413 research outputs found
An iterative method for the approximation of fibers in slow-fast systems
In this paper we extend a method for iteratively improving slow manifolds so
that it also can be used to approximate the fiber directions. The extended
method is applied to general finite dimensional real analytic systems where we
obtain exponential estimates of the tangent spaces to the fibers. The method is
demonstrated on the Michaelis-Menten-Henri model and the Lindemann mechanism.
The latter example also serves to demonstrate the method on a slow-fast system
in non-standard slow-fast form. Finally, we extend the method further so that
it also approximates the curvature of the fibers.Comment: To appear in SIAD
Canards in stiction: on solutions of a friction oscillator by regularization
We study the solutions of a friction oscillator subject to stiction. This
discontinuous model is non-Filippov, and the concept of Filippov solution
cannot be used. Furthermore some Carath\'eodory solutions are unphysical.
Therefore we introduce the concept of stiction solutions: these are the
Carath\'eodory solutions that are physically relevant, i.e. the ones that
follow the stiction law. However, we find that some of the stiction solutions
are forward non-unique in subregions of the slip onset. We call these solutions
singular, in contrast to the regular stiction solutions that are forward
unique. In order to further the understanding of the non-unique dynamics, we
introduce a regularization of the model. This gives a singularly perturbed
problem that captures the main features of the original discontinuous problem.
We identify a repelling slow manifold that separates the forward slipping to
forward sticking solutions, leading to a high sensitivity to the initial
conditions. On this slow manifold we find canard trajectories, that have the
physical interpretation of delaying the slip onset. We show with numerics that
the regularized problem has a family of periodic orbits interacting with the
canards. We observe that this family has a saddle stability and that it
connects, in the rigid body limit, the two regular, slip-stick branches of the
discontinuous problem, that were otherwise disconnected.Comment: Submitted to: SIADS. 28 pages, 12 figure
Integrated Digital Reconstruction of Welded Components: Supporting Improved Fatigue Life Prediction
In the design of offshore jacket foundations, fatigue life is crucial.
Post-weld treatment has been proposed to enhance the fatigue performance of
welded joints, where particularly high-frequency mechanical impact (HFMI)
treatment has been shown to improve fatigue performance significantly.
Automated HFMI treatment has improved quality assurance and can lead to
cost-effective design when combined with accurate fatigue life prediction.
However, the finite element method (FEM), commonly used for predicting fatigue
life in complex or multi-axial joints, relies on a basic CAD depiction of the
weld, failing to consider the actual weld geometry and defects. Including the
actual weld geometry in the FE model improves fatigue life prediction and
possible crack location prediction but requires a digital reconstruction of the
weld. Current digital reconstruction methods are time-consuming or require
specialised scanning equipment and potential component relocation. The proposed
framework instead uses an industrial manipulator combined with a line scanner
to integrate digital reconstruction as part of the automated HFMI treatment
setup. This approach applies standard image processing, simple filtering
techniques, and non-linear optimisation for aligning and merging overlapping
scans. A screened Poisson surface reconstruction finalises the 3D model to
create a meshed surface. The outcome is a generic, cost-effective, flexible,
and rapid method that enables generic digital reconstruction of welded parts,
aiding in component design, overall quality assurance, and documentation of the
HFMI treatment.Comment: 6 pages, 7 figures, submitted to 2023 IEEE International Conference
on Imaging Systems and Techniques (IST2023
- …