Self-excited Motion Research Articles

Efficacy of Tuned Mass Dampers for Bridge Flutter Control

This paper examines efficacy of tuned mass dampers (TMD) in controlling self-excited motion resulting from negative damping. New optimal TMD parameters are suggested which provide better performance than those suggested in the literature. The dependence of TMD performance on structural damping is highlighted. The equations of motion of a combined system comprised of multiple TMDs attached to a bridge deck are presented where the bridge motion is described in terms of reduced-order modal coordinates. Details concerning the multimode coupled flutter of long-span bridges with auxiliary TMDs are provided. The effectiveness and limitations of TMDs for controlling multimode bridge flutter are examined, emphasizing the dependence of TMD performance on the bridge dynamic and aerodynamic characteristics. This study shows that the effectiveness of TMDs is rather limited in controlling a hard-type flutter characterized by negative aerodynamic damping that grows rapidly with increasing wind speed beyond the onset of flutter. However, it is relatively effective in controlling a soft-type flutter in which the negative damping builds up slowly with increasing wind speed. Robust TMD design issues are also discussed in light of their sensitivity to design parameters in the vicinity of optimal values.

Bifurcation of a shaft with hysteretic-type internal friction force of material

The bifurcation of a shaft with hysteretic internal friction of material was analysed. Firstly, the differential motion equation in complex form was deduced using Hamilton principle. Then averaged equations in primary resonances were obtained using the averaging method. The stability of steady-state responses was also determined. Lastly, the bifurcations of both normal motion (synchronous whirl) and self-excited motion (nonsynchronous whirl) were investigated using the method of singularity. The study shows that by a rather large disturbance, the stability of the shaft can be lost through Hopf bifurcation in case the stability condition is not satisfied. The averaged self-excited response appears as a type of unsymmetrical bifurcation with high orders of co-dimension. The second Hopf bifurcation, which corresponds to double amplitude-modulated response, can occur as the speed of the shaft increases. Balancing the shaft carefully to decrease its unbalance level and increasing the external damping are two effective methods to avoid the appearance of the self-sustained whirl induced by the hysteretic internal friction of material.

Averaging analysis of self-excited motion of a quasi-axisymmetrical gyrostat

The averaging analysis was carried out to study the motion of a quasi-axisymmetrical gyrostat under a small-magnitude self-excited control torque. The common approach to investigating the problem of rigid body rotation under the action of a small torque known in the body frame was described. Using this approach, the problem (Grammel’s problem for the case of small torque) that is maintaining the angular velocity of a quasi-axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.

Self-excited motion of dust particles in a inhomogeneous plasma

Abstract Two novel types of instabilities in inhomogeneous dusty plasma are considered. It is shown that spatial dust charge variation provides an effective mechanism to excite the motion of particles. The results of experimental observation of various self-excited motions of dust particles in a dc-discharge plasma are presented. Conditions suitable for growing the considered instabilities in the dc-glow discharge are discussed.

Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

We investigate the nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact eddy-current damper. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the imbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

Dynamic Instabilities in the Sliding of Two Layered Elastic Half-Spaces

Two flat layered elastic half-spaces, of different material properties, are pressed together and slide against each other with a constant coefficient of friction. Although a nominally steady-state solution exists, an analysis of the dynamic motion yields complex eigenvalues with positive real parts, i.e., a flutter instability. These results demonstrate that self-excited (unstable) motion occurs for a wide range of material combinations. The physical mechanism responsible for this instability is that of slip-wave destabilization. The influence of the properties of the layers on the destabilization of sliding motion is investigated. These dynamic instabilities lead either to regions of stick-slip or to areas of loss-of-contact. Finally the dynamic stresses at the interfaces between the layers and the semi-infinite bodies are determined and compared to the nominally steady-state stresses. These dynamic stresses are expected to play an important role in delamination.

Self-Excited Oscillations in Sliding With a Constant Friction Coefficient—A Simple Model

The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. These self-excited oscillations can lead either to partial loss-of-contact or to stick-slip. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.

Self-excited soliton motion.

Centro de Fi ´sica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020 A, Venezuela~Received 14 December 1994; revised manuscript received 13 February 1996!We present an extensive analytical and numerical study of the dynamics of kink solitons in Klein-Gordonsystems with nonlinear damping. Particularly, the nonlinear damping could model the interaction of the soli-tons with an active medium. We analyze the existence and stability conditions of stationary states for thesoliton. We present a different kind of bifurcation: a structure-breaking bifurcation. After this bifurcation thesoliton enters a highly nonstationary state ~solitonic explosion!. We show the existence of self-sustainedoscillations of solitons ~solitonic limit cycles!. Finally, we present chaotic motion of solitons similar to theDuffing–Van der Pol type.@S1063-651X~96!05707-8#PACS number~s!: 05.45.1b, 52.35.Sb, 52.35.Mw, 02.30.JrI. INTRODUCTION

Self-Excited Oscillations of Two Elastic Half-Spaces Sliding With a Constant Coefficient of Friction

Two flat isotropic elastic half-spaces, of different material properties, are pressed together and slide against each other with a constant coefficient of friction. Although a nominally steady-state solution exists, an analysis of the dynamic problem demonstrates that the steady solution can be dynamically unstable. Eigenvalues with positive real parts give rise to self-excited motion which occurs for a wide range of material pairs, coefficients of friction, and sliding velocities (including very low speeds). These self-excited oscillations are generally confined to the region near the interface and can lead either to regions of loss of contact or to areas of stick slip. The mechanism responsible for the instability is essentially one of destabilization of interfacial (slip) waves. It is expected that these vibrations might play an important role in the behavior of sliding members with dry friction.

Analysis Of Self-excited Longitudinal Vibration Of A Moving Tape

Longitudinal vibration of a moving magnetic tape can be excited by frictional contact with a recording head, or with a guide that defines the path of the tape. The friction force depends on the velocity, relative to a stationary observer, of the tape element that is instantaneously located at the point of contact. The response of a moving tape under such non-linear dissipation is determined using new methods for the vibration analysis of axially moving materials. In a particular transport speed range, longitudinal motion of the tape is self-excited through negative (unstable) damping for small amplitude vibration and positive (stable) damping for large amplitudes. Independent of the initial conditions, almost all solutions are attracted to a stable limit cycle, the amplitude of which is sensitive to the transport speed and to the axial location of contact. Parameter combinations that reduce, or eliminate altogether, the self-excited motion are identified. Some of the conclusions differ from those of previous analyses that neglect the effects of convection on the tape's velocity and acceleration.

Linear Stability Analysis of Self-Excited Motion of Liquid-Liquid Interface with Chemical Reaction

Linear Stability Analysis of Self-Excited Motion of Liquid-Liquid Interface with Chemical Reaction

WIND TUNNEL STUDY ON GALLOPING OSCILLATIONS OF SUSPENDED FIGURE-8 TELECOMMUNICATION CABLES

It has been reported that many telecommunication cables of figure-8 section suffered from operating problems and sometimes even failed because of wind-induced large amplitude oscillation, the so-called galloping of cable. In this study, three-dimensional figure-8 cable models are tested at the wind tunnel and aeroelastic behaviour of the cable was observed in detail. It is found that wind-induced significant change of the angle of attack of the cable relative to wind is the fundamental cause of galloping. The critical wind speed that triggered galloping and the initial direction of the self-excited cable motion are explained by the Den Hartog's quasi-steady treatment of the aerodynamic force with some modification.