Acoustic band pinning in the phononic crystal plates of anti-symmetric structure

Acoustic bands are studied numerically for a Lamb wave propagating in an anti-symmetric structure of a one-dimensional periodic plate by using the method of supercell plane-wave expansion. The results show that all the bands are pinned in pairs at the Brillouin zone boundary as long as the anti-symmetry remains and acoustic band gaps (ABGs) only appear between certain bands. In order to reveal the relationship between the band pinning and the anti-symmetry, the method of eigenmode analysis is introduced to calculate the displacement fields of different plate structures. Further, the method of harmony response analysis is employed to calculate the reference spectra to verify the accuracy of numerical calculations of acoustic band map, and both the locations and widths of ABGs in the acoustic band map are in good agreement with those of the reference spectra. The investigations show that the pinning effect is very sensitive to the anti-symmetry of periodic plates, and by introducing different types of breakages, more ABGs or narrow pass bands will appear, which is meaningful in band gap engineering.