UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Predicting incipent instabilities and bifurcations of nonlinear dynamical systems modelling compliant off-shore structures

Leung, Lap Ming; (1991) Predicting incipent instabilities and bifurcations of nonlinear dynamical systems modelling compliant off-shore structures. Doctoral thesis (Ph.D), UCL (University College Londno). Green open access

[thumbnail of Predicting_incipient_instabili.pdf] Text
Predicting_incipient_instabili.pdf

Download (7MB)

Abstract

For engineers, the two most important aspects of dynamical analysis are high amplitude resonance vibrations and structural stability, i.e. whether a steady state solution is stable under small perturbations. For the former case, a novel and simple method based on Poincare mapping technique has been devised to predict an imminent flip bifurcation. This bifurcation represents the beginning of the second order subharmonic response. For the latter case, we discovered that while classical quantitative analytical techniques work well in establishing the 'local' structural stability of a steady state solution, the global geometric structure of the catchment region can alter dramatically such that even an initial condition close to the steady state can diverge from it rather than being attracted. This phenomenon known as fractal basin boundary occurs when the invariant manifolds of the saddle separating the steady state solution from any remote attractor cross. The critical point in which the invariant manifolds just touch can be accurately predict by the Melinkov's method. Because of the complicated interwoven nature of the invariant manifolds, it is called a tangle. If the invariant manifolds are originated from the same saddle, the crossing is known as a homoclinic tangle, if originated from different saddle, a heteroclinic tangle. The critical point is then known as homoclinic or heteroclinic tangency. Tangles are also intimately related to chaotic behaviour. The creation and destruction of chaotic attractors have been observed through a series of homoclinic and heteroclinic tangency. In fact, after the invariant manifolds of an inverting saddle cross, the unstable manifold becomes the chaotic attractor. This leads us to believe that all chaotic attractors are topologically the same.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Predicting incipent instabilities and bifurcations of nonlinear dynamical systems modelling compliant off-shore structures
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
URI: https://discovery.ucl.ac.uk/id/eprint/10124520
Downloads since deposit
0Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item