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...

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...

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....