Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Large Initial Displacements

Abstract For large initial rectilinear displacements, we investigate free response of a linear oscillator inertially coupled to rotational nonlinear energy sink (NES). Absent direct damping, two ranges orbitally stable solutions are accessible, in contrast one range at lower, intermediate energies (2021, J. Appl. Mech. 88, 121009). As lower energies, fractal and riddled basins attraction identified for both previously considered numerical combinations the dimensionless parameters (characterizing coupling motion). In this case, however, final amplitude, addition angular orientation, displays initial-condition sensitivity. parameter combination, most motionless conditions (MICs, with masses NES initially rest) lead discrete set “special” amplitudes, no MICs complete dissipation energy. other results similar those leading special solutions, many dissipation. Results strongly suggest that qualitatively new behavior occurs beyond here, nonrotating asymptotic special-amplitude having larger amplitude either not existing or only very small parts MIC space. With damping motion, transient chaos leads sensitivity settling time, case providing good guidance damped-case behavior.