13th April 2017 » Finie Element Modelling of Rock cutting​

Speaker: Nina Yari, CADR, University of Aberdeen

Date and Venue: Thursday at 3:00 pm, FN185 (Engineering seminar room)


Complexity of bit-rock interaction and formation fracture physics makes rock drilling a challenging issue from modelling perspective. One part of the presentation is on a finite element model which can plausibly capture the rock fractures while it is capable of evaluating drilling forces for various values of depth of cut, bit angular velocity and bit configuration. Additionally, the effect of introducing high frequency dynamic oscillations in combination with WOB and rotary action is investigated.The cutting forces are analyzed for different values of rake angle, initial depth of cut and cutter speed for a single-cutter linear cutting. The second part of the presentation is about contact fracturing of rock-like materials indented by a rigid cylindrical punch. A new mechanism dominant in fracturing will be introduced along with some experimental and numerical results.

9th March 2017 » Dynamics of the delayed dynamical systems

Speaker: Dr Lijun Pei, CADR, University of Aberdeen and School of Mathematics and Statistics, Zhengzhou University, China

Date and Venue: Thursday at 3:00 pm, Library Seminar room 224


Time delay is ubiquitous and has critical effects on the dynamics of the system. It can be seen as the link in time for system's state variables. In this talk, I will introduce my works on the stability and bifurcations, especially the nonresonant double Hopf bifurcation, of the delayed systems. It includes the nonresonant double Hopf bifurcations in the delayed Neural Networks and artificial pancreas in the diabetes,  Hopf bifurcation in the delayed TCP-RED congestion internet networks and a delayed ratio-dependent predator-prey system, and the stability of  a class of predator-prey model with delayed nutrient recycling.  It discloses the critical effects of delay on its dynamics.

11th January 2017 » Characterization of periodic windows in parameter plane​

Speaker: Dr Silvio de Souza, Federal University of São João del-Rei, Ouro Branco, Brazil

Date and Venue: Wednesday at 2:00 pm, FNB 185 (Engineering Seminar Room)


In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents.

25th November 2016 » Numerical modelling and stability analysis of non-smooth dynamical systems via ABESPOL​

Speaker: : Dr Antonio Chong, University of Aberdeen, Aberdeen, Scotland

Date and Venue: Friday at 10:30 am, FNB 185 (Engineering Seminar Room)


Systems characterised by non-smooth events are of great importance because non-smooth phenomena appear in many scientific fields and currently belong to the most investigated subject in the area of nonlinear dynamics. In mechanical engineering, some causes of non-smoothness are (a) impacts or intermittent contacts between the system components with motion constraints, and (b) dry friction, which gives rise to the non-smooth behaviour known as stick-slip motion. In electronic engineering, non-smoothness can be caused by switches and diodes, and some of the dynamical behaviours of these systems are regarded as impacts by analogy with mechanical impact oscillators.

In this work, a computational suite of numerical codes to study the dynamical responses of non-smooth dynamical systems has been developed, using Matlab as a platform. This suite is capable to undertake a comprehensive stability analysis of periodic orbits undergoing new types of bifurcations such as grazing (as an instance, the transition from a non-impacting orbit to an impacting orbit in the simplest case).

This computational suite, named ABESPOL, computes system dynamics, such as time histories, trajectories, Poincaré maps, bifurcation diagrams and basins of attraction through its module of direct numerical simulation. A module for numerical continuation has also been developed, which offers a user-friendly interface that links ABESPOL with the computational continuation core COCO [1], so that the general-purpose routines provided by COCO for numerical continuation and bifurcation analysis of periodic orbits can be easily employed.

Unlike any other available software, ABESPOL has these two modules connected, providing the user with the choice to start a numerical continuation directly from a bifurcation diagram computed by a direct numerical simulation. A two-parameter numerical continuation can be computed immediately after a one-parameter continuation, from any computed saddle-node, period-doubling or grazing bifurcation point. All in all, the user-friendly interface of ABESPOL makes the exploration of the system dynamics much more straightforward and intuitive than any other available software.

The practical applications that have been analysed with the developed computational suite were drawn from the projects investigated in the Centre for Applied Dynamics Research (CADR) of the University of Aberdeen. In this seminar, an asymmetrical piecewise linear impact oscillator excited by a harmonic force applied directly to the mass of the system will be used to show ABESPOL in execution.

[1] H. Dankowicz and F. Schilder. Recipes for Continuation. SIAM, 2013

15th September 2016 » The current methods of Directional Drilling in the North Sea​

Speaker: Andrew Penman, Halliburton, Aberdeen, Scotland

Date and Venue: Thursday at 3:00 pm, FNB 185 (Engineering Seminar Room)


Andrew is the BHA design lead within the Drilling Engineering Solutions (DES) department of Halliburton Sperry Drilling for Europe and Sub Saharan Africa (ESSA), and has vast experience working with Measurement While Drilling (MWD) and Directional Drilling (DD).

16th June 2016 » Suppression of Drill-String Torsional Vibrations: Numerical and Experimental Verification

Speaker: Dr Vahid Vaziri, School of Engineering, University of Aberdeen, Scotland, UK

Date and Venue: Thursday at 4:00 pm, FNB 185 (Engineering Seminar Room)


The drill-string is an important component in the oil well drilling rig used for hydrocarbon exploration and in other types of exploration drilling. A highly complex dynamical behaviour can be observed in a drill-string. These complex dynamics include uncontrolled vibrations which are harmful to the drilling process. They may cause premature wear and damage of the drilling equipment, which eventually results in expensive failures. Vibrations in the drill-string include different types of vibration such as torsional vibration and its extreme case stick-slip. There have been a few attempts in the past to overcome this problem. However there is a lack of academic experimental studies with real drilling processes to verify and calibrate models and control methods. This motivates me to pursue this experimental project.

In order to achieve further progress in this field, particular attention has been given to the drill-string torsional vibration which has been observed 50% of drilling time. In this study, torsional vibrations are analysed in the experimental drilling rig developed at the Centre for Applied Dynamics Research at University of Aberdeen. A realistic model of the experimental setup is then constructed, taking into account the dynamics of the drill-string and top motor. Physical parameters of the experimental drilling rig are estimated in order to calibrate the model to ensure the correspondence of the research results to the experimental conditions. Consequently, a control method is applied to suppress torsional and stick-slip oscillations exhibited in the experimental drilling rig. The experimental and numerical results considering delay of the actuator are shown to be in close agreement, including the success of the controller in significantly reducing the vibrations.

