John H G Macdonald

Lateral excitation of bridges by balancing pedestrians

On its opening day, the London Millennium Bridge (LMB) experienced unexpected large amplitude lateral vibrations due to crowd loading. This form of pedestrian–structure interaction has since been identified on several other bridges of various structural forms. The mechanism has generally been attributed to ‘pedestrian synchronous lateral excitation’ or ‘pedestrian lock-in’. However, some of the more recent site measurements have shown a lack of evidence of pedestrian synchronization, at least at the onset of the behaviour. This paper considers a simple model of human balance from the biomechanics field—the inverted pendulum model—for which the most effective means of lateral stabilization is by the control of the position, rather than the timing, of foot placement. The same balance strategy as for normal walking on a stationary surface is applied to walking on a laterally oscillating bridge. As a result, without altering their pacing frequency, averaged over a large number of cycles, the pedestrian effectively acts as a negative (or positive) damper to the bridge motion, which may be at a different frequency. This is in agreement with the empirical model developed by Arup from the measurements on the LMB, leading to divergent amplitude vibrations above a critical number of pedestrians.

Biomechanically inspired modeling of pedestrian-induced vertical self-excited forces

AbstractAlthough many models of pedestrian dynamic loading have been proposed, possible bidirectional interactions between the walker and the excited structure are generally ignored, particularly for vertical vibrations. This shortcoming has arisen from scarcity of data on gait-adaptation strategies used in the presence of structural motion and, as a consequence, the absence of a credible fundamental pedestrian model capable of capturing the underlying relations between the two dynamic systems. To address this inadequacy of current approaches, a biomechanically inspired inverted-pendulum pedestrian model has been applied to the human-structure interaction problem. The behavior of the model is studied when subjected to vertical motion of the supporting structure, in particular, in relation to potential self-excited forces that can be generated. A mechanism has been identified by which the timing of pedestrian footsteps can be altered subtly, giving a net damping effect on the structure, without necessarily...

Separation of the contributions of aerodynamic and structural damping in vibrations of inclined cables

Abstract Large amplitude cable vibrations have occurred on several major cable-stayed bridges. Complex mechanisms including rain-wind excitation and possibly cable–deck interaction have been responsible, but the extremely low level of damping of bridge cables has been an important contributory factor. Measurements of cable damping have been undertaken on several cable-stayed bridges, but previously, the full contribution of aerodynamic damping, which could be a significant proportion of the total measured damping, has not been considered. To address this issue, theoretical expressions for the aerodynamic damping are proposed for the general case of an inclined cable and an arbitrary wind velocity, for both in-plane and out-of-plane vibrations. Damping estimates from cable vibration tests during construction of the Second Severn Crossing cable-stayed bridge, with varying wind velocity, have shown the expression for in-plane cable vibrations to give good estimates of the actual aerodynamic damping. The remaining contribution from structural damping is also determined and the effects of the injection of corrosion prevention wax into the cable sheaths, temperature, and interaction with other cables are considered.

Misconceptions and Generalizations of the Den Hartog Galloping Criterion

Classical quasi-steady galloping analysis deals exclusively with cases of across-wind vibrations, leaving aside the more general situation where the wind and motion may not be normal. This can arise in many circumstances, such as in the motion of a power transmission cable about its equilibrium configuration that is swayed from the vertical plane as a result of the mean wind or in a tall slender structure in a skewed wind. Furthermore, the generalization to such situations, when this had been made, has only considered special issues. In this paper, the correct equations for the quasi-steady aerodynamic damping coefficients for a rotated system or wind are derived, and the differences from other variants are highlighted. Motion in two orthogonal structural planes is considered, potentially giving coupled translational galloping, for which previous analysis has often been limited or has even arrived at erroneous conclusions. For the two-degree-of-freedom case, the behavior is dependent on the structural as well as the aerodynamic parameters, in particular the orientation of the principal structural axes and the relative natural frequencies in the two planes. For the first time, the differences in the aerodynamic damping and zones of galloping instability are quantified between solutions from the correct perfectly tuned, well detuned, and classical Den Hartog equations (and also an incorrect generalization of the latter) for a variety of typical cross-sectional shapes. It is found that although the Den Hartog summation often gives a reasonable estimate for the actual aerodynamic damping, even in the rotated situation, in some circumstances the differences can be quite large.

