Abstract
A hybrid method combining the transfer-matrix and lumped-mass methods is proposed to study the band gaps of torsional vibration in one-dimensional (1D) phononic band gap (PBG)-like shafts, which periodically arrange local resonant multilayer rings. The present method shows advantages over the transfer-matrix and lumped-mass methods for determining the inertia of rubber rings and fast convergence with less computational requirements. For light local resonators, the torsional band gaps, which were studied in three 1D PBG-like shafts by the hybrid method, agree well with those studied by the finite method. In addition, more precise evaluations of the starting frequency of the band gaps were carried out analytically. The methodology of the approach presented can also be employed to study the band gaps of bending and longitudinal waves.
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