The present study deals with the harmful torsional resonance vibrations of textile rotor bearings, the amplitudes of which are reduced mainly by the use of high-capacity damping materials, characterized by an internal hierarchical structure and macroshape, added into the machine mechanical system. The additional materials are polymer matrix composites reinforced either by carbon nanofibers or carbon chopped microfibers and either aramid or carbon continuous fibers. The macroshape is based on a honeycomb with internal cavities. Torsional vibrations arise in mechanical systems as a result of fluctuations in the low-level pressing load of the flat belt driving the rotor-bearing pin and the changing of kinematic conditions within it, which, in the resonance area, leads to cage slip and unwanted impulsive torsional vibrations. Moreover, this occurs during high-frequency performance at around 2100 Hz, i.e., 126,000 min−1. The condition, before the redesign, was characterized by significantly reduced textile rotor-bearing life due to significant impulse torsional vibrations in the resonance area. The study showed a significant reduction in average and maximum torsional amplitudes in the resonance area by 33% and 43%, respectively. Furthermore, the paper provides visualization of the propagation of a stress wave at the microscale obtained by the explicit finite element method to show the dispersion of the wave and the fibers as one of the sources of high damping.