Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely spaced modes

Nonlinear Dynamics - It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle...     

Fast parametrically excited van der Pol oscillator with time delay state feedback

We investigate the effect of a fast vertical parametric excitation on self-excited vibrations in a delayed van der Pol oscillator. We use the method of direct partition of motion to derive the main autonomous equation governing the slow dynamic in the vicinity of the trivial equilibrium. Then, we apply the multiple scales method on this slow dynamic to derive a second-order slow flow system describing the modulation of slow dynamic. In particular we analyze the slow flow to obtain the effect of a fast excitation on the regions in parameter space where self-excited vibrations can be eliminated. We have shown that in the case where the time delay and the feedback gains are imposed, fast vertical parametric excitation can be an alternative to suppress undesirable self-excited vibrations in a delayed van der Pol oscillator.     

Effect of Coriolis acceleration on the vibrations of rotating disks

The changes effected by the Coriolis acceleration in the frequencies of inplane vibrations of a rotating disk are calculated. It is shown that the current practice to neglect this effect in everyday engineering calculations is quite justified. It is also shown that when disks are spun at ultra high speeds, say exceeding the one that corresponds with one-tenth of the lowest natural frequency of a stationary disk, the effect does become significant.     

Self-excited yawing vibrations of railway cars

The site [1] presents a video recording of the motion of empty freight railway cars. The video demonstrates that some railway cars experience angular self-excited vibrations in the horizontal plane (i.e., yawing). In the same reference, the main causes of such a “negative dynamics” of railway cars are listed. All causes are related to some defects in railway car manufacturing. We show that such self-excited vibrations are possible even in the case of absolutely ideal railway car without any defects at all. It is shown that, for a certain combination of parameters, the rectilinear (unperturbed) motion of a railway car may experience flutter instability. This type of self-excited vibrations of railway cars has not been studied earlier [2, 3].     

Minimal models for squealing of railway block brakes

Block brakes have been used to brake railway vehicles for approximately 200 years. During the last 40 years, disk brakes have replaced the block brakes at passenger cars but block brakes are still used for all freight wagons. One problem of block brakes is that they show an enormous tendency to squeal. Although the block brake is a very common and old technical component, there exists almost no scientific work on its noise behavior regarding squeal. On the other hand, a lot of work has been done on the problem of disk brake squeal especially concerning the modeling of the excitation mechanism. The goal of this paper is to investigate whether and how models from disk brake squeal can be modified to model block brake squeal. The starting point of these investigations is a minimal model for an automotive disk brake introduced by von Wagner et al. (J Sound Vibration, 51(1–2):223–237, 2007) that is adapted to the block brake problem. It can be shown that such a simple converted model does not show any instability at all. A deeper analysis suggests that the reasons for squeal in block brakes could originate from in-plane vibrations of the brake disk or specific geometrical properties of the railway wheel. The self-excited vibrations explaining the squeal occur at relatively low rotational speeds far below the first critical rotor speed which has rarely been observed in rotor dynamics.     

Andronov–Hopf bifurcations in wave models of torsional vibrations of drill strings

A wave model of torsional vibrations of rotating drill strings is set up. The ranges of rotational speed in which self-excited vibrations occur are found. Andronov–Hopf bifurcations occur at the limits of these ranges. The conditions for the occurrence and development of self-excited oscillatory processes are established     

基于有限元的高速列车车轮多边形磨耗成因分析

研究了中国高速列车车轮多边形磨耗的形成原因,考虑轮对的旋转惯量,建立了高速列车轮对-轨道-盘式制动系统有限元模型. 基于轮轨系统摩擦自激振动的理论,采用有限元复特征值分析法研究了高速列车制动时轮对-轨道-盘式制动系统的稳定性. 研究了饱和的轮轨蠕滑力和盘式制动系统摩擦力耦合作用对车轮多边形磨耗的影响,并调查了轮轨-轨道-盘式制动系统的参数敏感性. 数值模拟结果表明:在饱和的轮轨蠕滑力和盘式制动器摩擦力耦合作用下,轮轨系统的摩擦自激振动导致高速列车车轮多边形磨耗的产生,其导致的21~22阶和23~24阶车轮多边形磨耗占主导地位,这与中国高速列车高阶车轮多边形磨耗最为符合. 饱和的轮轨蠕滑力主要影响较低阶车轮多边形磨耗,盘式制动器摩擦力主要影响较高阶车轮多边形磨耗. 制动压力为13 kN时,车轮多边形磨耗形成的几率最小,发展速度最慢. 过高或者过低的垂向悬挂力均不利于抑制车轮多边形磨耗. 垂向悬挂力为75 kN时,车轮多边形磨耗形成的可能性最小,发展速度最慢.      