2nd June 2016 » Piecewise smooth systems: out with the new, in with the old

Speaker: Professor John Hogan, Faculty of Engineering, University of Bristol, UK

Date and Venue: Thursday at 11:00 am, Seminar Room 224 (Library)


In this talk, I will show some new results in piecewise smooth systems that have emerged from a close reading of Filippov's classic book on the subject. The focus will be on the classification of singularities and bifurcations in planar systems. The approach is mainly topological, with the emphasis on accessibility rather than rigour. This is joint work with Paul Glendinning (Manchester) and Martin Homer, Mike Jeffrey, Robert Szalai (Bristol).


5th May 2016 » Geometry of grazing and chatter for a simple impact oscillator

Speaker: Dr David Chillingworth, Mathematical Sciences, University of Southampton, UK

Date and Venue: Thursday at 4:00 pm, FNB 185 (Engineering Seminar Room)


A simple impact oscillator here means a second order ODE with one degree of freedom x and with T-periodic forcing, and such that whenever the value x = c (the clearance) is attained the velocity x′ is replaced by –rx′ with 0 < r < 1. A grazing orbit has x′ = 0 when x = c, while a chattering orbit has in nitely many impacts with x = c in fi nite time.We give insight into these and other phenomena using a general framework that exploitstools from singularity theory in order to convert analysis into geometry.

24th March 2016 » Dynamic Methods of Stiffness Identification in Impacting Systems for Rotary-Percussive Drilling Applications

Speaker: Maolin Liao, PhD student, CADR, University of Aberdeen

Date and Venue: Thursday at 4:00 pm, FNB 185 (Engineering Seminar Room)


Stiffness identification of an impacted constraint is the main issue discussed in this work. Primarily, a change of stability (bifurcation) is used to determine the dynamical stiffness of an impacted beam for a piecewise-linear impact oscillator. Detailed one- and two-parameter bifurcation analyses of this impacting system are carried out by means of experiments and numerical methods. Particularly, the two-parameter numerical continuation of the obtained codimension-one bifurcation (period-doubling bifurcation, or fold bifurcation) indicates a strong monotone correlation between the stiffness of the impacted beam and the frequency at which this bifurcation appears. In addition to the bifurcation techniques, another method for stiffness identification is analysis of impact duration. To accurately detect impact durations from numerical or experimental signals, nonlinear time series methods are utilised. Two impacting systems, including the piecewise-linear

impact oscillator and a drillbit-rock vibro-impact system, are studied to demonstrate the proposed method. For either system, the impact duration is nearly constant when the response of oscillator is a period-one one-impact motion, and it approximates half of the natural period of the oscillator-constraint system. When the mass of oscillator is constant, for an impacted constraint with a certain stiffness, the higher the stiffness, the lower the impact duration. This monotone correlation provides another mechanism to estimate the stiffness of the impacted constraint. Based on the developed two dynamical methods for stiffness identification, a control algorithm for parameter adjustment of the axial vibration of rotary-percussive drilling is designed. This control algorithm aims to maintain the optimum drilling state under the varying properties of the drilled formations. By this way, the efficiency of rotary-percussive drilling is expected to be promoted.

17th March 2016 » Delay feedback control of the Dynamical system

Speaker: Dr Shun Zhong, Department of Mechanics, Tianjin University, Tianjin, China; CADR Visiting Scholar, University of Aberdeen

Date and Venue: Thursday at 4:00 pm, Library Seminar Room 224 (Sir Duncan Rice Library, second floor)


Time-delay widely exists in all kinds of active control systems. The inevitability and uncertainty of the time-delay make the research on the delay feedback control systems more complicated and meaningful. We applied several method such as SD and CTA into the design of the control algorithm to reduce the effects brought by time-delay, which worked well on the determined time-delay feedback control system.

However, the control system based on the determined time-delay feedback control is not perfect, there are still a lot of multi-parameter multi-objective optimization problems to be solved; the existing delay identification algorithm is complex and poor real-time; at the same time, the researches on control and identification are mostly in theoretical aspects, but few experimental reports.

Supervisory control is an effective delay robust control strategy. Using a switching logic to determine which controller in a family of candidate controllers designed by certain theory is to be placed in the feedback loop, the strategy could overcome the uncertainty of the time-delay. And time-delay identification is important to the selection of the control strategies and fault diagnosis.

As a result, this research intends to carry out theoretical and experimental studies on uncertain time-delay feedback control system. First, based on continuous time approximation method and cell mapping theory, the optimal control problems will be solved. Second, according to the idea of the stability and optimization, the fast and high precision delay identification algorithm could  be developed. Finally,  applying the Quanser control experimental platform, the algorithm should be validated and the software toolbox can be developed. The subject results will have important scientific significances and application values.


10th March 2016 » Modelling the behaviour of church bells using experimentally validated hybrid dynamical model

Speaker: Piotr Brzeski, Lodz University of Technology, Lodz, Poland

Date and Venue: Thursday at 4:00 pm, FNB 185 (Engineering Seminar Room)


We investigate the dynamics of the yoke-bell-clapper impacting system using  a novel hybrid dynamical model. The model is verified experimentally by comparing the results of numerical simulations with experimental data obtained from the biggest bell in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. After validation of proposed model we  show a plethora of different dynamical behaviours that can be observed in the considered system. We indicate the solutions that can be considered as a proper working regimes of the instrument and describe how to obtain them. Detailed bifurcation analysis allow us to present how the design of the yoke and propulsion mechanism influence the response of the system. We show how to increase the chance that the instrument will work properly regardless of small changes of influencing parameters. Presented results prove the feasibility of the presented model and demonstrate the importance of nonlinear analysis in practical engineering application.

