Theoretical study on self-synchronization of two homodromy rotors coupled with a pendulum rod in a far-resonant vibrating system

The objective of this paper is to investigate the self-synchronization of two homodromy rotors coupled with a pendulum rod in a far-resonant vibrating system. Using the average method and revisionary small parameters, we derive the dimensionless equation of the self-synchronization criterion and synchronous stability of the vibrating system. Meanwhile, to prove the correctness of the theoretical analysis, the diversity feature of the vibrating system is simulated numerically. Both results of theoretical analysis and numerical simulation show that increasing the length of the pendulum rod or decreasing the mass of the rotor connected with pendulum rod can ensure the self-synchronization and synchronous stability of two homodromy rotors in the vibrating system

Study of synchronization for a rotor-pendulum system with Poincare method

A simplified model of the system of unbalanced rotors coupled with pendulum rod is examined. The model consists of two counter-rotating rotors, a rigid pendulum rod and a rigid vibrating body, which is horizontally connected to a fixed support by means of springs. The synchronous state of the system, i.e. synphase and antiphase synchronization of the rotors, is studied by means of the Poincare method. Moreover, the assessment of the synchronous state is converted to find a solution that should satisfy a balanced function and a stability function of the system. However, frequency ratios and installation angular are included in the two functions. It is demonstrated that the spring stiffness and the installation angular have a large influence on the existence and stability of the synchronization state in the coupling system. Finally, computer simulations are preformed to verify the theoretical computations

An optimized tuned mass damper/harvester device

Much work has been conducted on vibration absorbers, such as tuned mass dampers (TMD), where significant energy is extracted from a structure. Traditionally, this energy is dissipated through the devices as heat. In this paper, the concept of recovering some of this energy electrically and reuse it for structural control or health monitoring is investigated. The energy-dissipating damper of a TMD is replaced with an electromagnetic device in order to transform mechanical vibration into electrical energy. That gives the possibility of controlled damping force whilst generating useful electrical energy. Both analytical and experimental results from an adaptive and a semi-active tuned mass damper/harvester are presented. The obtained results suggest that sufficient energy might be harvested for the device to tune itself to optimise vibration suppression

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Dynamic suspension modeling of an eddy-current device : an application to Maglev

When a magnetic source is simultaneously oscillated and translationally moved above a linear conductive passive guideway such as aluminum, eddy-currents are induced that give rise to a time-varying opposing field in the air-gap. This time-varying opposing field interacts with the source field, creating simultaneously suspension, propulsion or braking and lateral forces that are required for a Maglev system. The 2-D analytic based transient eddy-current force and power loss equations are derived for the case when an arbitrary magnetic source is moving and oscillating above a conductive guideway. These general equations for force and power loss are derived using a spatial Fourier transform and temporal Laplace transform technique. The derived equations are capable of accounting for step changes in the input parameters, in addition to arbitrary continuous changes in the input conditions. The equations have been validated for both step changes as well as continuous changes in the input conditions using a 2-D transient finite-element model. The dynamics of an EDW Maglev is investigated by using both steady-state and transient eddy-current models. The analytic equations for the self as well as mutual damping and stiffness coefficients of an EDW Maglev are derived using the 2-D analytic steady-state eddy-current force equations. It is shown that the steady-state eddy-current model in which the heave velocity is included in the formulation can accurately predict the dynamic behavior of a 2-degree of freedom EDW Maglev vehicle. The 2-D EDW Maglev vehicle has been built using Matlab/SimMechanics™. A 1-degree of freedom pendulum setup of an EDW Maglev has been built in order to investigate the dynamics of an EDW Maglev. The dynamic model of an EDW Maglev has been validated using this pendulum setup. A multi-degree of freedom Maglev vehicle prototype has been constructed using four EDWs. The dynamics of the prototype Maglev has been investigated using the Matlab simulations. This prototype setup will be used to investigate the dynamic behavior of EDW Maglev in the future

Guidance of the resonance energy flow in the mechanism of coupled magnetic pendulums