Vibrations of a fan jet in running a supersonic jet into a notched obstacle

Some kinds of vibrations of a fan jet are described. A physical model of one kind of self-excited vibrations of the fan jet is formulated. The formulas to calculate the frequencies of self-excited vibrations are given. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 118–124, July–August, 1999.     

Theory of the shimmy phenomenon

The shimmy phenomenon is the appearance of angular self-excited vibrations of the carriage wheels. Such self-excited vibrations provide a serious safety hazard for motion, which explains the great interest of scientists in this phenomenon [1–6]. This problem is most serious for the aircraft fore wheels.     

Transverse Vibrations of a Centrally Clamped Rotating Circular Disk

The transverse vibrations of a circular disk of uniform thickness rotatingabout its axis with constant angular velocity are analyzed. The resultsspecialized to the linear case of disks clamped at the center and free atthe periphery are in good agreement with those reported in the literature.The natural frequencies of spinning hard and floppy disks are obtained for various nodal diameters and nodal circles. Primary resonance is shown to occur at the critical rotational speed at which, in the linear analysis, the spinning disk is unable to support arbitraryspatially fixed transverse loads. Using the method of multiple scales, wedetermine a set of four nonlinear ordinary-differential equations governingthe modulation of the amplitudes and phases of two interacting modes. Thesymmetry of the system and the loading conditions are reflected in thesymmetry of the modulation equations. They are reduced to an equivalentset of two first-order equations whose equilibrium solutions aredetermined analytically. The stability characteristics of thesesolutions is studied; the qualitative behavior of the response isindependent of the mode being considered.     

Frictional contact of two rotating elastic disks

We study the problem of constrained uniform rotation of two precompressed elastic disks made of different materials with friction forces in the contact region taken into account. The exact solution of the problem is obtained by the Wiener-Hopf method.An important stage in the study of rolling of elastic bodies is the Hertz theory [1] of contact interaction of elastic bodies with smoothly varying curvature in the contact region under normal compression. Friction in the contact region is assumed to be negligible. If there are tangential forces and the friction in the contact region is taken into account, then the picture of contact interaction of elastic bodies changes significantly. Although the normal contact stress distribution strictly follows the Hertz theory for bodies with identical elastic properties and apparently slightly differs from the Hertz diagram for bodies made of different materials, the presence of tangential stresses results in the splitting of the contact region into the adhesion region and the slip region. This phenomenon was first established by Reynolds [2], who experimentally discovered slip regions near points of material entry in and exit from the contact region under constrained rolling of an aluminum cylinder on a rubber base. The theoretical justification of the partial slip phenomenon in the contact region, discovered by Reynolds [2], can be found in Carter [3] and Fromm [4]. Moreover, Fromm presents a complete solution of the problem of constrained uniform rotation of two identical disks. Apparently, Fromm was the first to consider the so-called “clamped” strain and postulated that slip is absent at the point at which the disk materials enter the contact region.Ishlinskii [5, 6] gave an engineering solution of the problem on slip in the contact region under rolling friction. Considering the problem on a rigid disk rolling on an elastic half-plane, we model this problem by an infinite set of elastic vertical rods using Winkler-Zimmermann type hypotheses. Numerous papers of other authors are surveyed in Johnson’s monograph [7].The exact solution of the problem on the constrained uniform rotation of precompressed rigid and elastic disks under the assumptions of Fromm’s theory is contained in the papers [8, 9]. In the present paper, we generalize the solution obtained in [8, 9] to the case of two elastic disks made of different materials.     

