Low frequency torsional vibration gaps in the shaft with locally resonant structures

The propagation of torsional wave in the shaft with periodically attached local resonators is studied with the transfer matrix theory and the finite element method. The analytical dispersion relation and the complex band structure of such a structure is presented for the first time, which indicates the existence of low frequency gaps. The effect of shaft material on the vibration attenuation in band gap is investigated. The frequency response function of the shaft with finite periodic locally resonant oscillators is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The low frequency torsional gap in shafts provides a new idea for vibration control.