This paper presents a methodology of controlling the resonance energy exchange in mechanical system consisting of two weakly coupled magnetic pendulums interacting with the magnetic field generated by coils placed underneath. It is shown that properly guided magnetic fields can effectively change mechanical potentials in a way that the energy flow between the oscillators takes the desired direction. Studies were considered by using a specific set of descriptive functions characterizing the total excitation level, its distribution between the pendulums, and the phase shift. The developed control strategies are based on the observation that, in the case of antiphase oscillation, the energy is moving from the pendulum subjected to the repelling magnetic field, to the oscillator under the attracting field. In contrast, during the inphase oscillations, the energy flow is reversed. Therefore, closed-loop controller requires only the information about phase shift, which is easily estimated from dynamic state signals through the coherency index. Advantage of suggested control strategy is that the temporal rate of inputs is dictated by the speed of beating, which is relatively slow compared to the carrying oscillations

Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight by Oscillation Synchronization

This paper describes a fully decentralized nonlinear control law for spinning tethered formation flight, based on exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics. Motivated by oscillation synchronization in biological systems, we use contraction theory to prove that a control law stabilizing a single-tethered spacecraft can also stabilize arbitrary large circular arrays of spacecraft, as well as the three inline configuration. The convergence result is global and exponential. Numerical simulations and experimental results using the SPHERES testbed validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics

New results on cycle–slipping in pendulum–like systems

n this paper, we examine dynamics of multidimensional control systems obtained as feedback interconnections of stable linear blocks and periodic nonlinearities. The simplest of such systems is the model of mathematical pendulum (with viscous friction), so we call such systems pendulum-like. Other examples include, but are not limited to, coupled vibrating units, networks of oscillators, Josephson junction arrays and numerous synchronization circuits used in radio and telecommunication engineering. Typically, a pendulum-like system has infinite sequence of equilibria, and one of the central problems addressed in the theory of such systems is to find the conditions of "global stability", or gradient-like behavior ensuring that every solution converges to one of the equilibria points. If a system is gradient-like, another problem arises, being the main concern of this paper: can we find the terminal equilibrium, given the initial condition of the system? It is well known that solutions do not converge, in general, to the nearest equilibrium; this phenomenon is known as cycle-slipping. For a pendulum, cycle-slipping corresponds to multiple rotations of the pendulum about its suspension point. In this paper, we estimate the number of slipped cycles for general pendulum-like systems by means of periodic Lyapunov functions and the Kalman-Yakubovich-Popov lemma

Crowd-induced lateral bridge vibration

Vibration induced by walking pedestrians has motivated research in the civil engineering community for many years. An area within this broad field that has received particular attention is the dynamic interaction that can occur between pedestrians and laterally flexible bridge structures. Perhaps the most notable example occurring on the opening day of London's Millennium Bridge. The enduring interest in this research problem is fuelled by two of its key features; (i) the sensitivity and adaptability of human balance to lateral motion and (ii) the spatial and temporal variation in flow characteristics exhibited by a pedestrian crowd. Both of these features are addressed herein. In this project an experimental campaign was executed with the aim of identifying the interaction mechanism by which pedestrians produce force harmonics, that resonate with the oscillating structure on which they walk. These so-called self-excited forces have been experimentally identified by others but the underlying reason for their existence has remained an open question. In an effort to address this, human balance behaviour while walking on a laterally oscillating treadmill was recorded using 3-dimensional motion capture equipment. Subsequent analysis revealed that human response to sinusoidal base motion is dominated by periodic alteration of foot placement position. This produces amplitude modulation of the lateral component of the ground reaction force and is ultimately responsible for the self-excited force harmonics. It was further revealed that human centre of mass motion while walking on an oscillating structure is predominantly passive. The passive inverted pendulum model is thus an excellent model of pedestrian frontal plane balance. The second facet of this work is concerned with developing a crowd-structure interaction model that builds upon the current state of the art. The model presented utilises the understanding of human-structure interaction identified above and employs an agent-based modelling approach. Thus, the resulting 'virtual crowd' is capable of simulating key crowd features, such as inter-subject variability and emergent velocity-density flow behaviour. Using this model, it is shown that the experimentally identified human-structure interaction mechanism can lead to large amplitude lateral deck oscillations, consistent with field observations reported in the literature. The model successfully predicts the multi-mode instability of Bristol's Clifton Suspension Bridge in the absence of step frequency tuning among the crowd. This provides supporting evidence for the model's validity. The work described above has resulted in a clearer understanding of the feedback between pedestrian balance behaviour and bridge response. Furthermore, the modelling techniques developed have potential for application in the wider study of crowd-induced vibration of dynamically susceptible structures