3rd March 2016 » Novel type of tuned mass damper with inerter which enables changes of inertance

Speaker: Professor Przemyslaw Perlikowski, Professor Lodz UT, Lodz University of Technology, Lodz, Poland

Date and Venue: Thursday at 4:00 pm, FNB 185 (Engineering Seminar Room)


We propose the novel type of tuned mass damper and investigate its properties. Characteristic feature of the device is that it contains a special type of inerter equipped with a continuously variable transmission and gear-ratio control system which enables stepless and accurate changes of inertance. We examine the damping properties of the proposed tuned mass damper with respect to one-degree-of-freedom harmonically forced oscillator. To prove the potential of introduced device we test its four different embodiments characterized by four different sets of parameters. We generalize our investigation and show that proposed device has broad spectrum of applications, we consider three different stiffness characteristics of damped structure i.e. linear, softening and hardening. We use the frequency response curves to present how considered devices influence the dynamics of analyzed systems and demonstrate their capabilities.

21st January 2016 » Symmetry and bifurcations of vibro-impact systems

Speaker: Dr Yue Yuan, Associate Professor School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu; Visiting Research Assistant, CADR, University of Aberdeen
Date and Venue: Thursday at 4:00 pm, FNB 185 (Engineering Seminar Room)


Because of the existence of impacts, the vibro-impact system is discontinuous and strongly non-linear, such as hammer-like devices, rotor-casing dynamical systems, heat exchangers, fuel elements of nuclear reactor, gears, piping systems, wheel-rail interaction of high speed railway coaches. Researches into the dynamic behavior of vibro-impact systems have important significance in optimization design of machinery and noise suppression. Hence, the complication of the dynamics of vibro-impact system has received great attention. A great deal of issues on vibro-impact dynamics interest many researchers greatly, but little attention has been paid to the symmetry characteristic of the Poincaré map and its influence on possible bifurcations in vibro-impact systems. For the three-degree-of-freedom vibro-impact system with symmetric two-sided constraints, it is certain that the Poincaré map has some symmetry property, which suppresses period-doubling bifurcation, Hopf-flip bifurcation and pitchfork-flip bifurcation of the symmetric period n-2 motion. When the control parameter changes successively, symmetry-breaking bifurcation and symmetry-restoring bifurcation will occur at some point, and the attractor may change between symmetry and antisymmetry repeatedly. It is shown that the unsymmetric implicit map captures the symmetry of the dynamics. 

11th December 2015 » Impact Biomechanics & Design of Head Protection Devices

Speaker: Professor Michael D. Gilchrist, School of Mechanical Engineering, University College Dublin, Dublin, Ireland
Date and Venue: Friday at 10:00 am, FNB 156 (Mathematics Seminar Room)


This presentation describes the development and use of experimentally-informed, computer simulation methods which could constitute a valuable set of forensic tools for investigating cases of impact trauma that involve lesions such as laceration, neurotrauma and skull fracture. The use of finite element models and multi-body dynamics models relies on knowing physical properties including kinematic joint stiffnesses, the strength of biological materials such as cranial bone, skin, muscle and neural tissue. Having accurate information on the rate dependent properties of biological tissue and using sufficiently sophisticated models, it becomes possible to relate the extent of injuries to causative forces. This method could help forensic pathologists to infer the mechanical causes of various lesions and to determine whether probable causes of fracture were accidental or intentional.  Similarly, it can also assist engineers to design more effective head protection systems.


20th November 2015 » For Better or Worse: Applications of the Transfer Matrix Approach for Analyzing Axial and Torsional Vibration


Speaker: Roman Shor, PhD candidate in Petroleum Engineering at the University of Texas at Austin; Visiting student at the University of Cambridge, Dynamics and Vibrations Group, Department of Engineering
Date and Venue:  Friday at 1:00 pm, FNB 185 (Engineering Seminar Room)


The response of the drilling system to axial and torsional vibration inputs has a significant impact on drilling performance. Usually the goal is to minimize dynamic response to limit the effects of potentially damaging phenomena in the low frequency range (e.g. bit bounce and torsional stick-slip) and high frequency range (e.g. axial chatter and torsional resonance). However, in some cases the goal is to maximize dynamic response, for example when introducing oscillation tools to overcome wellbore friction while directional drilling or to free stuck pipe. Whether the intention is to maximize or minimize, a suitable mathematical model is required. A transfer matrix model is proposed to predict the harmonic response of the drillstring and is then compared with various field studies, including bit bounce and induced axial oscillation.


28 August 2015 » Nonlinear Dynamics, Chaos and Control of Smart Systems

Speaker: Professor Marcelo A. Savi, Department of Mechanical Engineering, Federal University of Rio de Janeiro, Brazil.
Date and Venue:  28 August 2015, Friday at 1:00 pm, FNB 185 .

Inspired by nature, researchers are trying to create systems and structures that can repair themselves, presenting an adaptive behaviour according to its environment. Among many options of smart sensors and actuators, shape memory alloys (SMAs) is an interesting option since they are easy to manufacture, relatively lightweight, and able of producing high forces or displacements with low power consumption. SMAs are metallic compounds with the ability to return to a previous shape or dimension, when subjected to an appropriate thermomechanical procedure. Due to their remarkable properties, SMAs have been used in many areas of human knowledge. This seminar discusses some SMA applications and its thermomechanical behaviour. Despite the great number of applications, its thermomechanical description stills the objective of many research efforts. It is presented a constitutive model that explores phenomenological features of the thermomechanical response. This constitutive model is employed in order to describe some interesting behaviours and potential applications of SMA devices involving dynamical behaviour. In this regard, it should be highlighted their rich response including chaos and attractor multistability. Chaos control is also employed showing situations where tiny perturbations can avoid undesirable behaviours.

16 June 2015 » George Duffing, the Equation Named after Him and its Applicability Today

Speaker: Professor Michael Brennan, Department of Mechanical Engineering, State University of São Paulo (UNESP), Ilha Solteira, Brazil.
Date and Venue:  16 June 2015, Tuesday at 4:00 pm, FNB 185.

Nonlinearity in structural dynamics increases in its importance every year. One reason for this is that we demand more from our structures and systems, without increasing weight and cost, and one way of doing this is to harvest the benefits of nonlinearity. More than 100 years ago George Duffing studied a simple system that has a stiffness nonlinearity (a pendulum) which can be described approximately by a second order nonlinear ordinary differential equation. This equation is now called the Duffing equation. In this talk, a potted history of Duffing and his equation will be presented. Some simple systems that can be modelled by this equation will also be described, together with a simple experiment in which the nonlinear stiffness can be determined.

