Emergence of the London Millennium Bridge instability without synchronisation

The pedestrian-induced instability of the London Millennium Bridge is a widely used example of Kuramoto synchronisation. Yet, reviewing observational, experimental, and modelling evidence, we argue that increased coherence of pedestrians’ foot placement is a consequence of, not a cause of the instability. Instead, uncorrelated pedestrians produce positive feedback, through negative damping on average, that can initiate significant lateral bridge vibration over a wide range of natural frequencies. We present a simple general formula that quantifies this effect, and illustrate it through simulation of three mathematical models, including one with strong propensity for synchronisation. Despite subtle effects of gait strategies in determining precise instability thresholds, our results show that average negative damping is always the trigger. More broadly, we describe an alternative to Kuramoto theory for emergence of coherent oscillations in nature; collective contributions from incoherent agents need not cancel, but can provide positive feedback on average, leading to global limit-cycle motion.

Self-excited Vibration of Ink Rollers

A vibration having a character of self-excited chatter oscillation known from machine tools is observed during intermittent motion of ink rollers of offset printing machines. This vibration occurs under specific operating conditions and is often accompanied by an increased noise level. To explain this unusual vibration behavior, a simple analytical model of two rollers interaction is derived. The calculated oscillation is compared with the measurement of ductor roller displacement. The model results confirm the possibility of self-excited vibration development in the presence of viscous forces, negative damping effects and continuous supply of external energy from roller rotation.

Analysis Method of NSV and Influence of Tip Clearance Flow Instabilities on NSV in an Axial Transonic Compressor Rotor

The relationship between tip clearance flow (TCF) and blade vibration in locked-in region is numerically investigated on a transonic rotor. The numerical method is verified by citing references. The phase of TCF changes with the operating condition. A separation method of the unsteady pressure caused by TCF and blade vibration is developed. The unsteady pressure during NSV is separated into the TCF and vibration components under 1B and 8th modes. The unsteady pressure of TCF is similar with that of rigid blade. The unsteady pressure of blade vibration is larger at part span, and its distribution depends on the modal shape and vibrating amplitude. The unsteady pressure of TCF and blade vibration determine the aerodynamic damping in locked-in region. The aerodynamic damping of TCF changes with the TCF phase. TCF provides positive damping at some phases and negative damping at other phases. The aerodynamic work of TCF and blade vibration increases linearly and at the rate of square with the vibrating amplitude, respectively. TCF is dominant in the initial stage of vibration. With the vibrating amplitude increasing, the aerodynamic work of vibration catches up gradually. NSV occurs when TCF provides negative damping and the unsteady pressure of vibration provides positive damping. If the work of vibration is negative, vibration will be enlarged until failure. The maximum amplitude of NSV canbe obtained by calculating the balance of work. For the 8th mode, the limit amplitude under 0ND is 0.0926%C corresponding to vibration stress of 60MPa.

Stability Analysis of Different Regulation Modes of Hydropower Units

The dynamic characteristics of hydropower unit governing systems considerably influence the stability of hydropower units and the connected power system. The dynamic performances of hydropower units with power regulation mode (PRM) and opening regulation mode (ORM) are different. This paper establishes a detailed linear model of a hydropower unit based on the Phillips–Heffron model. The damping characteristic and stability of two regulation modes with different water inertia time constants TW were analyzed. ORM tended to provide negative damping, while PRM often provided positive damping in the major parts of the frequency range within the normal frequency oscillations when TW was large. Eigenvalue analysis illustrated that PRM has better stability than ORM. To validate the analysis, a simulation under two typical faults WAS conducted based on a nonlinear model of a hydropower unit. The simulation results illustrated that the responses of units with PRM are more stable in terms of important operating parameters, such as output power, rotor speed, and power angles. For hydropower units facing challenges in stable operation, PRM is recommended to obtain good dynamic stability.

