circular cylindrical tanks are studied theoretically for the first time. The influence of liquid height and initial geometric imperfections is investigated in detail. The tank motions are described by a nonlinear model based on Flügge׳s shell theory, and the liquid motions are modelled by means of linearized potential flow theory. Equations of motion are obtained using the extended Hamilton׳s principle and are discretized by expanding the solution with trigonometric functions in the circumferential direction and the cantilevered beam eigenfunctions in the axial direction. The geometric boundary conditions are satisfied exactly, while the natural ones are satisfied in an energy minimization sense. The system is integrated numerically by employing the appropriate modal composition of the solution to guarantee convergence. Results are presented in the form of frequency–response curves in the neighbourhood of the lowest natural frequency. It is found that the response may be of softening or hardening type, depending on the liquid height and the imperfection parameters.     

弹性杆与结构接触冲击的冲击力计算研究

本文提出了一种将杆与结构的接触冲击问题简化为集中力与集中阻尼的常规结构动力学问题的计算模型。对于大型结构，可采用一种特殊的人工边界，只需对人工边界域内的结构用有限元法进行计算。这种人工边界是齐次的，可根据冲击影响区的大小人为地确定     

盘-销摩擦系统摩擦接触力测试与特性分析

测量分析动态摩擦接触力是研究摩擦振动与噪声发生机理的关键.本文中建立了盘-销系统摩擦尖叫试验台架,成功再现了摩擦尖叫.采用三向力传感器对有无摩擦尖叫条件下的动态摩擦接触力进行了测量,并利用小波信号分解、概率密度函数、功率谱密度函数、时频分析等方法进行了分析和讨论.研究发现:在发生摩擦尖叫时,动态摩擦力和法向力发生高频波动,是系统噪声的激励源;无摩擦尖叫时的摩擦力和法向力的动态分量为典型的白噪声随机过程,呈非高斯分布;有摩擦尖叫时的摩擦力和法向力为窄带高频类谐波信号,摩擦力呈非高斯分布,而法向力近似为高斯分布;模态耦合是导致盘-销系统发生动态接触力高频波动以及摩擦尖叫的原因.     

Approximate Solution of an Axisymmetric Contact Problem with Allowance for Tangential Displacements on the Contact Surface

A structurally nonlinear contact problem of a punch shaped like a paraboloid of revolution is studied. An equation for the contactpressure density is derived with allowance for the radial tangential displacements of the boundary points of an elastic halfspace. A method for constructing a closedform approximate solution is proposed. The effect of the tangential displacements on the main contact parameters is discussed.     

偏心量对轴向碰摩系统弯扭耦合非线性振动特性影响的分析

对偏心量改变导致的轴向碰摩系统的弯扭耦合非线性振动特性的变化进行了初步研究。建立了转静子耦合系统计算模型,利用数值积分和Poincare映射方法,对转子系统由于轴向碰摩故障导致的非线性动力学行为进行了数值仿真研究,给出了系统响应随偏心量变化的分岔图和一些典型的Poincare截面图、相轨图、轴心轨迹、幅值谱图和时域响应等。研究结果表明:偏心量是激起碰摩的一个主要因素,且系统响应对偏心量的变化比较敏感,随偏心量的增加,系统的响应将呈复杂化;碰摩发生后,振动响应的主要成分为1/3、1/2、2/3和1倍频,但各成分的存在与否与偏心量大小有关,有时会导致高阶频率成分的出现;碰摩发生后时域波形和轴心轨迹有明显的改变;分岔图是判别系统是否碰摩的有效工具;转、静子的扭转振动响应,对碰摩的发生和消失表现得更为明晰和精确,且其特征也不同于已知的其它故障类别,尤其是静子机匣,故应用扭转振动特性来监测和诊断碰摩故障是可取的;依据单一的振动谱图分析系统的特征较为困难,甚至有可能误判,因此应结合几种谱图综合判断。     

Non-axisymmetric oscillations of a hemispherical drop

Natural oscillations of a hemispherical drop on a solid substrate are considered. The Hocking condition is used to take into account the contact angle dynamics. The natural oscillations attenuate due to dissipation on the contact line and the degeneracy in the azimuthal number is eliminated. Forced oscillations of the drop are studied for tangential vibrations of the substrate. For the case of a fixed contact line, the amplitude of the forced oscillations grows without bound near the fundamental requency. In other cases, the amplitude is finite.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 8–20. Original Russian Text Copyright © 2004 by Lyubimov, Lyubimova, Shklyaev.     