24 April 2015 » Nonlinear Time Series Analysis Applied to Resonance Enhanced Drilling

Speaker: Dr Mukthar Sayah, CADR, School of Engineering, University of Aberdeen.
Date and Venue:  24 April 2015 at 3:00 pm, FNB 185.

Nonlinear time series analysis has been used to infer the changes in the system dynamics. Using the acceleration time-series as a measurement of simulated and experimental impact oscillators representing a drilling model with intermittent impacts, the systems attractors were reconstructed and used to calculate the deviation of the attractors to infer the stiffness. Based on the developed framework, it is now possible to classify stiffness of the impacted material in a simple way and in real-time.

A new experimental impact drilling rig was designed to study the influence of the system parameters on the high-frequency impact drilling. The rig is a small and simple apparatus designed to mimic the Resonance Enhanced Drilling (RED) whilst avoiding complexity of the whole RED experimental rig. Physical and mathematical models of the new rig were developed and their parameters were identified.

27 February 2015 » An experimental procedure to determine the shock-sensitivity of drill-strings and thin shells

Speaker: J. Michael T. Thompson, FRS Sixth Century Professor, CADR, Aberdeen.
Date and Venue:  27 February 2015 at 12:00 noon, FNB 185.

A compressed and twisted rod, such as drill string, is akin to a thin shell in the sense that it has an unstable post-buckling path generated at a subcritical bifurcation. So under operational conditions, at loads less than the critical, there exists an unstable state which forms an energy barrier against small (static or dynamic) lateral disturbances. If the energy barrier is too low, such disturbances can induce premature collapse and failure.

This talk presents a new non-destructive experimental testing procedure to evaluate the magnitude of this energy barrier for a rod or shell under sub-critical compression. A small lateral probe imposes a rigidly controlled displacement, q, and the passive resisting force, Q, is measured. A lateral load-deflection curve, Q(q) is thus generated, which in general reaches a maximum of Q and then falls to Q = 0. At this zero force condition, we have determined in a controlled and stable fashion (due to the rigid control of q) the post-buckling state of the system: and we can determine its energy barrier, E, by evaluating the area under the Q(q) graph. This procedure can be repeated at different values of the overall compressive load, P, to obtain the shock-sensitivity graph of E(P).

If the lateral probe induces a local instability giving a bifurcation of the Q(q) graph, we show that the introduction of a second rigid control can be used to stabilise the process, so that the energy barrier can again be determined.

4 February 2015 » A Geometrical Insight into Non-smooth Bifurcations of a Soft Impact Oscillator

Speaker: Dr Haibo Jiang, Yancheng Teachers University, China.
Date and Venue:  4 February 2015 at 4:00 pm, FNB 185.

The concept of discontinuity geometry of rigid impact oscillators is extended to soft impact oscillators and the mechanism of grazing bifurcations of an impact oscillator with one-sided elastic constraint is studied by the geometric and dynamical systems methods. The existence conditions of periodic solutions are obtained by using the discontinuity geometry methods and used to derive the discontinuity curves. Several bifurcation scenarios near grazing bifurcation are investigated to examine the evolution of dynamical behaviour from a geometry point view. New geometric insights are gained into whether there is a discontinuous jump or a continuous transition from a non-impacting attractor to a period-1 impacting attractor at a grazing bifurcation.

21 November 2014 » Modelling and Qualitative Analysis of Non-smooth Dynamics

Speaker: Professor Alain Léger, CNRS, Laboratoire de Mécanique et d'Acoustique.
Date and Venue:  21 November 2014 at 12:30 pm, FNB 156.

Taking contact and friction conditions into account in the mechanics of continuous media leads to open and difficult problems. But as far as simple models are chosen conveniently, they might allow some qualitative investigation which would not be possible for continuous bodies. This lecture will present the basic features of the dynamics in presence of contact and friction in the case of a simple model: a mass-spring system moving over an obstacle. We shall first show that the equations of the motion should be understood as equalities between measures, which changes all the classical results of the theory of ordinary differential equations.Then we shall focus on the qualitative answer to a periodic excitation. Starting from initial data in contact with the obstacle, we shall see that the classical (period, amplitude) plane is divided into several ranges. In the first one there exist infinitely many equilibrium states and all the trajectories lead to equilibrium in finite time. In the second range equilibrium states no longer exist but there exist periodic solutions the number of which depends on the frequency. And in the last range in which all the trajectories loose contact and involve jumps. As a model for the coupling between smooth and non-smooth nonlinearities, special attention will be paid to the case where the restoring force is nonlinear such as when large deformations are taken into account.

4 July 2014 » Nonlinear Dynamics-Based Methods for Atomic Force Microscopy

Speaker: Dr Andrew Dick, Rice University, USA.
Date and Venue: 4 July at 12:00 pm, FN 185.

Atomic force microscopy (AFM) provides the means to measure topographical information and material properties of a wide variety of samples at the micro- and nano-scale. The AFM is a valuable research tool and has been used in areas including bioscience, nano-mechanics, and polymer chemistry. By using the atomic interaction forces between the atoms on the tip of the probe and the surface of the sample, measurements can be made well below the threshold of optical methods and without requiring conductive properties of the sample. These atomic interaction forces are intrinsically nonlinear, consisting of far-field attractive forces and near-field repulsive forces. As a result, the AFM is capable of exhibiting a range of complicated and interesting nonlinear behaviour. While conventional methods seek to operate in a linear regime, our work has focused on understanding the nonlinear behaviour and using the nonlinearity to improve the performance and capabilities of the AFM. By using analytical and numerical methods, this research has studied qualitative response changes associated with a specific range of off-resonance excitation frequencies and the potential use of this phenomenon to perform nonlinear-dynamics-based nano-scale material characterization of the sample. Dual-frequency excitation methods have also been studied as a means to maintain desired response characteristics of conventional methods while incorporating the qualitative response changes produced by using the nonlinear methods. This work provides a foundation for the development of nonlinear dynamics-based methods which will provide improved performance and capabilities of conventional AFM systems through a greater understanding of the nonlinear behaviour of the system.

