http://hdl.handle.net/1983/27 2013-06-05T14:44:24Z http://hdl.handle.net/1983/1786 Multi-parameter bifurcation study of shimmy oscillations in a dual-wheel aircraft nose landing gear Thota, P; Krauskopf, B; Lowenberg, MH We develop and investigate a mathematical model of an aircraft nose landing gear with a dual-wheel configuration. The main aim here is to study the influence of a dual-wheel configuration on the existence of shimmy oscillations. To this end, we consider a model that describes the torsional and lateral vibrational modes and the nonlinear interaction between them via the tyre-ground contact. More specifically, we perform a bifurcation analysis (with the software package AUTO) of the model in the two-parameter plane of forward velocity of the aircraft and vertical load on the nose landing gear. This two-parameter bifurcation diagram allows one to identify regions of different dynamics, and the question addressed here is how it depends on two key parameters of the dual-wheel configuration. Namely, we consider the influence of, first, the separation distance between the two wheels and, second, of gyroscopic effects arising from the inertia of the wheels. For both cases we find that, with increasing separation distance and wheel inertia, respectively, the lateral mode becomes more stable and the torsional mode becomes less stable. More specifically, we present associated bifurcation scenarios that explain the transitions between qualitatively different two-parameter bifurcation diagrams. Overall, we find that the separation distance and gyroscopic effects due to wheel inertia may have a significant influence on the quantitative and qualitative nature of shimmy oscillations in aircraft nose landing gears. In particular, the torsional and the lateral modes of a dual-wheel nose landing gear may interact in a quite complicated fashion. 2011-08-31T00:00:00Z http://hdl.handle.net/1983/1785 Dynamical systems analysis of spike-adding mechanisms in transient bursts Nowacki, J; Osinga, HM; Tsaneva-Atanasova, KT Transient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition, that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold of the fast subsystem organise the spike-adding transition and investigate the behaviour of the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two saddle-unstable sheets of the slow manifold. We also discuss a different parameter regime, where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism. 2011-08-31T00:00:00Z http://hdl.handle.net/1983/1783 Continuation analysis of aircraft ground loads during high-speed turns Krauskopf, B; Coetzee, EB; Lowenberg, MH The current lateral ground loads requirement, FAR25.495, for an aircraft during a high-speed turn, was written in the middle of the last century, when relatively small aircraft with tricycle landing gear arrangements started to emerge. This requirement is known to be conservative when applied to large modern passenger aircraft. Nonlinearities (such as tyre forces) have a significant effect at the edge of operating envelopes, placing a renewed interest on analysis methods that can classify the dynamics in these regions. In this paper we use continuation methods to assess the loads that can be generated for different aircraft configurations during high-speed turns, and compare the results to the original requirement. A comparison is made between test results from an FAA study and continuation results, where all the significant test data points are located within an envelope constructed from continuation analysis. Continuation methods therefore provide a conservative estimate of the maximum lateral load factors. These values are however less than the value prescribed in the regulation. 2011-08-01T00:00:00Z http://hdl.handle.net/1983/1761 Proactive Empty Vehicle Redistribution for Personal Rapid Transit and Taxis Lees-Miller, JD; Wilson, RE The empty vehicle redistribution (EVR) problem is to decide when and where to move empty vehicles in a Personal Rapid Transit or taxi system. These decisions are made in real time by an EVR algorithm. A reactive EVR algorithm moves empty vehicles only in response to known requests; in contrast, a proactive EVR algorithm moves empty vehicles in anticipation of future requests. This paper describes two new proactive EVR algorithms, called Sampling and Voting (SV) and Dynamic Transportation Problem (DTP), that move empty vehicles proactively based on demand estimates from historical data. It also develops methods for assessing the performance of EVR algorithms absolutely in terms of both throughput and passenger waiting times. In simulation tests, the proposed algorithms provide lower passenger waiting times than other algorithms in the literature, and proactive movement of empty vehicles significantly reduces waiting times, usually with a modest increase in empty vehicle travel. A preprint document to be published in the journal of Transportation Planning and Technology, by Taylor and Francis. 2011-07-18T13:28:28Z