Asymptotic construction of nonlinear normal modes for continuous systems

This paper provides a review of some asymptotic methods for construction of nonlinear normal modes for continuous system (NNMCS). Asymptotic methods of solving problems relating to NNMCS have been developed by many authors. The main features of this paper are that (i) it is devoted to the basic principles of asymptotic approaches for constructing of NNMCS; (ii) it deals with both traditional approaches and, less widely used, new approaches; and (iii) it pays a lot of attention to the analysis of widely used simplified mechanical models for the analysis of NNMCS. The author has paid special attention to examples and discussion of results.     

表面力仪及固体表面微观接触机理的实验研究

利用以等色序条纹技术为核心的表面力仪,使２个分子级光滑的圆柱状云母表面在一定载荷下接触,测量其接触区尺寸和接触表面和变形情况。在两表面间使用不同介质以进行有粘着接触和无粘着接触２种条件下的实验,并将测量结果与Ｈｅｒｔｚ理论（无粘着接触）和ＪＫＲ理论（有粘着接触）进行对比。发现在无粘着接触条件下的试验结果与Ｈｅｒｔｚ理论相吻合;而在有粘着接触条件下则测量到了ＪＫＲ理论所预言的“颈缩”现象。     

Response and bifurcation analysis of a MDOF rotor system with a strong nonlinearity

A new HB (Harmonic Balance)/AFT (Alternating Frequency Time) method is further developed to obtain synchronous and subsynchronous whirling response of nonlinear MDOF rotor systems. Using the HBM, the nonlinear differential equations of a rotor system can be transformed to algebraic equations with unknown harmonic coefficients. A technique is applied to reduce the algebraic equations to only those of the nonlinear coordinates. Stability analysis of the periodic solutions is performed via perturbation of the solutions. To further reduce the computational time for the stability analysis, the reduced system parameters (mass, damping, and stiffness) are calculated in terms of the already known harmonic coefficients. For illustration, a simple MDOF rotor system with a piecewise-linear bearing clearance is used to demonstrate the accuracy of the calculated steady-state solutions and their bifurcation boundaries. Employing ideas from modern dynamics theory, the example MDOF nonlinear rotor system is shown to exhibit subsynchronous, quasi-periodic and chaotic whirling motions.     

Nonstationary nonplanar free motions of an orbiting string with multiple internal resonances

The paper discusses the nonlinear free dynamics of an orbiting string satellite system. The focus is on the transversal oscillations, which are governed by two partial integro-differential equations in two transversal displacement components with quadratic nonlinearities. The system is weakly nonlinear but in practice works in conditions of simultaneous internal resonance. The investigation focuses on nonstationary motions arising from perturbed steady-state nonplanar oscillations. A four-mode model is used to study the problem: two modes are necessary to describe the basic oscillation and at least two other modes are involved in the resonance phenomena when the motion is perturbed. The multiple time scales method is used to obtain the equations that govern the amplitude and phase modulations. For increasing levels of system energy, fundamental and bifurcated paths of fixed points of the seven first-order differential equations are determined and their stability is investigated. The trajectories of motion of periodically modulated amplitude solutions and their stability are also studied. A model with a higher number of modes is used to evaluate the accuracy of the stability analysis of two-mode nonplanar oscillations perturbed by a two-mode disturbance.

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Sommario Nel presente lavoro si studia la dinamica libera nonlineare di un sistema filo-satellite. L'attenzione è rivolta alle oscillazioni trasversali, governate da due equazioni integro-differenziali, con nonlinearità quadratiche, nelle due componenti di spostamento. Il sistema è debolmente nonlineare ma praticamente lavora in condizioni di risonanza interna. Lo studio è concentrato sui moti nonstazionari generati da perturbazioni delle oscillazioni stazionarie spaziali. Per studiare il problema è stato sviluppato un modello con quattro modi: due sono necessari per descrivere il moto base mentre almeno altri due sono interessati dai fenomeni di risonanza interna quando il moto viene perturbato. Per ottenere le equazioni nelle ampiezze e fasi è stato utilizzato il metodo delle scale multiple. Del sistema di sette equazioni differenziali del primo ordine ottenuto, sono stati studiati i percorsi fondamentali di equilibrio e i rami biforcati, prendendo come parametro il livello di energia totale. È stata inoltre esaminata la stabilità di questi rami. Sono state studiate le traiettorie dei moti periodicamente modulati e la loro stabilità. Infine, è stato utilizzato un modello con un numero più alto di modi per valutare l'accuratezza dell' analisi di stabilità delle oscillazioni bimodali spaziali, nella quale la perturbazione è stata descritta da due soli modi.