26 June 2014 » Dynamics of Nonlinear Oscillators with Friction

Speaker: Professor S. Narayanan, Indian Institute of Technology Madras.
Date and Venue: 26 June at 1:00 pm, FN 2.

Nonlinear oscillators with friction belong to a class of discontinuous dynamical systems. A multi- harmonic framework to obtain steady state periodic solutions of a harmonically excited nonlinear oscillator with friction. One dimensional contact element under macro-slip condition under constant and variable normal loads is used to model the friction contact interface. The relative displacements at the interface are expressed in terms of a Fourier series. The transition times between different states of stick, slip and separation are accurately determined using analytical conditions of force balance at the interface and incorporated into the multi-harmonic procedure. Three cases of lumped parameter models representative of contact conditions in turbo-machinery bladed system are considered as examples. Frequency response plots for different normal loads help to identify optimum normal load for minimal dynamic response.

Systems with dry friction belong to a category of Fillipov systems where the phase plane is divided into sub-regions in which the vector fields representing the states are smooth and separated by non-overlapping discontinuity surfaces. The shooting method in combination with the switch model is used to obtain the periodic solutions of the Fillipov systems. An event based numerical integration is used in the process. Discontinuity induced bifurcations like sliding and grazing bifurcations are explained and illustrated in the case of a mass sliding on a moving belt with dry friction and other nonlinearities.

5 December 2013 » Dynamic of Coupled Spherical Pendula

Speaker: Blazej Witkowski, Lodz University of Technology, Poland.
Date and Venue: 5 December at 4:30 pm, FN 185.

The dynamics of co- and counter rotating coupled spherical pendulums (two lower pendulums are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. The linear modes allow us to understand the nonlinear normal modes, which are visualized in frequency-energy plots. With the increase of energy in one mode we observe a symmetry breaking pitchfork bifurcation. In the second part of the paper we consider energy transfer between pendulums having different energies. The results for co-rotating (all pendulums rotate in the same direction) and counter-rotating motion (one of lower pendulum rotates in opposite direction) are presented. In general, the energy fluctuation in counter-rotating pendulums are found to be higher than in co-rotating case.

5 December 2013 » Rare Attractors

Speaker: Dr Przemysław Perlikowski, Lodz University of Technology, Poland.
Date and Venue: 5 December at 4:00 pm, FN 185.

We discuss the mechanism leading to the multistability in the externally excited van der Pol-Duffing oscillator. We define rare attractors and argue that they are typical for the forced nonlinear systems operating in the neighbourhood of the principal resonance. We show the dependence of system dynamics on set of accessible initial conditions.

14 November 2013 » Stochastic Dynamics of a Parametric Pendulum with application to Wave Energy Harvesting

Speaker: Dr Daniil Yurchenko, Heriot-Watt University, UK.
Date and Venue: 14 November at 4:00 pm, FN 110.

There are different renewable energy technologies available today. Devices and arrays capturing solar, wind, biomass, geothermal and hydro energy are currently being used or tested. The figures show that clean energy is constantly fulfilling a bigger portion of the total energy usage. However, some technical issues such as robustness, efficiency, ecosystem impact still form constraints as well as the cost remain the main challenges.
In this context, the interest on renewable energy sources - RES - among the academia remains at its peak. One of the most promising, yet almost totally unexploited, sources for clean, unlimited energy is the Ocean Wave Energy. Much higher energy density compared to solar or wind energy and slower variations constitute the reasons why it is considered having great potential. However, only a handful of devices have been commercialized so far with limited success. The electricity cost is estimated at over five times higher than the conventional coal-produced one, which along with the occasional severe weather conditions and the technical issues stemming from the offshore locating might explain the slower growth of this form of RES. According to UK Carbon Trust reports there is "a need for cost reduction" and "next generation technology" of wave energy converters.
In this presentation a new concept of a Wave Energy Converter, proposed earlier [1], is revised. The original concept is based on the parametric excitation of a pendulum by ocean waves [1] and directly converts the heaving motion of waves into rotational motion. However, the waves motion can barely be considered as deterministic and thus their random nature has to be accounted for [2]. Will the rotational motion be sustainable in the presence of randomness? The typical average value of the wave frequency is 0.1Hz, implying that a nearly 100m long pendulum would be required. Is it possible to reduce the size of the device? If we were able to reduce the size of the device would the device be still cost efficient? In this presentation we try to give answers to these and other related and challenging questions.

[1] X. Xu, M. Wiercigroch, M.P. Cartmell, Rotating orbits of a parametrically-excited pendulum, Chaos, Solitons & Fractals, 23 (2005), 1537-1548.
[2] D. Yurchenko, A. Naess, P. Alevras, Pendulum\'s rotational motion governed by a stochastic Mathieu equation, Probabilistic Engineering Mechanics, 31 (2013), 12-18.

3 May 2013 » Relating Material’s Performance to Microstructure: Challenges and Opportunities

Dr Igor Sevostianov, Department of Mechanical and Aerospace Engineering, New Mexico State University, USA.
Date and Venue: 3 May at 4:00 pm, FN110.

The presentation covers two interconnected topics:
Proper quantitative characterization of microstructures, for the purpose of modelling the effective properties, is discussed. This is a broad subject that covers different physical properties (elastic, conductive, transport, etc.), as well as various types of microstructures. The presentation focuses on microstructures that can be characterized as continuous matrices containing isolated inhomogeneities of diverse shapes, properties and orientations. We address their proper quantitative characterization in the context of elastic and conductive properties (transport and fracture-related properties are also briefly discussed). Proper microstructural parameters must correctly represent the individual inhomogeneity contributions to the considered property. They may differ for different physical properties. The key problem is to identify the mentioned individual contributions. For the elastic properties, we demonstrate, on a number of microstructures, how the proper parameters are implied by the elastic potential. Relative importance of various “irregularity factors” (shape irregularities, orientation scatter) is analysed. We discuss similarities and differences between microstructural parameters intended for different physical properties. The possibility of explicit cross-property connections between two physical properties depends on whether the proper microstructural parameters for these two properties are sufficiently similar.

