Summary
Many relevant structures in engineering are rotationally periodic, meaning that they consist of a discrete number of sectors with the same properties that are circumferentially assembled with cyclic symmetry. Their resonant vibrations can lead to strong fatigue problems, as it is especially known for bladed disks in turbomachinery. We explore the use of vibro-impact absorbers to suppress these forced resonant vibrations by considering a cyclic chain of oscillators with ten sectors of which each consists of a single degree of freedom oscillator that hosts a vibro-impact absorber. Our simulations show that the absorbers are able to synchronize to the global motion of the structure, with a 1:1 resonance between absorbers and oscillators in all sectors, and thus lead to an outstanding reduction of its resonant amplitude. However, this synchronization can also happen locally in a subset of all sectors which then show larger amplitudes than the remaining ones. Based on the single-term Harmonic Balance ansatz, we develop an analytical model of these synchronized solutions and study their practical stability and largest possible amplitudes numerically.
