Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

Discrete element modelling of a rotating drum and drum granulation

This thesis reports the results of DEM (Discrete Element Method) simulations of rotating drums operated in a number of different flow regimes. DEM simulations of drum granulation have also been conducted. The aim was to demonstrate that a realistic simulation is possible, and further understanding of the particle motion and granulation processes in a rotating drum. The simulation model has shown good qualitative and quantitative agreement with other published experimental results. A two-dimensional bed of 5000 disc particles, with properties similar to glass has been simulated in the rolling mode (Froude number 0.0076) with a fractional drum fill of approximately 30%. Particle velocity fields in the cascading layer, bed cross-section, and at the drum wall have shown good agreement with experimental PEPT data. Particle avalanches in the cascading layer have been shown to be consistent with single layers of particles cascading down the free surface towards the drum wall. Particle slip at the drum wall has been shown to depend on angular position, and ranged from 20% at the toe and shoulder, to less than 1% at the mid-point. Three-dimensional DEM simulations of a moderately cascading bed of 50,000 spherical elastic particles (Froude number 0.83) with a fractional fill of approximately 30% have also been performed. The drum axis was inclined by 50 to the horizontal with periodic boundaries at the ends of the drum. The mean period of bed circulation was found to be 0.28s. A liquid binder was added to the system using a spray model based on the concept of a wet surface energy. Granule formation and breakage processes have been demonstrated in the system.

The effects of yoked prisms on body posture and egocentric perception in a normal population

The principal theme of this thesis is the effect of yoked prisms on body posture and egocentric perception. Yoked prisms have been clinically used in the management of a variety of visual and neuro-motor dysfunctions. Most studies have been conducted in pathological populations by studying the effects of prismatic adaptation, without distinguishing short and long term effects. In this study, postural and perceptual prismatic effects have been studied by preventing prism adaptation. A healthy population was selected in order to investigate the immediate prismatic effects, when there is no obvious benefit from their use for the individual. Posturography was used to assess changes in weight distribution and shifts in centre of pressure (barycentre). In addition, photographic analyses were used to assess effects on posture on the x and z axis. Experiments with space board and visual midline shift were used for the evaluation of spatial perception and egocentric localisation. One pair of 8 Δ yoked prisms base left (BL) and one pair of 8 Δ yoked prisms base up (BU) were applied randomly and compared to a pair of plano lenses. Results suggest that immediate prismatic effects take place on a perceptual level and are reflected on an altered body posture respectively without significant changes in weight distribution. Yoked prisms BL showed a rightward rotational effect on spatial perception by expanding space on the z axis when viewing through the base of the prism and constricting space through the apex of the prism. Body posture responded respectively to what was visually perceived by altering posture. A rightward shift and tilt of the head was recorded along with the hips shift and shoulders tilt in the dame direction. Additionally, right shoulder shifted backwards and an angular midline shift to the right was recorded. The egocentric localisation was affected by shifting the midline perception to the left. Yoked prisms BU resulted on a head shift forward and a reduction of the head-neck angle by bringing the chin closer to the chest. The egocentric localisation was altered on the vertical axis providing subjects the perception that their eye level was higher during the experiment. In conclusion, yoked prisms seemed to induce changes in body posture, mainly in the upper body and head, without any significant changes in weight distribution. These changes are partially reflected in spatial perception tests and egocentric localisation before any prismatic adaptation takes place.

Failure mechanism of the all-polyethylene glenoid implant

Fixation failure of glenoid components is the main cause of unsuccessful total shoulder arthroplasties. The characteristics of these failures are still not well understood, hence, attempts at improving the implant fixation are somewhat blind and the failure rate remains high. This lack of understanding is largely due to the fundamental problem that direct observations of failure are impossible as the fixation is inherently embedded within the bone. Twenty custom made implants, reflecting various common fixation designs, and a specimen set-up was prepared to enable direct observation of failure when the specimens were exposed to cyclic superior loads during laboratory experiments. Finite element analyses of the laboratory tests were also carried out to explain the observed failure scenarios. All implants, irrespective of the particular fixation design, failed at the implant-cement interface and failure initiated at the inferior part of the component fixation. Finite element analyses indicated that this failure scenario was caused by a weak and brittle implant-cement interface and tensile stresses in the inferior region possibly worsened by a stress raiser effect at the inferior rim. The results of this study indicate that glenoid failure can be delayed or prevented by improving the implant/cement interface strength. Also any design features that reduce the geometrical stress raiser and the inferior tensile stresses in general should delay implant loosening.