Cross-property connections for heterogeneous materials belong to the realm of fundamental problems of engineering science. Whereas connections between properties governed by mathematically similar laws are straightforward (say, electric and thermal conductivities), the ones between the elastic properties and conductivities constitute a much more complex problem. Moreover, their very existence is not obvious: besides being governed by different differential equations, they are characterized by tensors of different ranks. Their practical usefulness lies in the fact that one physical property (say, electric conductivity) may be easier to measure than the other (say, full set of anisotropic elastic constants In the presentation, approximate connections between conductivities and elastic compliances are discussed and specified for several heterogeneous anisotropic microstructures and verified by comparison with experimental data. The tensor of elastic compliances is expressed in terms of the conductivity tensor in the closed form. The cross-property connections are derived in the framework of non-interaction approximation. In the practical cases, when the interactions between inhomogeneities cannot be neglected, we hypothesize that the interactions affect both groups of properties – elastic and conductive – in a similar way, so that the cross-property correlations continue to hold, although this approximation may yield substantial errors for each of the properties separately (this idea was first suggested by Bristow, 1960 for a material with randomly oriented microcracks). This assumption is confirmed by comparison with experimental data on various materials: plasma sprayed ceramic coatings, short glass fibre reinforced thermoplastics and aluminium foams. The similar type of cross-property connection is also obtained for granular materials.

22 March 2013 » Beyond Navier-Stokes: how do we deal with fluid mechanics at micro and nano scales?

Professor Jason Reese, University of Strathclyde.
Date and Venue: 22 March at 1:00 pm, St Mary's G3.

Micro- and nano-scale fluid systems can behave very differently from their macro-scale counterparts. Their thermodynamic non-equilibrium and non-continuum nature makes these flows uniquely complex, and not predictable by the conventional Navier-Stokes flow equations. In fact, remarkably, there is currently no sufficiently accurate and computationally efficient fluid dynamic model that can capture this important behaviour. In this talk I will outline ongoing work at Strathclyde University on developing and exploring new models for these next-generation flow devices. I will describe the successes and failures of various hydrodynamic and molecular models in capturing the flow physics, and give examples of current test applications in micro- and nano-technologies.

16 January 2013 » Dynamics of unidirectionally coupled Duffing oscillators

P. Perlikowski, Technical University of Lodz, Poland.
Date and Venue: 16 January at 3:00 pm, FN 110.

We investigate the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behaviour. We study these transitions in detail for small number of individual nodes. For networks with more than five systems the transition to chaos occurs though stable three dimensional torus. Our results are confirmed by an experiment based on the coupled Duffing electronic circuits.

16 January 2013 » The dynamics of the pendulum suspended on the forced Duffing oscillator

P. Brzeski , Technical University of Lodz, Poland.
Date and Venue: 16 January at 3:00 pm, FN 110.

We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.

14 December 2012 » Chatters in Plunge and Transverse Grinding

Yao Yan, School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China.
Date and Venue: 14 December at 4:00 pm, FN 185.

This topic focuses on the chatter vibrations in both plunge and transverse grinding processes. To discuss these phenomena, respective dynamical models are proposed to describe the grinding processes. After that, the grinding stabilities are investigated through eigen-value analysis, both theoretically and numerically. More specifically, the continuation algorithm and the perturbation method are employed to find the critical values of the system parameters, which may lead to the onset of the grinding chatters. Therefore, the chatter boundaries, which divide the chatter and chatter-free regions, are obtained. Starting from the boundaries, we gradually find the chatter motions through bifurcation analysis. In the plunge grinding process, the approximate analytical solutions of the chatter motions are obtained by the method of multiple scales (MMS) directly. By contrast, in the transverse grinding process, the envelopes of the chatter motions are acquired through bifurcation analysis as well. After the mechanism of the grinding chatters is clarified, the rest of this research utilizes a control strategy to suppress the chatter vibrations. Instead of constant speeds, time-varying rotational speeds of the work-piece and the grinding wheel are employed for chatter suppression. Analytically, the sufficient condition for successful chatter suppression is obtained. Finally, it is found that this strategy is very efficient when the values of the system parameters are near the chatter boundaries.

10 December 2012 » One-dimensional Turbulence in a System with a Dry Friction

Dr Sergey Kryzhevich, University of Aveiro, Portugal.
Date and Venue: 10 December at 1:00 pm, FN 185.

A simple model of s.d.f. motion with a dry friction, first offered by Wiercigroch and Krivtsov, is studied. We give a description of regimes of the considered system, describe the corresponding dynamics. Also, some conditions, sufficient for existence of an infinite set of periodic motions, are given. The key point of the talk is an application of the theory of low-dimensional topological dynamics to mechanical systems with a dry friction. No special knowledge in Dynamical Systems is requested, everybody is welcome.

2 November 2012 » Exploitation of Nonlinear Damping for Structural Systems Vibration Control

Speaker: Dr Zi-Qiang Lang, Department of Automatic Control and Systems Engineering, University of Sheffield.
Date and Venue: 2 November at 4:00 pm, FN 185.

In this talk, the beneficial effects of nonlinear damping on structural system vibration control are investigated via rigorous analytical studies using nonlinear system frequency domain analysis approaches developed at Sheffield. The results indicate that the introduction of odd powered nonlinear damping devices can effectively overcome the well-known problems with linear damping which can attenuate the vibration energy around resonant frequencies but may be detrimental for vibration suppression over other frequency ranges. Experimental results are used to demonstrate the beneficial effects of nonlinear damping revealed by the theoretical studies. Finally, a novel approach based on integrating the instantaneous harmonic control (IHC) with nonlinear damping is introduced to resolve the robustness problem with IHC, which relies on an accurate knowledge of disturbance frequency to achieve an ideal control performance. Both simulation and experimental study results are provided to demonstrate the effectiveness of the new technique which exploits the effects of nonlinear damping to achieve a robust and much better harmonic control.

20 July 2012 » Numerical Bifurcation Analysis of a Jefcott Rotor with a Bearing Clearance

Speaker: Dr Joseph Paez Chavez, Centre for Applied Dynamics Research, University of Aberdeen.
Date and Venue: 20 July at 4:00 pm, FN 185.

In this presentation we study numerically bifurcations occurring within a two-degree-of-freedom model of a rotor system with a bearing clearance. During operation the rotor makes intermittent contacts with an outer snubber ring, which results in a complex dynamical behaviour. These interactions produce a rich variety of dynamics, which includes fold, period-doubling and grazing bifurcation of periodic orbits, as well as chaotic motion. The system will be analysed numerically by a path following method, where we will use the toolbox TC-HAT, a module allowing to model non-smooth systems by AUTO 97.

