Using an exact Mie scattering solution,this paper investigates the mode conversions during the Mie scattering of a single bi-or one-component sphere in unbounded epoxy.Then the formation mechanism of the first complete gap in the corresponding tri-or bi-component phononic crystal is investigated by the multiple-scattering method.It is shown that the heavy density of the scatterer plays an essential role in the Mie resonance and the formation of the gaps for both types of the phononic crystals.For the tri-component phononic crystal,the gap is mainly induced by the Mie resonance of the single scatterer.For the bi-component phononic crystal,the transverse wave (by mode-conversion during the Mie scattering under a longitudinal wave incidence) is modulated by the periodicity and governed by the Bloch theory,which induces the gap cooperatively.
The propagation of coupled flexural-torsional vibration in the periodic beam including warping effect is investigated with the transfer matrix theory. The band structures of the periodic beam, both including warping effect and ignoring warping effect, are obtained. The frequency response function of the finite periodic beams is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The effect of warping stiffness on the band structure is studied and it is concluded that substantial error can be produced in high frequency range if the effect is ignored. The result including warping effect agrees quite well with the simulated result.
