The torsional wave band gap properties of a two-dimensional generalized phononic crystal (GPC) are investigated in this paper. The GPC structure considered is consisted of two different materials being arranged with radial and circumferential periodicities simultaneously. Based on the viewpoint of energy distribution and the finite element method, the power flow, energy density, sound intensity vector together with the stress field of the structure excited by torsional load are numerically calculated and discussed. Our results show that, the band gap of Bragg type exists in these two-dimensional composite structures, and the band gap range is mainly determined by radial periodicity while the circumferential periodicity would result in some transmission peaks within the band gap. These peaks are mainly produced by two different mechanisms, the energy leakage occurred in circumferential channels and the excitation of the local eigenmodes of certain scatterers. These results may be useful in torsional vibration control for various rotational parts and components, and in the application of energy harvesting, etc.
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