Experimental identification of the behaviour of and lateral forces from freely-walking pedestrians on laterally oscillating structures in a virtual reality environment

Highlights • A novel setup for investigating pedestrian–structure interaction is presented.• Foot-placement is the main balance control mechanism on laterally vibrating ground.• All components of pedestrian force are uncovered, including self-excited forces.• Inverted pendulum pedestrian model qualitatively captures the nature of forces.• The ground and visual conditions cause significant changes in pedestrian loading.

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. Contact person: N.Nikitas, University of Bristol, Queens Building, University Walk, BS8 1TR, Bristol, UK, Tel: +44 117 331 7396, Fax: +44 117 928 7783, E-mail N.Nikitas@bristol.ac.uk Wind tunnel testing of an inclined aeroelastic cable modelPressure and motion characteristics, Part I N. Nikitas, J.H.G. Macdonald, T.L. Andersen, J.B. Jakobsen, M.G. Savage,

Galloping Analysis of a Stay Cable with an Attached Viscous Damper Considering Complex Modes

AbstractThe use of viscous dampers to mitigate cable vibrations on cable-stayed bridges is very popular. A viscous damper attached to a stay cable results in complex mode shapes. Such complexity co...

Nonlinear Models of Cable-Stayed Bridges

Cable-stayed bridges frequently experience vibrations due to a variety of mechanisms, exacerbated by their very low inherent damping. A research group of the University of Bristol has focused lately on the study of cable-stayed bridges, some advances have led to the identification of vortex-induced deck vibrations occurring at the Second Severn Crossing (SSC) and improved methods of analysis of field vibration data. Based on such experience, it aims to study the autoparametric excitation which, due to very great amplitudes, can seriously damage the structure. It has been suggested that this may have been the mechanism of excitation of some large amplitude cable vibrations on real bridges, but the details of the behaviour are not very well understood and several cases of large cable vibrations on full scale bridges have not been fully explained. In this paper we examine a previously established cable-deck model and compare it to a new, more exact model in a different coordinate basis.

Modal Parameter Identification from Measurements of Vehicle-Bridge Interaction

The rise of output-only modal analysis has offered an economical and efficient way to identify modal parameters of civil engineering structures, namely natural frequencies, damping ratios and mode shapes. However, since the forcing is unknown, it is not possible to directly estimate modal masses, and estimates of damping ratios may be inaccurate. With the advancement of wireless sensor networks both vehicle and bridge responses can be simultaneously measured. This offers the possibility of estimating true Frequency Response Functions (FRFs), since the vehicle acceleration gives an estimate of the force input to the bridge. Hence in principle it is possible to estimate modal masses and more accurate damping ratios. However, the spatial and temporal variation of the moving load from a passing vehicle gives challenges to this idea and precludes the direct use of existing single-input-multiple-output (SIMO) system identification methods. Even if the system is treated as a multiple-input-multiple-output (MIMO) one, the inputs are highly correlated so existing methods for these systems are not applicable either. For this reason, a two-stage strategy is proposed to modify an existing method to solve this moving load problem.

Damping Performance of Taut Cables with Passive Absorbers Incorporating Inerters

As stay cables are prone to vibrations due to their low inherent damping, a common method to limit unwanted vibrations is to install a viscous damper normal to the cable near one of its supports. This paper investigates the potential performance improvement that can be delivered by a numbers of candidate absorbers that incorporate inerters. The inerter device is the true network dual of a spring, with the property that the force is proportional to the relative acceleration between its two terminals. A finite element taut cable model is used for this study. A specific cost function indicating the damping performance of a cable with an absorber attached is proposed. An optimisation of the performance is then carried out. Based on optimisation results, the best damping performance for each of the candidate absorber structures against a specific range of inertance values is presented.