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

Abstract

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. This work illustrates, in a preliminary manner, the results that can be obtained reducing the aforementioned constraints thanks to the implementation of algorithms based on a parallel computing approach. In particular, by focusing on basins of attraction, four applications are discussed. i) The full domain of attraction for a four-dimensional (4D) system describing a linear oscillator coupled with a nonlinear absorber is calculated. ii) The variation of a safe basin with respect to the system dimension is then analyzed. It is highlighted how 4D and 3D analyses provide more confident results with respect to 2D analyses. iii) The parametric variation of a 2D system with a reduced step is performed by building a 3D representation which allows to highlight a smooth transition between the states. iv) A convergence study of a basin of attraction resolution is carried out. The integrity factor is used as a comparison measure.