Modal stability of inclined cables subjected to vertical support excitation

In this paper the out-of-plane dynamic stability of inclined cables subjected to in-plane vertical support excitation is investigated. We compute stability boundaries for the out-of-plane modes using rescaling and averaging methods. Our study focuses on the 2:1 internal resonance phenomenon between modes that occurs when the excitation frequency is twice the first out-of-plane natural frequency of the cable. The second in-plane mode is excited directly, while the out-of-plane modes can be excited parametrically. An analytical model is developed in order to study the stability regions in parameter space. In this model we include nonlinear coupling effects with other modes, which have thus far been omitted from previous models of parametric excitation of inclined cables. Our study reflects the importance of such effects. Unstable parameter regions are defined for the selected cable configuration. The validity of the proposed stability model was tested experimentally using a small-scale cable actuator rig. A comparison between experimental and analytical results is presented in which very good agreement with model predictions was obtained. r 2008 Elsevier Ltd. All rights reserved

Aerodynamic forcing characteristics of dry cable galloping at critical Reynolds numbers

This article attempts to highlight characteristics of the aerodynamic forcing on a rigid circular cylinder experiencing dry galloping vibrations. Observations from a series of wind tunnel tests are studied comparatively with the literature on rain–wind cable vibrations and on flow past inclined lifting bodies such as missiles, for drawing similarities. Unsteadiness and spatial variation of the flow, both previously undermined, are significant during the large cylinder motions recorded. Thus, they are here suspected to play a role in triggering unstable behaviour. Instabilities were restricted to specific ranges of cable-wind angles and Reynolds numbers. The transitional features identified refute the view of simple bursting separation bubbles that rhythmically produce lift and suggest that there is a multitude of paths for energetically feeding dry galloping. Finally explanations are provided and a mechanism incorporating unstable features is proposed for future modelling

Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation

AbstractCables are often prone to potentially damaging large amplitude vibrations. The dynamic excitation may be from external loading or motion of the cable ends, the latter including direct excitation, normally from components of end motion transverse to the cable, and parametric excitation induced by axial components of end motion causing dynamic tension variations. Geometric nonlinearity can be important, causing stiffening behaviour and nonlinear modal coupling. Previous analyses of the vibrations, often neglecting sag, have generally dealt with direct and parametric excitation separately or have reverted to numerical solutions of the responses. Here a nonlinear cable model is adopted, applicable to taut cables such as on cable-stayed bridges, that allows for cable inclination, small sag (such that the vibration modes are similar to those of a taut string), multiple modes in both planes and end motion and/or external forcing close to any natural frequency. Based on the method of scaling and averaging it is found that, for sinusoidal inputs and positive damping, non-zero steady state responses can only occur in the modes in each plane with natural frequencies close to the excitation frequency and those with natural frequencies close to half this frequency. Analytical solutions, in the form of non-dimensional polynomial equations, are derived for the steady state vibration amplitudes in up to three modes simultaneously: the directly excited mode, the corresponding nonlinearly coupled mode in the orthogonal plane and a parametrically excited mode with half the natural frequency. The stability of the solutions is also identified. The outputs of the equations are consistent with previous results, where available. Example results from the analytical solutions are presented for a typical inclined bridge cable subject to vertical excitation of the lower end, and they are validated by numerical integration of the equations of motion and against some previous experimental results. It is shown that the modal interactions and sag (although very small) affect the responses significantly

Pedestrian lateral foot placement and lateral dynamic instability of bridges

The most often purported mechanism causing the lateral dynamic instability of the London Millennium Footbridge is the synchronisation of footsteps to the lateral structural motion. However, evidence from full-scale measurements and treadmill tests has challenged this notion. Instead, an active control of foot placement is advocated to be the source of destabilising forces to the structure, occurring even without synchronisation. This is to say that, while walking on a laterally oscillating surface, pedestrians maintain their balance primarily by controlling the position of their feet, rather than adjusting the timing. Similar behaviour was previously observed in experimental tests measuring the response of pedestrians to an impulsive perturbation of gait. The analysis of the collected data suggested a simple linear foot placement control law, whereby the position of the foot at the instant of foot placement immediately following the perturbation depends on the instantaneous lateral velocity of the centre of mass and a constant offset. However, it is has been uncertain whether the same foot placement control law applies while walking on laterally oscillating structures. To test this proposition, an experimental campaign was conducted on a laterally oscillating treadmill with a test subject monitored with an optical motion capture system. The motion of the body centre of mass and the position of the feet were identified and analysed. It was found that a simple linear foot placement control law applies. Further tests were conducted to test the influence of the visual information on pedestrian stepping behaviour using virtual reality delivered via a head mounted display. It was found that the identified foot placement control law is very robust for different walking surface conditions and visual environments

Identification of aeroelastic forces and static drag coefficients of a twin cable bridge stay from full-scale ambient vibration measurements

Despite much research in recent years, large amplitude vibrations of inclined cables continue to be of concern for cable-stayed bridges. Various excitation mechanisms have been suggested, including rain-wind excitation, dry inclined cable galloping, high reduced velocity vortex shedding and excitation from the deck and/or towers. Although there have been many observations of large cable vibrations on bridges, there are relatively few cases of direct full-scale cable vibration and wind measurements, and most research has been based on wind tunnel tests and theoretical modelling.This paper presents results from full-scale measurements on the special arrangement of twin cables adopted for the Øresund Bridge. The monitoring system records wind and weather conditions, as well as accelerations of certain cables and a few locations on the deck and tower. Using the Eigenvalue Realization Algorithm (ERA), the damping and stiffness matrices are identified for different vibration modes of the cables, with sufficient accuracy to identify changes in the total effective damping and stiffness matrices due to the aeroelastic forces acting on the cables. The damping matrices identified from the full-scale measurements are compared with the theoretical damping matrices based on the quasi-steady theory, using three different sets of wind tunnel measurements of static force coefficients on similar shaped twin or single cables, with good agreement. The damping terms are found to be dependent on Reynolds number rather than reduced velocity, indicating that Reynolds number governs the aeroelastic effects in these conditions. There is a significant drop in the aerodynamic damping in the critical Reynolds number range, which is believed to be related to the large amplitude cable vibrations observed on some bridges in dry conditions.Finally, static drag coefficients are back-calculated from the full-scale vibration measurements, for first time, with reasonable agreement with direct wind tunnel measurements. The remaining discrepancies are believed to be due to the higher turbulence intensity on site than in the wind tunnel

Wind tunnel testing of an inclined aeroelastic cable model-Pressure and motion characteristics, Part I

The current paper considers large vibrations of circular cylinders, inclined and yawed to the flow. The case of a nominally perfect cylinder prone to galloping-like instabilities, when subjected to some critical flow conditions, is seemingly a paradox since symmetry and aerodynamic galloping are contradictory. Symmetry-breaking parameters in the flow geometry were suspected to be associated with triggering mechanisms of such vibration phenomena. A series of wind tunnel tests was performed on a full-scale inclined spring-supported cable model for a range of conditions in order to assess this idea further. We herein describe the experimental setup, present deduced results and attempt to provide explanations for the observed behaviour in the light of established knowledge in the field. We use instantaneously recorded pressure measurements to map flow transitions, recover energetic structures around the cylinder body and examine force correlations. Incidents of large response with negative aerodynamic damping are examined considering axial flow, spanwise vortex shedding and Reynolds number influences.Peer reviewed: YesNRC publication: Ye