Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise...

The Stability of a Bicycle-Rider System: Basin of Attraction Identification and its Sensivity to Neural Time Delay

Part of the goal of Europe’s Strategy Vision Zero is to eliminate all severe cycling accidents in Europe by 2030. The majority of cycling accidents are single vehicle accidents; this term indicates the absence of collisions with other road participants and implies a fall of the cyclist. Research has shown that mainly elderly cyclists are victim...

Robustness of attractors in tapping mode atomic force microscopy

In this work, we perform a comprehensive analysis of the robustness of attractors in tapping mode atomic force microscopy. The numerical model is based on cantilever dynamics driven in the Lennard–Jones potential. Pseudo-arc-length continuation and basins of attraction are utilized to obtain the frequency response and dynamical integrity of...

The Kuramoto model on ring networks: Cluster synchronization and the size of the Basin of Attraction

The phenomenon of cluster synchronization in ring networks is studied in the first part of this thesis by means of Representation Theory. The second part of this thesis is devoted to the determination of the size of the Basin of Attraction for a stable node.

Revealing compactness of basins of attraction of multi-DoF dynamical systems

Global properties of Multi-Degrees-of-Freedom (M-DoF) systems, in particular phase space organization, are largely unexplored due to the computational challenge requested to build basins of attraction. To overcome this problem, various techniques have been developed, some trying to improve algorithms and to exploit high speed computing,...

Improving the global analysis of mechanical systems via parallel computation of basins of attraction

Numerical integrations represent a time-consuming element in the long-term dynamics analysis of mechanical systems. This limits the resolution of the computations and the dimension of the system to be investigated numerically. In fact, even pushing memory resources to their thresholds, only few tools can deal with higher-dimensional systems....

Predictability and unpredictability in optical system optimization

Local optimization algorithms, when they are optimized only for speed, have in certain situations an unpredictable behavior: starting points very close to each other lead after optimization to different minima. In these cases, the sets of points, which, when chosen as starting points for local optimization, lead to the same minimum (the so...