The Application of an Impedance-Passivity Controller in Haptic Stability Analysis

This paper proposes a passivity theorem on the basis of energy concepts to study the stability of force feedback in a virtual haptic system. An impedance-passivity controller (IPC) was designed from the two-port network perspective to improve the chief drawback of haptic systems, namely the considerable time required to reach stability if the equipment consumes energy slowly. The proposed IPC can be used to achieve stability through model parameter selection and to obtain control gain. In particular, haptic performance can be improved for extreme cases of high stiffness and negative damping. Furthermore, a virtual training system for one-degree-of-freedom sticking was developed to validate the experimental platform of our IPC. To ensure consistency in the experiment, we designed a specialized mechanical robot to replace human operation. Finally, compared with basic passivity control systems, our IPC could achieve stable control rapidly.

Exponential Damping: The Key to Successful Containment of COVID-19

Due to its excessive capacity for human-to-human transmission, the 2019 coronavirus disease (COVID-19) has now been declared a global public health emergency. Here we propose a simple model based on exponential infectious growth, but with a time-varying, largely damping, transmission rate. This model provides an excellent fit to the existing data for 46 countries with 10,000+ cases by 16 May 2020, five continents and the entire world. Hence, the model has largely captured the transmission patterns of the COVID-19 outbreak under a variety of intervention and control measures. The damping rate ranged from −0.0228 to 0.1669 d−1 globally (a negative damping rate represents acceleration in spread) and can greatly affect the duration of the outbreak and the eventual number of infections. Our model suggests that it is possible to defeat the COVID-19 pandemic by the end of 2020 through achieving a high damping rate (0.0615 d−1). However, the global damping rate is rather low (0.0504 d−1 before 26 April) and has dropped even further since late April (0.0168 d−1). Easing currently implemented control measures in countries with weak or no damping in transmission could lead to an exponential rebound of COVID-19 spread.

Mitigation of Stick-Slip Vibrations in Drilling Systems with Tuned Top Boundary Parameters

Aiming at preventing stick-slip oscillations in drilling systems for oil and gas explorations, a reduced-order model is proposed to capture the nonlinear torsional dynamics of drilling operations. In this model, the drill-string structure is simplified as a single-DOF system suffering from dry frictions at the drill bit, while the electromechanical boundary generated by the top-drive system is modeled as another tunable DOF used for stick-slip suppression. To simplify and parameterize the problems, a normalized 2-DOF system with negative damping and tunable parameters is deduced via nondimensionalization and linearization. Based on this system, stability criteria are obtained analytically in the 5-dimensional parametric space. Stable regions as well as the optimized boundary parameters are found analytically. The results suggest that the system can be stabilized by an optimally tuned boundary when and only when the magnitude of the negative damping is no greater than 2. It also reveals that the stability deteriorates if the inertia on the top is huge and non-adjustable, which is the commonest scenario for commercial drilling rigs nowadays. Finally, applications of the tuned boundary in a typical drilling system for stick-slip mitigation are conducted and verified numerically. The results indicate that the control performance can be potentially enhanced by three to five times, via an additional virtual negative inertia generated by the top-drive motor. This research provides an alternative approach to fully optimize the top boundary for curing stick-slip vibrations in drilling systems.

Investigation of the generation mechanism of squeal noise under non-negative damping conditions

The traditionally known generation mechanism of squeal noise is generally agreed to be the negative damping theory, which is represented by the negative slope of friction creepage curve. Recently, however, it was found that squeal noise still can be generated when the negative slope is eliminated. To investigate this phenomenon, water-based and oil-based friction modifiers are applied on a test rig to create non-negative damping conditions. The adhesion ratios at various rolling speeds are measured, and it is found that the negative slopes of friction curves can be eliminated when using friction modifiers, but squeal noise still exists. To investigate this phenomenon, a model involving the effect of vertical dynamics on squeal noise is developed in this research. The results show that the involvement of vertical dynamics has negligible effect on wheel vibration velocity when the friction creepage curve has a negative slope. When the friction creepage curve has a zero or positive slope, however, the results show that a stable lateral vibration still can be generated when vertical dynamics is involved. The generation mechanism of wheel squeal involving vertical dynamics is illustrated from the perspective of power input. Furthermore, the sound pressure levels of squeal noise are simulated using this model and the results correlate well with experimental measurements. Therefore, the results indicate that the vertical dynamics may be the reason why squeal noise still exists under non-negative damping conditions.