Evolution of low-frequency phononic band gaps using quasi-periodic/defected phononic crystals

Abstract

Quasi-periodic structures can offer solutions to overcome the problem of low-frequency phononic band gaps with very small-size compared with the periodic or defected ones. In the present work, the conventional Bragg reflector structures were studied theoretically to produce low-frequency band gaps. For this purpose, two models are presented, defected and quasi-periodic Fibonacci 1D phononic crystal structures. A PDMS material was used in the proposed structures due to it a flexible soft and ease of fabrication. The reflection spectra for the incident elastic waves are calculated based on the transfer matrix method. The results showed that the frequency of the phononic band gaps was diminished to the audible frequency (11200 Hz) in a phononic crystal with a small thickness equals to the value 4.5 mm. Also, local resonant modes were created inside the defected/quasi-periodic phononic crystal structures at different frequencies. For the quasi-periodic structure, the band gap frequency was deceased to the value 300 Hz. The studied structures are considered local resonant structures, so they do not obey the conventional Bragg diffraction law. Moreover, the band gap width/frequency were enlarged when Fibonacci quasi-periodic structures hybridized with local resonant modes. Finally, the strong correlation between the band gap width and resonant peaks intensity in the reflection spectra is demonstrated. These results reveal an innovative solution for noise suppression devices and low band gap structures.