Acoustic Wave Propagation in a Quasi-Periodic Waveguide System Based on the Symmetric Fibonacci Sequence

In this article, we have examined the propagation of acoustic waves at normal incidence in a quasi-periodic 1D Fibonacci-type structure in comparison with a periodic system. This waveguide structure is composed of two blocks arranged in various quasi-periodic Fibonacci sequences. The first block is a closed acoustic resonator and the second an open resonator. Each kind of resonator is connected to a main waveguide segment. The theoretical analysis is based essentially on the mathematical method of the transfer matrix and the Fibonacci sequence recursive relation. The propagation of acoustic waves in this quasi-periodic system results in the creation of the band gaps of null transmission, separated by the pass bands of total transmission. We have shown that the number and width of these band gaps increase as the Fibonacci sequence increases. The increase in the Fibonacci sequence also leads to the creation of several narrow transmission peaks in the acoustic band gaps. These transmission peaks appear on the forbidden bands as flat bands and sometimes as acoustic resonance modes. The precise value of the golden ratio applied to the simple Fibonacci sequence is also studied in this article. We have found that using the precise value of the gold number is an interesting candidate for creating wider band gaps and a larger number of transmission peaks than in the usual Fibonacci sequence. These results are important for acoustic wave filtering and noise attenuation, due to the creation of new acoustic band gaps.