Tunability of local resonant modes in Fibonacci one-dimensional phononic crystals by hydrostatic pressure

Abstract

In this research, the effect of the applied hydrostatic pressure on the one-dimensional quasi-periodic phononic crystals (PnCs) based on the Fibonacci sequence has been studied. The designed structure is composed of hard (Si) and polymer materials (PMMA). Also, the PnC designs are imposed to be surrounded by water from all sides. The mechanical properties of PMMA are calculated under the effect of an applied hydrostatic pressure depending on the direct relationship between Young’s modulus and hydrostatic pressure. The transmittance spectra were calculated theoretically based on the transfer matrix method (TMM). Our numerical results revealed that the band gap width increases in the case of quasi-crystals than the periodic design accompanied with the appearance of resonant peaks in their transmission spectra. In addition, the band gap and resonant mode shifted toward higher frequencies as the applied pressure increases coupled with decreasing in band gap widths for quasi-crystals. Therefore, the transmission spectrum of PnCs can be tuned without insertion any defects by hydrostatic pressure in quasi-periodic PnCs. Finally, the research observed the splitting of the resonant peak to four peaks in the case of Fibonacci sequence S7 with increasing their transmission intensity under the applied pressure. The obtained results can be useful for sensing small perturbations in underwater signals, hydrostatic pressure and in the design of narrowband filters.