29 June 2012 » Nonlinear impact systems in the game of hurling - Analyses, numerics and experiments

Speaker: Dr Amjad Alsakarneh, Centre for Applied Dynamics Research, University of Aberdeen.
Date and Venue: 29 June at 4:00 pm, FN 115.

High-speed mechanical impacts between non-linear materials are particularly difficult to model due to the rapidly time-varying behaviour of the non-linear materials during impact. This is particularly the case where one or both of materials involved in the impact are natural in origin and therefore subject to the variations in material properties inherent in non-artificial materials. Here, an experimentally verified methodologies for the modelling of these types of impacts is presented. It considers, in particular, the material set of ash wood and rubber in the context of the impact between the bat (the "hurley" made of ash wood) and the ball (the "sliotar" made of polyurethane-cork composite) in the Irish game of hurling.
For the theoretical approach, modified Maxwell and Kelvin-Voigt's viscoelastic models were used to derive an analytical formula to predict the sliotar's restitution and the sliotar-hurley impact. Moreover, a transient nonlinear three-dimensional finite element (FE) model was developed to simulate the sliotar-hurley impact, and to provide a simple tool for further studies on such impact.
Finally, a high-speed camera was used to film the impact events to validate the models behaviour, where a designed 32 experimental impacts were carried out covering a range of sliotar and hurley brands, impact locations and impact speeds. The success of the modelling methodology in this challenging application suggests that it can be readily extended to analogous impacts involving other nonlinear materials impact.

15 June 2012 » Starting Homoclinic Tangencies near 1:1 Resonances

Speaker: Dr Joseph Paez Chavez, Centre for Applied Dynamics Research, University of Aberdeen.
Date and Venue: 15 June at 4:00 pm, FN 110.

A typical problem in the numerical analysis of homoclinic orbits is the choice of an appropriate initial solution that could lead us, via e.g. Newton iterations, to the homoclinic connection we want to analyse. In this presentation we develop a theory-based numerical method for the construction of such initial solution. We concentrate on discrete-time systems of arbitrary dimension ≥ 2, having 1:1 resonances at the origin. The method relies on numerical centre manifold reduction and flow approximation. The effectiveness of the method is illustrated by numerical examples.

8 June 2012 » Synchronization of Slowly Rotating Pendulums

Speaker: Professor Tomasz Kapitaniak, Division of Dynamics, Technical University of Lodz, Poland.
Date and Venue: 8 June at 1:00 pm, FN 110.

We study synchronization of a number of rotating pendulums mounted on a horizontal beam which can roll on the parallel surface. It has been shown that after the initial transient different states of pendulums' synchronization occur. We derive the analytical equations for the estimation of the phase differences between phase synchronized pendulums. We argue that the observed phenomena are robust as they occur in the wide range of both initial conditions and system parameters.

14 May 2012 » The Residue Harmonic Balance in Bifurcation, Limit Cycle and Wave Analyses

Speaker: Professor Andrew YT Leung, Chair of Sustainable Construction, City University of Hong Kong.
Date and Venue: 14 May at 1:00 pm, FN 110.

The harmonic balance method replaces ODEs in time to algebraic equations in frequency describing frequency distribution in the steady state response of the nonlinear system. The residue harmonic balance concentrates on the annihilation of the residues and can double the effective harmonic terms in each iteration step and can be considered as an extension of the Newton iteration from algebraic equations to ODEs. The systems being considered include rational and irrational nonlinearity; integral and fractional derivatives; and single and multiple degrees of freedom. The method is extended to steady state response of time delay systems and of wave described by PDEs. Examples include famous oscillators with fractional derivative damping and with time delay; applications in aerospace and in structural dynamics.

16 March 2012 » Helical Buckling of a Drill-String within its Casing under Dead and Rigid Loading

Speaker: Professor J Michael T Thompson, FRS, School of Engineering, University of Aberdeen, and Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
Date and Venue: 16 March at 3:30 pm, FN 110.

Helical buckling and post-buckling of an elastic rod within a cylindrical casing arises in many disciplines, but is particularly important in the petroleum industry. Here, a drill-string, subjected to an end twisting moment combined with axial tension or compression, is particularly prone to buckling within its bore-hole — with potentially serious results.
A theoretical study of this instability is presented, giving new results for the advanced stage when the rod is in continuous contact with the cylinder. Results, drawing on a new instability theorem, include rigorous stability analyses and contact pressure assessments.
Two approximate solutions give insight, universal graphs and parameters, for the practically relevant case of small angles, and highlight the existence of a critical cylinder diameter. Excellent agreement with experiments is achieved.

24 February 2012 » Aerodynamic Control of Wind Turbine Blades and Long-Span Bridges

Speaker: Professor Mike Graham FREng, Department of Aeronautics, Imperial College, London.
Date and Venue: 24 February at 3:30 pm, FN 110.

Wind turbines (and also long-span suspension bridges) stand in the lower part of the Atmospheric Boundary Layer of the natural wind which is both highly turbulent and subject to significant mean shear. Both of these phenomena as well as wake impact from other rotors generate high levels of unsteady loading on horizontal axis wind turbine rotor blades. The unsteady loads together with cyclic gravitational loads largely determine the fatigue life of the blades. This is a major design driver with a strong influence on the ultimate cost of the energy produced..
Similar effects with, in addition, the effects of incident waves, apply to tidal stream turbines.
The talk will describe an investigation into the effectiveness of controlled trailing edge flaps in counteracting unsteady loads. The flaps may be of small chord (<5% blade chord) if rapid activation is desired and numerical simulation and laboratory experiments will be described which have shown that short flaps can achieve as much as an 80% reduction in the amplitude of unsteady loading using the blade section lift as the control input. The possibility of using variable flexibility of the blade section camber as an alternative to flaps will also be discussed.
Long span bridges suffer from buffeting but in addition are subject to the increasing difficulty as spans become longer of keeping the bridge stiff enough in torsion and heave so that the critical flutter speed remains well above the maximum 'once-in-fifty-year' gust speed. The use of controlled flaps, which because of the possibility of winds from either direction include leading edge flaps, can aid this problem by significantly raising flutter speeds as well as contributing a reduction in buffet loads.