Self-excited vibration of the shell-liquid coupled system induced by dry friction

The nonlinear vibration theory and the experimental modal analysis are used in this paper to study the self-excited vibration of the shell-liquid coupled system induced by dry friction. The effect of dry friction stick-slip coefficients and rubbing velocity on self-excited vibration, and the limit cycle and Hopf bifurcation solution of the system are obtained. In particular, it is shown that the phenomenon of 4 point (or 6 point) water droplet spurting of the Chinese cultural relic Dragon Washbasin is the result of the perfect combination of the self-excited vibration induced by dry friction and its special modes, which indicates the significant scientific value of the Chinese cultural relic Dragon Washbasin.     

Stick-slip vibrations of a self-excited SD oscillator with Coulomb friction

Nonlinear Dynamics - In this paper, the stick-slip vibrations of an archetypal self-excited smooth and discontinuous (SD) oscillator are investigated. The mathematical model of the self-excited SD...     

Self-excited vibration caused by dry friction between two elastic structures

Based on our previous work^[1], self-excited vibration of a multi-degree-of-freedom system caused by dry friction between two elastic structures is investigated using the Chinese cultural relic dragon washbasin as an example. Some new characteristics of the self-excited vibration in this kind of system are found. The conditions under which self-excited vibration occurs at low-order or high-order modes are discussed. Effects of changes in parameters of the system on the self-excited vibration are analyzed. The vibration mechanism of the water droplets spurting phenomenon of the Chinese cultural relic dragon washbasin is further explained. This investigation presents a new idea for modeling the self-excited vibration caused by dry friction interaction between two elastic structures. The project supported by the National Natural Science Foundation of China     

Nonlinear stability analysis of a disk brake model

It has become commonly accepted by scientists and engineers that brake squeal is generated by friction-induced self-excited vibrations of the brake system. The noise-free configuration of the brake system loses stability through a flutter-type instability and the system starts oscillating in a limit cycle. Usually, the stability analysis of disk brake models, both analytical as well as finite element based, investigates the linearized models, i.e. the eigenvalues of the linearized equations of motion. However, there are experimentally observed effects not covered by these analyses, even though the full nonlinear models include these effects in principle. The present paper describes the nonlinear stability analysis of a realistic disk brake model with 12 degrees of freedom. Using center manifold theory and artificially increasing the degree of degeneracy of the occurring bifurcation, an analytical expression for the turning points in the bifurcation diagram of the subcritical Hopf bifurcations is calculated. The parameter combination corresponding to the turning points is considered as the practical stability boundary of the system. Basic phenomena known from the operating experience of brake systems tending to squeal problems can be explained on the basis of the practical stability boundary.     

The effect of friction reduction in the presence of in-plane vibrations

A reduction of friction by vibrations has been observed in various experiments. This effect can be applied to actively control frictional forces by modulating vibrations. Moreover, common methods of controlling friction rely on lubricants and suitable material combinations. The superimposition of vibrations can further reduce the friction force. This study presents a theoretical approach based on the Dahl friction model that describes the friction reduction observed in the presence of the tangential vibrations at an arbitrary angle. Analysis results indicated that the tangential compliance should be considered in modeling the effect of vibrations in reducing friction. At any vibration angle, the tangential compliance of the contacts reduces the friction reduction effect. The vibrations parallel to the macroscopic velocity are most effective for friction reduction.     

Influence of Initial Geometric Imperfections on the Vibrations and Dynamic Stability of Elastic Shells

The results from studies into the vibrations and dynamic stability of thin elastic shells with initial geometric imperfections are analyzed. The corresponding dynamic problems are solved in both linear and nonlinear formulations. The influence of initial axisymmetric and nonaxisymmetric deflections on natural, forced, parametrically excited, and self-excited vibrations (flutter) is studied. The dynamic buckling of imperfect shells under short-term impulsive loading is examined. Some aspects of experimental investigation into the vibrations of shells with small geometric imperfections (deviations from the design shape) are considered     

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.     

Dynamics and wave propagation in nonlinear piezoelectric metastructures

Nonlinear Dynamics - Mode-coupling instabilities are known to trigger self-excited vibrations in sliding contacts. Here, the conditions for mode-coupling (or “flutter”) instability in...