In this paper, the model of a one-dimensional (1D) phononic crystal with quasi-periodical structure is proposed. The transmission coefficients of elastic waves through the 1D qusi-periodical phononic crystal are numerically calculated, and the obtained transmission coefficients are compared with those of the phononic crystal with periodical structure. The results show that the band gap can also be found in the phononic crystal with quasi-periodical structure, and the frequency range of the gap is the same as that of the periodical structure. However, the only difference is that strongly localized resonant modes appear in the gap of the qusi-periodical phononic crystal. This study to the properties of the localized modes is useful to the fabrication of the acoustic or elastic wave filters.
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