16 December 2011 » Nonlinear Methods for Studying Structure and Dynamics at Molecular Scale

Speaker: Dr Johannes Kiefer, School of Engineering, University of Aberdeen.
Date and Venue: 16 December at 1:00 pm, Room 105(156) St Mary's.

The talk aims at giving an overview of the research activities in which we apply nonlinear optical methods to investigate structures and dynamics at the molecular level.
The first part of the talk will give an introduction to light-matter interactions with a focus on nonlinear phenomena and their analogy regarding the mechanics of materials. Different approaches for gaining structural and dynamic information in the frequency and time domain will be discussed.
The second part of the talk will focus on engineering and scientific applications of nonlinear optical techniques. This includes, for instance, remote thermometry in combustion environments, the measurement of physicochemical properties in complicated solutions, and the investigation of ultrafast vibrational dynamics in room-temperature ionic liquids.

25 November 2011 » Structural Stability and Shadowing in Dynamical Systems

Speaker: Prof Sergei Yu Pilyugin, St Petersburg State University, St Petersburg, Russia.
Date and Venue: 25 November at 1:00 pm, Room 105(156) St Mary's.

Consider a dynamical system generated by a diffeomorphism f of a smooth closed manifold. The system is called structurally stable if any diffeomorphism g, C¹ close to f, is topologically conjugate to f (i.e., the patterns of trajectories of the corresponding dynamical systems are the same from the topological point of view). The system has the shadowing property if, for any approximate trajectory, there is a close exact trajectory. It is known that a structurally stable system has the shadowing property while the converse is not always true. We show that, under some additional assumptions, the shadowing property implies structural stability.

4 November 2011 » Impact Problems in Engineering

Speaker: Dr Joanna Mason, National University of Ireland, Galway, Ireland.
Date and Venue: 4 November at 1:00 pm, Room 105(156) St Mary's.

This talk introduces two impact problems which originate from intermittent noise and vibration problems in vacuum pumps, and unpredictable silence in church bells.
The first part of my talk will concentrate on a gearing mechanism, which was found to be the source of the noise in the vacuum pumps. An impact model is used to describe a pair of meshing gears, where the discontinuities in the model arise from the backlash between the gear teeth. To gain insight into the underlying dynamics, a classical approach of basin-of-attraction computations, bifurcation diagrams and manifold computations is used in conjunction with the recently developed discontinuity-geometry framework. We find that there is a complex interplay between both smooth and discontinuity-induced bifurcations.
The second part of my talk will focus on the Emperor's bell in Cologne Cathedral, Germany, a dramatic example of a church bell that would not ring reliably. An impacting-contact model of a church bell is described, where the bell and clapper are modelled as two coupled pendulums. We outline our numerical methods for investigating the underlying dynamics. Current simulations illustrate that the bell exhibits complex dynamics, including coexisting solutions, quasiperiodicity, and an impact-adding sequence from incomplete to complete chattering.

21 October 2011 » Dynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension

Speaker: Dr Krzysztof Kecik, Lublin University of Technology, Poland.
Date and Venue: 21 October at 4:00 pm, Room 105(156) St Mary's.

This work presents vibration analysis of an autoparametric pendulum-like mechanism subjected to harmonic excitation. To improve dynamics and control motions, a new suspension composed of a semi-active magnetorheological damper and a nonlinear spring is applied. The influence of essential parameters such as the nonlinear damping or stiffness on vibration, near the main parametric resonance region, are carried out numerically and next verified experimentally in a special experimental rig. Results show that the magnetorheological damper, together with the nonlinear spring can be efficiently used to change the dynamic behaviour of the system. Furthermore, the nonlinear elements applied in the suspension of the autoparametric system allow to reduce the unstable areas and chaotic or rotating motion of the pendulum.

25 August 2011 » Numerical and Experimental Bifurcation Control using Continuous Chaos Control Methods

Dr Aline Souza de Paula from the Department of Mechanical Engineering at the University of Brasilia is currently visiting the dynamics group and has kindly agreed at a very short notice to give a seminar tomorrow at 4pm.

Speaker: Dr Aline Souza de Paula, The University of Brasilia, Brazil.
Date and Venue: 25 August at 4:00 pm, Fraser Noble 3.

19 August 2011 » Nonlinear Dynamics and Chaos in Mechanical Systems

Professor Marcelo Savi from the Department of Mechanical Engineering at the Federal University of Rio de Janeiro is currently visiting the dynamics group and has kindly agreed at a very short notice to give a seminar this Friday. Details are given below.

Speaker: Prof Marcelo Savi, The Federal University of Rio de Janeiro, Brazil.
Date and Venue: 19 August at 4:00 pm, Fraser Noble 1.

3 June 2011 » Introduction to Well Logging and FEA for Logging Tools

Speaker: Dr Xu Xu, Lead Specialist Downhole Technology, GE Oil and Gas.
Date and Venue: 3 June at 4:00 pm, Fraser Noble 3.

For the first part of the presentation, well logging for the purpose of formation evaluation is introduced. It is aimed to give a general idea what is well logging and formation evaluation, and how and what we can do with well logging in real life of oil industry. For the second part of the presentation, the topic is how FEA contributes to the development of logging tools, and then focuses on the introduction of finite element method. Finally and hopefully, my experience would be helpful for the modelling of resonance enhanced drilling.

27 May 2011 » Dynamics and synchronisation of parametric pendulums for wave energy extraction

Speaker: Anna Najdecka, Centre for Applied Dynamics, School of Engineering, University of Aberdeen

The aim of my research is to study the dynamics and synchronization of a two pendulum system with a view to its application for wave energy extraction. The idea is based on the conversion of the oscillatory movement of sea waves into rotation of the parametric pendulums, utilizing their synchronisation to stabilise the floating structure. I will present both numerical and experimental results demonstrating the dynamics of the system and its tendency to synchronise. At first the behaviour of the system under harmonic excitation was studied. Then the influence of noise in the excitation and parameter mismatch between the two pendulums will be considered. Finally, control of the system will be discussed including control of the rotational motion and energy extraction.